Patent Publication Number: US-2022230209-A1

Title: Marketing inference engine and method therefor

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of: 
     U.S. provisional application 62/851,289 filed on May 22, 2019, entitled “METHOD AND SYSTEM FOR MACHINE-AIDED MARKETING BASED ON RELATING COMMODITIES TO TRAITS OF RESPECTIVE CONSUMERS” (Attorney docket number AFI-011-US-prov); 
     International PCT application PCT/IB2019/061346 filed Dec. 24, 2019 entitled “MARKETING ENGINE BASED ON TRAITS AND CHARACTERISTICS OF PROSPECTIVE CONSUMERS” (Attorney docket number AFI-010-PCT); and 
     U.S. provisional application 62/937,333 filed Nov. 19, 2019 entitled “METHOD AND APPARATUS FOR DIRECTING ACQUISITION OF INFORMATION IN A SOCIAL NETWORK” (Attorney docket number AFI-013-US-prov); 
     the entire contents of all applications being incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to machine-aided marketing based on relating commodities to traits of respective consumers. 
     BACKGROUND 
     It is well recognized that characterizing prospective consumers of a commodity is essential for enabling a focused marketing effort, hence successful promotion of the commodity. Conventionally, distinguishing potential consumers has been based on static and/or quasi static properties of members of a tracked population. 
     There is a need, however, to further explore methods for more inclusively associating a commodity with a respective segment of the tracked population. 
     SUMMARY 
     In accordance with an aspect, the invention provides a method comprising executing instructions causing a processor to perform processes leading to determining prospective clients for a specific commodity (product or service). 
     A superset of communities of a universe of users, each community corresponding to a respective trait of a superset of predefined traits is either determined in a pre-processing stage or acquired from external sources. For a specific commodity selected from a list of commodities of interest, data relevant to prior clients of the specific commodity is acquired and a set of relevant traits of the prior clients is determined based on the prior clients&#39; data. A set of primary communities, corresponding to the set of relevant traits, is then selected from the superset of communities. A set of prospective clients is determined as a function of the primary communities. Information relevant to the specific commodity is then communicated to the set of prospective clients. 
     The relevance of a specific trait of the superset of predefined traits is based on a ratio of a number of clients of the set of prior clients determined to have the specific trait to the size of the community of the set of communities corresponding to the specific trait. A preferred procedure for determining a set of relevant traits comprises processes of acquiring the size of each community of the superset of communities, initializing a set of relevant traits as an empty set, and determining for each trait of the superset of predefined traits a respective trait score as a number of clients of the set of prior clients determined to have the trait. The following iterative processes are then performed:
         (1) prorating each trait score to a nominal community size to produce prorated initial scores;   (2) transferring a particular trait of highest prorated score to the set of relevant traits; and   (3) adjusting the score of each of the remaining traits of the superset of predefined traits to exclude users already included in the particular trait.       

     The iterative processes continue until the highest score of the remaining traits is below a predefined level. 
     So far, the set of prospective clients is selected from the primary communities of users. In order to expand the set of prospective clients, other communities of high kinship to the primary communities may be considered. Thus, the method further determines a set of secondary communities from the superset of communities based on a measure of kinship of each community, excluding the primary communities, to the set of primary community. The set of prospective clients is then expanded to be based on both the primary communities and the secondary communities. 
     According to an embodiment, the measure of kinship is a weighted sum of pairwise kinship values of each candidate secondary community to the set of primary community determined as: 
     
       
         
           
             
               
                 Λ 
                 k 
               
               * 
             
             = 
             
               
                 Σ 
                 
                   0 
                   ≤ 
                   j 
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               ⁡ 
               
                 ( 
                 
                   
                     η 
                     j 
                   
                   × 
                   
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                       j 
                       . 
                       k 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     where: 
     η j  denotes a relevance level of a primary community of index j, and Λ j,k  denotes pairwise kinship of a candidate community of index k to a primary community of index j,  0 ≤j&lt;Γ, Γ≤k&lt;H, H being a count of the total number of communities of the set of communities, Γ being a count of the primary communities, indexed as 0 to (Γ−1). 
     A first measure of pairwise kinship, hereinafter referenced as a “type-1 kinship”, of a first community to a second community is based on a number of users belonging to the first community, a number of users belonging to the second community, and a number of common users belonging to both communities. The type-1 kinship may be defined as:
         (1) a ratio of the number of common users to a number of users belonging to the union of the two communities;   (2) a ratio of the number of common users to an arithmetic mean value of the number of users belonging to the first community and the number of users belonging to the second community; or   (3) a ratio of the number of common users to a geometric mean value of the number of users belonging to the first community and the number of users belonging to the second community.       

     The method further comprising processes of segmenting the universe of users into a set of clusters according to individual characteristics of each user of the universe of users and determining a saturation-score vector of each community of the superset of communities as a size of intersection of each community with each cluster of the set of clusters. The saturation-score vector is normalized to a sum of unity to produce a saturation-level vector. 
     A second measure of pairwise kinship, hereinafter referenced as a “type-2 kinship”, of a first community to a second community, is based on proximity of saturation-level vectors of the two communities. A third measure of pairwise kinship, hereinafter referenced as a “type-3 kinship”, of a first community to a second community, is based on cross-correlation of saturation-level vectors of the two communities. 
     The type-1 pairwise kinship of a first community of index u to a second community of index v is determined as: 
     
       
         
           
             
               
                 g 
                 
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               = 
               
                 
                   N 
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           or 
         
       
       
         
           
             
               
                 g 
                 
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             ; 
           
         
       
     
     wherein Nu is a number of users belonging to the first community, Nv is the number of users belonging to the second community, and Nc is the number of users belonging to the intersection of the first community and the second community. 
     The type-2 pairwise kinship of the first community to the second community is determined as: g 2,u,v =1.0−Σ K |α j −β j |, 0≤j&lt;K, 
     where:
         K is a number of clusters, K&gt;1,   α j  is a normalized saturation level of the first community within cluster j determined as a ratio of the number of users belonging to both the first community and cluster j to the number of users belonging to the first community; and   β j  is a normalized saturation level of the second community within cluster j determined as a ratio of the number of users belonging to both the second community and cluster j to the number of users belonging to the second community.       

     The type-3 pairwise kinship of the first community to the second community is determined as: 
     
       
         
           
             
               
                 g 
                 
                   3 
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               = 
               
                 
                   ( 
                   
                     
                       
                         Σ 
                         
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                       ⁡ 
                       
                         ( 
                         
                           
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     wherein: 
     n j , is a saturation score of the first community within cluster j, 
     m j  is saturation score of the second community within cluster j,  0 ≤j&lt;K, 
     &lt;n&gt; is the mean value of saturation scores of the first community, 
     &lt;m&gt; is the mean value of saturation scores of the second community, 
     σ n  is the standard deviation of the saturation score of the first community, and 
     σ m  is the standard deviation of the saturation score of the second community. 
     The kinship measure of any secondary community to any primary community may be determined as a function of at least two of: 
     a ratio the intersection of the two communities to the union of the two communities; 
     a proximity coefficient of saturation vectors of the two communities; and 
     a cross-correlation coefficient of saturation vectors of the two communities. 
     Preferably, the processes of determining a set of communities of the universe of users and segmenting the universe of users into a set of clusters are performed a priori in pre-processing modules for frequent use in determining prospective clients for different commodities. 
     In accordance with another aspect, the invention provides a method of advertising implemented at an apparatus comprising a processor and memory devices. The method comprises accessing a database providing traits, of a predefined superset of traits, of each user of a population of users and determining a superset of communities, each community comprising users determined to have a respective trait of the predefined superset of traits. 
     Upon receiving identifiers of a set of primary communities of interest, where the primary communities belong to the superset of communities, a set of secondary communities, belonging to the superset of communities, having a significant kinship to the set of primary communities is determined. 
     The set of secondary communities is initialized as an empty set and each community of the superset of communities, excluding the set of primary communities, is a candidate for joining the set of secondary communities. 
     For each candidate community, a measure of kinship to the set of primary communities is determined. A candidate community having a measure of kinship exceeding a predefined level is added to the set of secondary communities. A set of prospective clients is then determined based on the set of primary communities and the set of secondary communities. Appropriate marketing information is communicated to the community of prospective clients. 
     The set of prospective clients is determined as a union of the primary communities of the set of primary communities and the secondary communities of the set of secondary communities. Furthermore, users belonging to intersections of communities, primary or secondary, may be considered principal prospective clients. 
     The measure of kinship of a candidate community to the set of primary communities is determined as a sum of pairwise kinship levels of the candidate community to each primary community of the set of primary communities. 
     The method further comprises segmenting the plurality of users into a number K of clusters, K&gt;1, according to individual characteristics of users of the plurality of users. The characteristics of users may be determined from the aforementioned database, or from another source. A K-dimensional saturation vector of any community within the K clusters is determined according to intersection of the community with each cluster of the K clusters. 
     A pairwise kinship levels of a candidate community to a specific primary community of the set of primary communities may be determined according to:
         (a) a number of users belonging to the candidate community, a number of users belonging to the specific primary community, and a number of common users belonging to both the candidate community and the specific primary community;   (b) proximity of a K-dimensional saturation vector of the candidate community to a K-dimensional saturation vector of the specific primary community; or   (c) cross-correlation of the K-dimensional saturation vector of the candidate community to the K-dimensional saturation vector of the specific primary community.       

     According to an embodiment, a pairwise kinship level of the candidate community to the specific primary community is a composite kinship level determined as: 
     
       
         
           
             
               
                 e 
                 
                   j 
                   , 
                   k 
                 
               
               = 
               
                 
                   
                     q 
                     1 
                   
                   × 
                   
                     g 
                     
                       1 
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                       j 
                       , 
                       k 
                     
                   
                 
                 + 
                 
                   
                     q 
                     2 
                   
                   × 
                   
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                       2 
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                     3 
                   
                   × 
                   
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                       j 
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             ; 
           
         
       
         
         
           
             0≤j&lt;Γ, Γ≤k&lt;H, H being a count of the total number of communities of the superset of communities, Γ being a count of the primary communities of the set of primary communities, indexed as 0 to (Γ−1). 
           
         
       
    
     The weighting factors q 1 , q 2 , and q 3  of the kinship coefficients g 1,j,k , g 2,j,k , and g 3,j,k ; are prescribed; q 1 +q 2 +q 3 =1.0. 
     The type-1 kinship coefficient, g 1,j,k , is based on a number of users belonging to the candidate community, a number of users belonging to the specific primary community, and a number of common users belonging to both the candidate community and the specific primary community. 
     The type-2 kinship coefficient, g 2,j,k , is based on proximity of the K-dimensional saturation vector of the candidate community to a K-dimensional saturation vector of the specific primary community. 
     The type-3 kinship coefficient, g 3,j,k; k , is based on cross-correlation of the K-dimensional saturation vector of the candidate community to the K-dimensional saturation vector of the specific primary community. 
     According to a further aspect, the invention provides a marketing inference engine comprising a first module for determining a superset of communities of users of a tracked population of users. Each community comprises users of a respective trait of a predetermined superset of predefined traits. A second module determines relevant traits for a specific commodity based on records of prior client transactions. A third module determines primary communities of the superset of communities corresponding to the relevant traits. A fourth module determines prospective clients based on at least the primary communities. 
     A fifth module determines a type-1 pairwise kinships of candidate communities of the superset of communities to the primary communities based on overlap of each candidate community with the primary communities. A sixth module selects secondary communities based on values of the type-1 pairwise kinship of candidate communities and supplies data relevant to the secondary communities to the fourth module for expanding the set of prospective clients to account for both the primary communities and the secondary communities. 
     A seventh module segments the population of users into a set of clusters according to individual characteristics of each user of the universe of users. An eighth module determines a saturation-score vector of each community of the superset of communities as a size of intersection of said each community with each cluster of the set of clusters. The module is configured to determine type-2 pairwise kinships of communities based on trait saturation within individual clusters of the set of clusters. Accordingly, type-2 pairwise kinship values of candidate communities of the superset of communities to the primary communities are determined based on proximity of a saturation-level vector of each candidate community to a respective saturation-level vector of each primary community. 
     The eighth module is further configured to determine type-3 pairwise kinships of candidate communities of the superset of communities to the primary communities based on cross-correlation of a saturation-level vector of each candidate community and a respective saturation-level vector of each primary community. 
     A ninth module determines secondary communities according to the type-2 pairwise kinships of communities, or the type-3 pairwise kinships of communities, and communicates data relevant to the secondary communities to the fourth module for expanding the set of prospective clients to account for both the primary communities and the secondary communities. 
     In accordance with yet another aspect of the invention, there is provided a marketing system, comprising: a processor; and a marketing inference engine, comprising a memory device having computer executable instructions stored thereon for execution by the processor, forming: a first module for determining a superset of communities of users, of a tracked population of users, wherein each community comprises users of a respective trait of a predetermined superset of predefined traits, a second module for determining relevant traits for a specific commodity based on records of prior client transactions, a third module for determining primary communities of the superset of communities corresponding to the relevant traits, and a fourth module for determining prospective clients based on at least the primary communities. 
     In accordance with one more aspect of the invention, there is provided a system for determining prospective clients for a specific commodity, comprising: a processor, a computer memory storing processor executable instructions thereon, for execution by the processor, causing the processor to: select a specific commodity from a list of commodities of interest, acquire data relevant to prior clients of the specific commodity, determine a set of relevant traits of the prior clients based on said data, the set of relevant traits belonging to a predefined superset of traits, determine a superset of communities of a universe of users, each community corresponding to a respective trait of the predefined superset of traits, select a set of primary communities, corresponding to the set of relevant traits, from the superset of communities, and determine a set of prospective clients comprising users belonging to the primary communities. 
     In accordance with yet one more another aspect of the invention, there is provided a system for advertising a specific commodity, comprising: a processor, a computer memory storing processor executable instructions thereon, for execution by the processor, causing the processor to: access a database indicating traits, of a predefined superset of traits, of each user of a population of users, determine a superset of communities, each community comprising users, of the population of users, possessing a respective trait of the predefined superset of traits, receive identifiers of a set of primary communities of interest belonging to the superset of communities, initialize a set of secondary communities as an empty set, for said each community, excluding said set of primary communities: determine a measure of kinship to the set of primary communities, and add said each community to the set of secondary communities subject to a determination that the measure of kinship exceeds a predefined level, and determine a set of prospective clients based on the set of primary communities and the set of secondary communities. 
     Thus, an improved marketing engine and a method therefor have been provided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present invention will be further described with reference to the accompanying exemplary drawings, in which: 
         FIG. 1  illustrates a marketing-inference system in accordance with an embodiment of the present invention; 
         FIG. 2  illustrates components of a filter of the marketing-inference system; 
         FIG. 3  illustrates a process for determining principal communities of users of relevant traits and extended communities of users of significant kinship to the principal communities, in accordance with an embodiment of the present invention; 
         FIG. 4  is a schematic of a fully configured marketing-inference engine, in accordance with an embodiment of the present invention; 
         FIG. 5  is a schematic of the principal segment (core) of marketing-inference engine; 
         FIG. 6  is a schematic of a first extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both primary communities and secondary communities having a type-1 kinship to the primary communities; 
         FIG. 7  is a schematic of a second extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both primary communities and secondary communities having a type-2 kinship to the primary communities or having a type-3 kinship to the primary communities; 
         FIG. 8  is a schematic of a third extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both primary communities and secondary communities selected according to a composite kinship to the primary communities defined in terms of type-1, type-2, and type-3 kinships to the primary communities. 
         FIG. 9  is a schematic of a variation of marketing-inference engine of  FIG. 4   
         FIG. 10  illustrates a process for determining primary traits, hence primary communities of users, based on prior demand for a specific commodity, in accordance with an embodiment of the present invention; 
         FIG. 11  illustrates a method of determining significant traits for a selected commodity, in accordance with an embodiment of the present invention; 
         FIG. 12  illustrates a first measure of trait-pair kinship, for use in an embodiment of the present invention; 
         FIG. 13  illustrates pairwise trait kinship according to the first measure of kinship; 
         FIG. 14  illustrates examples of determination of significant secondary traits based on the first measure of kinship 
         FIG. 15  illustrates communities of users of the universe of tracked users defined according to respective user traits; 
         FIG. 16  illustrates a universe of tracked users segmented into clusters based on characteristics of individual users; 
         FIG. 17  illustrates superposition of communities onto clusters, for use in an embodiment of the present invention; 
         FIG. 18  illustrates determining first-stratum communities of consumers of a specific commodity, in accordance with an embodiment of the present invention; 
         FIG. 19  illustrates determining a pairwise composite kinship as a weighted sum of corresponding type-1, type-2, and type-3 kinship levels, in accordance with an embodiment of the present invention; 
         FIG. 20  illustrates a first method of determining prospective clients for a commodity, in accordance with an embodiment of the present invention; 
         FIG. 21  illustrates associating at least one community of users with one user trait determined from a set of specific tracked users, in accordance with an embodiment of the present invention; 
         FIG. 22  illustrates associating at least two communities of users with two user traits determined from a set of specific tracked users, in accordance with an embodiment of the present invention; 
         FIG. 23  illustrates an example of four communities of users associated with two user traits determined from a set of specific tracked users, in accordance with an embodiment of the present invention; 
         FIG. 24  illustrates another example of four communities of users associated with two user traits determined from a set of specific tracked users, in accordance with an embodiment of the present invention; 
         FIG. 25  illustrates saturation levels of communities within clusters, for use in an embodiment of the present invention; 
         FIG. 26  illustrates a method of determining a second measure of trait-pair kinship based on proximity of trait saturation levels within clusters, in accordance with an embodiment of the present invention; 
         FIG. 27  illustrates a method of determining a third measure of trait-pair kinship based on cross-correlation of trait saturation levels within clusters, in accordance with an embodiment of the present invention; 
         FIG. 28  illustrates a method for determining trait-pair kinship for use in determining second-stratum communities of consumers of a specific commodity, in accordance with an embodiment of the present invention; 
         FIG. 29  illustrates a method of determining trait-pair kinship, in accordance with an embodiment of the present invention; 
         FIG. 30  illustrates a second method of determining prospective clients for a commodity, in accordance with an embodiment of the present invention; 
         FIG. 31  illustrates a table of inter-trait kinships (inter-community kinships), for use in an embodiment of the present invention; 
         FIG. 32  illustrates a pre-processing stage for determining clusters of users based on characteristics of users and communities of users based on traits of users, for use in an embodiment of the present invention; 
         FIG. 33  illustrates trait-pair kinship values of exemplary traits based on the kinship measures of  FIG. 26  and  FIG. 27 ; 
         FIG. 34  illustrates exemplary trait-saturation scores within a number of clusters; 
         FIG. 35  illustrates normalized trait-saturation levels corresponding to the trait-saturation scores of  FIG. 24 ; 
         FIG. 36  illustrates a table of trait-saturation scores and a table of normalized trait-saturation levels corresponding to  FIG. 34  and  FIG. 35 , respectively; 
         FIG. 37  illustrates pairwise trait-kinship values according to the kinship measure of  FIG. 26  and the kinship measure of  FIG. 27 ; 
         FIG. 38  further illustrates pairwise trait-kinship values of  FIG. 37 ; 
         FIG. 39  illustrates trait-saturation patterns within a number of clusters of a first trait pair; 
         FIG. 40  illustrates trait-saturation patterns within a number of clusters of a second trait pair; 
         FIG. 41  illustrates trait-saturation patterns within a number of clusters of a third trait pair; and 
         FIG. 42  illustrates trait-saturation patterns within a number of clusters of a fourth trait pair. 
     
    
    
     REFERENCE NUMERALS 
     
         
           100 : Overview of a marketing-inference system 
           110 : A commodity to promote 
           112 : Data relevant to a population of tracked users considered a population of potential clients (potential consumers) 
           120 : A marketing-inference engine 
           140 : Relevant consumers data 
           160 : A filter identifying prospective clients from the population of tracked users based on consumers traits associated with commodity  110   
           180 : A module for determining prospective clients 
           200 : Components of filter  160   
           210 : Data memory devices 
           220 : Memory storing acquired input data such as data relevant to tracked users 
           230 : Memory storing computed intermediate data such as relevant users&#39; traits, communities of users of common traits, and clusters of users formed according to characteristics of users 
           240 : Memory storing data relevant to prospective clients 
           300 : A schematic of a process for determining principal communities of users of relevant traits and extended communities of users of significant kinship to the principal communities 
           310 : Compatible communities of users 
           320 : Module for determining primary communities of users 
           340 : Module for determining secondary communities of users 
           400 : A schematic of the marketing-inference engine 
           410 : Commodity-relevant data 
           411 : A list of commodities to be promoted 
           412 : Records of transactions of clients of each listed commodity 
           413 : A superset of predefined traits considered to be determinants of consumer tendencies 
           414 : Maintained data of tracked users of interest; for example, tracked social-media users 
           415 : A set of predefined characteristics according to which a population is segments into distinct clusters 
           416 : Population-relevant data 
           420 : A module for determining relevant traits for a specific commodity 
           430 : A module for determining a superset of communities of users where each community comprises users of a respective trait 
           440 : A module for determining a set of clusters of users where each cluster comprises users of close characteristics 
           450 : Pairwise kinship of communities of users based on common membership of a pair of communities 
           460 : A module for determining pairwise kinships of communities based on common membership of a pair of communities 
           470 : A module for determining pairwise kinships of communities based on trait saturation within individual clusters of the set of clusters formed in module  440   
           462 : Module for determining secondary communities according to pairwise kinships of communities determined in module  460   
           472 : Module for determining secondary communities according to pairwise kinships of communities determined in module  470   
           500 : Schematic of the principal segment (core) of marketing-inference engine 
           520 : An assembly of modules  420 ,  430 , and  450  for determining relevant traits to a selected commodity 
           600 : Schematic of a first extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both primary communities and secondary communities having a type-1 kinship to the primary communities 
           620 : An assembly of modules  460  and  462  for determining secondary communities based on a type-1 kinship of the set of primary communities determined in module  450  to other communities of the set of communities determined in module  430   
           700 : Schematic of a second extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both primary communities and secondary communities having a type-2 kinship to the primary communities or having a type-3 kinship to the primary communities 
           720 : An assembly of modules  440 ,  470  and  472  for determining secondary communities based on a type-2 kinship or a type-3 kinship of the set of primary communities determined in module  450  to other communities of the set of communities determined in module  430   
           800 : Schematic of a third extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both primary communities and secondary communities selected according to a composite kinship to the primary communities defined in terms of type-1, type-2, and type-3 kinships to the primary communities. 
           820 : An assembly of modules  440 ,  850  and  880  for determining secondary communities based on a composite kinship of the set of primary communities determined in module  450  to other communities of the set of communities determined in module  430   
           900 : A schematic of a variation of marketing-inference engine  400   
           910 : A list of commodities to be promoted together with known relevant traits for each commodity 
           920 : An assembly of modules  430  and  450  for determining relevant traits to a selected commodity based on known relevant traits of prior clients of a specific commodity 
           1000 : A process for determining primary traits, hence primary communities of users, based on prior demand for a specific commodity 
           1012 : A specific user of the tracked users 
           1020 : Membership count of each community of the set of communities  430 , denoted W 0  to W 8 , corresponding to traits T 0  to T 8    
           1030 : A set of prior clients for a specific commodity 
           1032 : A client typified as having traits T 0 , T 4 , T 5 , and T 6  of the superset of predefined traits  413  denotes T 0  to T 8    
           1040 : Initial trait score defined as a number of clients of the set  1030  of prior clients having a specific trait of the superset of predefined traits  413   
           1042 : Prorated initial trait score determined according to a ratio of a trait score to membership count of a community corresponding to the trait 
           1045 : First selected trait of highest prorated initial trait 
           1050 : First adjusted trait score to account for common membership of each remaining trait with the first selected trait 
           1052 : Prorated first-adjusted trait score determined as a ratio of a trait score to membership count of a community corresponding to the trait 
           1055 : Second selected trait of highest prorated first-adjusted trait 
           1060 : Second adjusted trait score to account for common membership of each remaining trait with the second selected trait 
           1062 : Prorated second-adjusted trait score determined as a ratio of a trait score to membership count of a community corresponding to the trait 
           1065 : Third selected trait of highest prorated second-adjusted trait 
           1100 : A process for determining secondary traits, hence secondary communities of users, based on kinship of the primary communities (corresponding to the primary traits) to each of the remaining communities 
           1110 : A selected commodity 
           1120 : Candidate primary traits 
           1130 : Measures of relevance of significant primary traits (denoted T 3 , T 5 , and T 6 ) to selected commodity  1110   
           1140 : Candidate secondary trait (candidate primary traits excluding the significant primary traits) 
           1150 : A measure of kinship of a significant primary trait to a candidate secondary trait 
           1160 : A measure of kinship of a candidate secondary trait to the set of significant primary traits 
           1200 : Pairwise trait kinship; a first measure of kinship of a second trait to a first trait 
           1210 : A community of users determined to have the first trait 
           1220 : A community of users determined to have the second trait 
           1215 : Users belonging to both communities, i.e., intersection of community  1210  and community  1220   
           1230 : A first definition of the first measure of kinship 
           1240 : A second definition of the first measure of kinship 
           1250 : A third definition of the first measure of kinship 
           1300 : Examples of pairwise trait kinship according to the first measure 
           1310 : First example of pairwise kinship 
           1320 : Second example of pairwise kinship 
           1330 : Third example of pairwise kinship 
           1400 : Examples of determination of significant secondary traits based on the first measure of kinship 
           1500 : Communities of users formed according to traits of individual users 
           1520 : A community of users corresponding to a single trait 
           1600 : Clusters of users formed according to characteristics of individual users 
           1620 : Universe of tracked users 
           1700 : Superposition of communities onto clusters 
           1800 : First-stratum communities of users corresponding to a specific commodity 
           1810 : Prior transactions data 
           1820 : Significant traits corresponding to the specific commodity 
           1830 : Communities of users having a one-to-one correspondence to the significant traits 
           1910 : A table of pairwise type-1 kinship of candidate communities to primary communities 
           1920 : A table of pairwise type-2 kinship of the candidate communities to the primary communities 
           1930 : A table of pairwise type-3 kinship of the candidate communities to the primary communities 
           1940 : A table of pairwise composite kinship of the candidate communities to the primary communities 
           1950 : Indices of primary communities 
           1960 : Indices of candidate communities 
           2000 : A first method of determining prospective clients for a specific commodity 
           2010 : A step of selecting a commodity from a list of commodities of interest 
           2020 : A process of acquiring a set of tracked clients of the specific commodity 
           2030 : A process of determining a set of significant first-stratum traits of the tracked clients 
           2050 : A process of determining a union of communities of the significant first-stratum traits 
           2060 : A process of communicating with the union of communities of the significant first-stratum traits 
           2100 : An illustration of trait-defined users for a single significant trait 
           2110 : A set of tracked users of a specific trait 
           2120 : A community of users of the specific trait 
           2130 : A set of first-stratum users of the specific trait 
           2140 : A community of users of considerable kinship to community  2120   
           2141 : A community of users of slight kinship to community  2120   
           2142 : Another community of users of slight kinship to community  2120   
           2143 : Another community of users of slight kinship to community  2120   
           2144 : Another community of users of slight kinship to community  2120   
           2150 : A set of first-stratum and second-stratum users of the specific trait 
           2200 : A first illustration of trait-defined users for two significant traits 
           2210 : A set of tracked users of a first trait 
           2212 : A set of tracked users of a second trait 
           2220 : Community of users of the first trait 
           2222 : Community of users of the second trait 
           2230 : A set of first-stratum users of the first and second traits 
           2240 : A community of users of considerable kinship to community  2220   
           2241 : A community of users of slight kinship to community  2220   
           2242 : A community of users of considerable kinship to community  2222   
           2243 : A community of users of slight kinship to community  1122   
           2250 : A set of first-stratum and second-stratum users of the first and second traits 
           2300 : A second illustration of trait-defined users for two significant traits 
           2310 : A set of tracked users of a first trait 
           2312 : A set of tracked users of a second trait 
           2320 : Community of users of the first trait 
           2330 : Community of users of the second trait 
           2340 : A community of users of considerable kinship to community  2320   
           2350 : A community of users of considerable kinship to community  2330   
           2360 : A set of first-stratum and second-stratum users of the first and second traits 
           2400 : A third illustration of trait-defined users for two significant traits 
           2450 : A community of users of considerable kinship to community  1230   
           2460 : A set of first-stratum and second-stratum users of the first and second traits 
           2500 : Saturation levels of communities of users within a set of clusters 
           2510 : A cluster of users 
           2520 : A segment of a community of users within a cluster 
           2600 : Illustration of a second measure of trait-pair kinship based on proximity of trait saturation levels within clusters 
           2610 : Absolute value of a difference of saturation levels of two traits within a same cluster 
           2700 : Illustration of a third measure of trait-pair kinship based on cross-correlation of trait saturation levels within clusters 
           2710 : Trait-saturation pattern of a first trait within a set of clusters 
           2720 : Trait-saturation pattern of a second trait within the set of clusters 
           2800 : Method of determining trait-pair kinship 
           2810 : A reference community of users corresponding to a specific trait and belonging to a specific first-stratum community of users for a specific commodity 
           2812 : A candidate community of users 
           2820 : A process of selecting a kinship criterion 
           2830 : A process of determining common memberships of the reference community and the candidate community 
           2840 : A process of determining saturation patterns of the reference community and candidate community within a set of user clusters 
           2832 : A process of kinship evaluation based on common memberships of the reference community and the candidate community 
           2842 : A process of kinship evaluation based on proximity of the saturation patterns of the reference community and the candidate community 
           2844 : A process of kinship evaluation based on cross-correlation of the saturation patterns of the reference community and the candidate community 
           2850 : A process of deciding whether to include or exclude the candidate community in a set of second-stratum communities of users relevant to the reference community. 
           2900 : A method of determining trait-pair kinship 
           2910 : Input data 
           2920 : Identifier of a first trait 
           2921 : Identifier of a second trait 
           2930 : Process of acquiring (pre-computed) community of users of the first trait 
           2940 : Process of acquiring (pre-computed) community of users of the second trait 
           2950 : Process of determining kinship of the first and second traits 
           3000 : A second method of determining prospective clients for a specific commodity 
           3040 : A process of determining a set of significant second-stratum traits relevant to the set of first-stratum traits 
           3050 : A process of determining a union of communities of significant traits 
           3060 : A process of communicating with the union of communities of the significant traits 
           3100 : Matrix of trait-pair kinship 
           3110 : A first-trait identifier 
           3120 : A second-trait identifier 
           3130 : Kinship of a trait pair 
           3200 : A pre-processing stage for determining clusters of users and communities of users 
           3270 : Preprocessing module 
           3300 : Trait-saturation patterns 
           3330 : Pattern of normalized trait-saturation levels 
           3400 : Exemplary trait-saturation scores within a number of clusters 
           3430 : A pattern of trait-saturation scores 
           3500 : Normalized trait-saturation levels 
           3530 : A pattern of trait-saturation levels 
           3600 : A table of trait-saturation scores 
           3620 : A table of normalized trait-saturation levels 
           3630 : Trait-saturation score 
           3640 : Normalized trait-saturation level 
           3710 : Pairwise trait-kinship values based on proximity of trait-saturation levels within clusters 
           3712 : Kinship level based on proximity 
           3720 : Pairwise trait-kinship values based on cross-correlation of trait-saturation levels within clusters 
           3722 : Kinship level based on cross correlation 
           3800 : Comparison of proximity-based and cross-correlation based kinship levels 
           3810 : Kinship levels based on proximity of trait-saturation patterns 
           3820 : Kinship levels based on cross correlation of trait-saturation patterns 
       
    
     Terminology 
     User: The term denotes a member of any population of interest, such as a population under consideration for developing a marketing system for specific commodities or for conducting a study aiming at gaining insight for policy development. The population may include users of social media or respondents to surveys, among many other entities. The term refers to an individual, or any other automaton, to which attention is directed. 
     Universe of users: The terms “population of users” and “universe of users” are herein used synonymously. 
     Characteristics of a user: The characteristics of a user represent slowly-varying properties (such as wealth), quasi-static properties (such as height of an adult), and/or permanent attributes such as place of birth. The characteristics of a user may comprise numerous attributes represented as a vector. 
     Traits of a user: The traits of a user represent evolving properties, such as societal views, favourite entertainment or sport, etc. 
     Cluster: A population under consideration may be segmented into a number of clusters according to values of a predefined set of characteristics for each member of the population. The number of clusters may be predefined or determined automatically under specific constraints. 
     Community: Members of the population possessing a specific trait form a respective community. The number of communities equals the number of predefined traits of interest. A user belongs to a one cluster but may belong to numerous communities. 
     Saturation pattern of a community: The term refers to intersection of a community with a set of clusters. The saturation pattern of a community is also referenced as the saturation pattern of the trait corresponding to the community. 
     Saturation-score vector: The counts of users of a community within a number K of clusters (K&gt;1) form a K-dimensional saturation-score vector of the community (also called saturation-score vector of the trait defining the community). 
     Saturation-level vector: The proportion of users of a community within a number K of clusters (K&gt;1) form a K-dimensional saturation-level vector of the community (also called saturation-level vector of the trait defining the community). 
     Kinship: For each trait of a predefined superset of traits, a community of users determined to have the trait is identified based on analysis of data characterizing a population of users under consideration. A kinship level of two traits is determined according to the contents (memberships) of respective communities. According to a first measure of kinship, a pairwise kinship level is based on intersection (overlap) of two communities. According to a second measure of kinship, a pairwise kinship level is based on proximity of saturation vectors of the two communities within a predetermined set of user clusters. According to a third measure of kinship, a pairwise kinship level is based on cross-correlation of the saturation vectors of the two communities. 
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a marketing-inference system  100  comprising a memory device having computer executable instructions stored thereon for execution by a hardware processor, forming a marketing-inference engine  160  configured to determine prospective clients  180  for a commodity (product or service)  110  from a population of users based on data  112  describing the population of users. The marketing engine  160  comprises a module  120  for determining relevant consumers&#39; traits associated with commodity  110  and a filter  140  configured to identify prospective clients from the population of users based on consumers traits associated with commodity  110 . 
       FIG. 2  illustrates components  200  of filter  140  of the marketing-inference engine  160 . The filter comprises data memory devices  210 , a network interface  280 , a memory device  260  storing processor-executable instructions, and at least one hardware processor  250 . The data memory devices  210  include:
         a memory device  220  storing input data acquired from external sources such as data relevant to tracked users;   a memory device  230  storing computed intermediate data such as relevant users&#39; traits, communities of users of common traits, and clusters of users formed according to characteristics of users; and   a memory device  240  storing data relevant to prospective clients.       

       FIG. 3  depicts a schematic  300  of basic components of filter  140  for determining “primary communities” of users of relevant traits and “secondary communities” of users of significant kinship to the principal communities. To promote a specific commodity  110 , specific user traits  140  compatible with the commodity are acquired. The specific user traits may be conjectured or determined from historical transaction data as described below with reference to  FIG. 10 . 
     Communities of users, of a population of tracked users, possessing the specific user traits would be considered likely future clients. Such communities of users are herein referenced as “primary communities” or “first-stratum” communities. 
     Communities of users, herein referenced as “secondary communities” or “second-stratum communities”, having significant kinship levels to the first-stratum communities of users may also be considered as likely future clients. Multi-stratum communities may likewise be considered with third-stratum communities of users having significant kinship to the second-stratum communities and so on. However, it may suffice to seek prospective clients  180  within the first-stratum and second-stratum communities. 
     A module  320  determines the primary communities based on data  112  relevant to the population of users and the relevant user traits. A module  340  determines the secondary communities based on data  112  and the primary communities determined in module  320  as illustrated in  FIG. 11 . A module  380  determines prospective clients  180 , In accordance with an implementation, prospective clients  180  may be based solely on the primary communities. In accordance with a preferred implementation, the prospective clients  180  are determined according to both the primary communities and the secondary communities. 
       FIG. 4  is a schematic  400  of a marketing-inference engine configured to process commodity-relevant data  410  and population-relevant data  416  to produce data identifying prospective clients (target users)  180 . The commodity-relevant data  410  comprise a list  411  of commodities to be promoted and records  412  of client transactions of each listed commodity. 
     The population-relevant data  416  comprise a superset  413  of predefined traits considered to be determinants of consumer tendencies, maintained (and regularly updated) data  414  of tracked users of interest (for example, tracked social-media users), and a set  415  of predefined characteristics according to which a population is segmented into distinct clusters. 
     A fully-configured marketing-inference engine comprises:
         (i) module  420  (an implementation of module  120  of  FIG. 1 ) for determining relevant traits for a specific commodity of the list  411  of commodities based on records  412  of client transactions as described below with reference to  FIG. 10 ;   (ii) module  430  for determining a set of communities of users where each community comprises users of a respective trait;   (iii) module  440  for determining a set of clusters of users where each cluster comprises users of close characteristics;   (iv) module  450  (an implementation of module  320  of  FIG. 3 ) for determining the primary communities (first-stratum communities) based on the set of communities determined in module  430  and the relevant traits produced in module  420 ;   (v) module  460  for determining pairwise type-1 kinship of communities of users based on common membership of a pair of communities as detailed below with reference to  FIGS. 11 to 14 ;   (vi) module  470  for determining pairwise type-2 and type-3 kinship of communities based on trait saturation within individual clusters of the set of clusters formed in module  440  as described below with reference to  FIGS. 25 to 28 ;   (vii) module  462  (a first variation of module  340  of  FIG. 3 ) for determining secondary communities (stratum-2A communities) based on the pairwise type-1 kinship of communities determined in module  460 ;   (viii) module  472  (a second variation of module  340  of  FIG. 3 ) for determining secondary communities (stratum-2B communities) based on the pairwise type-2 and type-3 kinship of communities determined in module  470 ; and   (ix) module  480  for determining prospective clients (target users) based on the primary communities determined in module  450  and, optionally, stratum-2A or stratum-2B communities.       

       FIG. 5  is a schematic  500  of the principal segment (core) of the marketing-inference engine which determines prospective clients  180  based on the primary communities only. An assembly  520  (assembly-I) of modules  420 ,  430 , and  450  processes records  412  of client transactions for a selected commodity of the list  411  of commodities to determine relevant traits to the selected commodity. The relevant traits belong to the predefined superset  413  of traits. 
     Module  480 A determines a set of prospective clients (target users) based only on the primary communities of users determined in module  450 . The set of prospective clients may be determined as the union of the primary communities of users. However, users belonging to an intersection of two or more primary communities may be considered more promising. 
       FIG. 6  is a schematic  600  of a first extension of the principal segment of the marketing-inference engine where target users (prospective clients)  180  are determined according to both primary communities and other communities having a type-1 kinship to the primary communities. Each community of the set of communities determined in module  430 , excluding the primary communities determined in module  450 , is a candidate for selection as a relevant secondary community. 
     An assembly  620  (assembly-II) of modules  460  and  462  determines secondary communities based on a type-1 kinship of the set of primary communities determined in module  450  to other communities of the set of communities determined in module  430  as described below with reference to  FIGS. 11 to 14 . A type-1 kinship is based on a count of common users of a community pair. 
     Module  480 B determines a set of prospective clients (target users) based on the primary communities of users determined in module  450  and the secondary communities determined in module  462 . The set of prospective clients may be determined as the union of the primary communities of users and the secondary community of users. However, users belonging to an intersection of two or more primary or secondary communities may be considered more promising. 
       FIG. 7  is a schematic  700  of a second extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both the primary communities and other communities having a type-2 kinship to the primary communities or a type-3 kinship to the primary communities. A type-2 kinship of two communities is based on proximity of intersection levels of each of the two communities with a set of clusters of users as illustrated in  FIG. 25  and  FIG. 26 . A type-3 kinship of two communities is based on cross-correlation of intersection levels of each of the two communities with a set of clusters of users as illustrated in  FIG. 25  and  FIG. 27 . 
     An assembly  720  (assembly-III) of modules  440 ,  470  and  472  determines secondary communities based on a type-2 kinship or a type-3 kinship of the set of primary communities determined in module  450  to other communities of the set of communities determined in module  430  as described below with reference to  FIGS. 11 and 25 to 28 . 
     Module  480 C determines a set of prospective clients (target users) based on the primary communities of users determined in module  450  and the secondary communities determined in module  472 . The set of prospective clients may be determined as the union of the primary communities of users and the secondary community of users. However, users belonging to an intersection of two or more primary or secondary communities may be considered more promising. 
       FIG. 8  is a schematic  800  of a third extension of the principal segment of the marketing-inference engine where target users (prospective clients) are determined according to both primary communities and secondary communities selected according to a composite kinship to the primary communities defined in terms of type-1, type-2, and type-3 kinships to the primary communities. Module  850  determines composite kinship of the set of primary communities determined in module  450  to other communities of the set of communities determined in module  430 . Module  880  determines secondary communities based on the pairwise type-1, type-2 and type-3 kinship of communities determined in modules  460  and  470 . Computation of a composite kinship is described below with reference to  FIG. 19 . 
     An assembly  820  (assembly-IV) of modules  440 ,  850  and  880  determines secondary communities based on type-1, type-2, and type-3 kinships of the set of primary communities determined in module  450  to other communities of the set of communities determined in module  430 . 
     Module  480 D determines a set of prospective clients (target users) based on the primary communities of users determined in module  450  and the secondary communities determined in module  880 . The set of prospective clients may be determined as the union of the primary communities of users and the secondary community of users. However, users belonging to an intersection of two or more primary or secondary communities may be considered more promising. 
       FIG. 9  is a schematic  900  of a variation of marketing-inference engine of  FIG. 4  where relevant traits for a specific commodity are conjectured instead of being determined in module  420  from historical transaction data. A list  910  of commodities to be promoted together with known relevant traits for each commodity are acquired from appropriate sources. Thus, assembly-I of modules  420 ,  430 , and  450  is reduced to assembly-V (reference  920 ) of modules  430 , and  450 . 
     Table-I below indicates a count of prior clients corresponding to each trait of a set of nine traits, denoted T 0  to T 8 , to each commodity of set of Π, Π≥1, commodities denoted Φ 0  to Φ (Π−1) . A simplified measure of relevance of a specific trait to a specific commodity may be based on a proportion of prior clients determined to have the specific trait. According to a straightforward approach, a trait is considered to be relevant to the specific commodity if the simplified measure of relevance exceeds a predefined threshold. For example, with a sample of 100 prior clients of commodity Φ 0 , trait T 1  has a relevance score of 68, traits T 5  has a relevance score of 57, trait T 4  has a relevance score of 7, and trait T 7  has a relevance score of 2. The sum of the scores exceeds 100 because a client may be determined to have multiple traits. Traits T1, T4, T5, and T7 have simplified measures of relevance of 0.68, 0.07, 0.57, and 0.02, respectively. With a predefined threshold of 0.2, for example, only Traits T 1  and T 5  are considered and given normalized relevance levels of 68/(68+57) and 57/(68+57); that is 0.544 and 0.456, respectively. 
     
       
         
           
               
             
               
                 TABLE I 
               
             
            
               
                   
               
               
                 Score of prior clients corresponding to each trait 
               
            
           
           
               
               
            
               
                 Community 
                 Trait identifier 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 identifier 
                 T 0   
                 T 1   
                 T 2   
                 T 3   
                 T 4   
                 T 5   
                 T 6   
                 T 7   
                 T 8   
               
               
                   
               
               
                 Φ 0   
                 0 
                 68 
                 0 
                 0 
                 7 
                 57 
                 0 
                 2 
                 — 
               
            
           
           
               
            
               
                 . 
               
               
                 . 
               
               
                 . 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Φ (Π-1)    
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
       FIG. 10  illustrates a process  1000  for determining primary traits, hence primary communities of users, based on prior demand for a specific commodity. An exemplary superset  413  ( FIG. 4 ) of predefined traits comprises nine traits denoted T 0  to T 8 . The sizes  1020  of corresponding communities W 0  to W 8  (reference  430 ,  FIG. 4 ) are determined from data  112  ( FIG. 1 ) relevant to a population of tracked users. A tracked user may belong to multiple communities. The illustrated user  1012 , having traits T 1 , T 3 , T 4 , and T 7 , belongs to communities W 1 , W 3 , W 4 , and W 7 . 
     Data, such as sales transactions, relevant to a set  1030  of prior clients for a specific commodity may be used to determine primary traits relevant to the specific community. Traits of each client of the set of prior clients are determined from records  412  of transactions of clients of each listed commodity. The illustrated client  1032  is typified as having traits T 0 , T 4 , T 5 , and T 6  of the superset of predefined traits  413  denotes T 0  to T 8 . An initial trait score  1040  of each of the traits T 0  to T 8 , of the superset of predefined traits  413  is determined as a number of clients of the set  1030  of prior clients having a specific trait. In order to properly compare relevance of individual traits to a specific commodity, the initial trait scores  1040  for traits T 0  to T 8  are prorated to a nominal community size to produce prorated initial scores  1042 . The nominal community size is selected to be  1000  in the example of  FIG. 10 . Thus, a raw score Sj of trait Tj, 0≤j&lt;9, is prorated to ((1000×S j )/Q j ), Q j  being the size of community W j  for Sj≤Q j  or prorated to the nominal community size if Sj&gt;Q j . 
     Trait T 6 , having the highest prorated initial score of 45.1, is considered the most relevant trait and is the first selected trait  1045 . Since a client of the set  1030  of prior clients for the specific commodity may have multiple traits, a first-adjusted trait score  1050  which accounts for common membership of each remaining trait with the first selected trait is produced. The initial score  1040  of each of the traits, excluding T 6 , may be adjusted to exclude users already included in the initial score of T 6 . Trait T 2  has an initial score of 32 clients of which 13 clients are also counted in the initial score of T 6 . Thus, the score of T 2  is reduced from 32 to 19. Trait T 3  has an initial score of 25 clients of which one client is also counted in the initial score of T 6 . Thus, the score of T 3  is reduced from 25 to 24. Trait T 5  has an initial score of 18 clients of which one client is also counted in the initial score of T 6 . Thus, the score of T 5  is reduced from 18 to 17. 
     The first-adjusted trait score  1050  of each remaining trait is prorated to the aforementioned nominal community size to produce a prorated first-adjusted trait  1052 . Thus, a first-adjusted score S (1)   j  of trait Tj, 0≤j&lt;9, j≠6, is prorated to ((1000×S (1)   j )/Q j ), Q j  being the size of community W j . Trait T 3 , having the highest prorated first-adjusted trait  1052  of 31.6, is then the second selected trait  1055 . 
     The first-adjusted score  1050  of each of the traits, excluding T 6  and T 3 , may be adjusted again to exclude users already included in the first-adjusted score of T 3  to produce a second-adjusted trait score  1060 . Trait T 2  has a first-adjusted score of 19 clients of which 7 clients are also counted in the first-adjusted score of T 3 . Thus, the score of T 2  is reduced again from 19 to 12. Trait T 5  has a first-adjusted score of 17 clients none of which is counted in the first-adjusted score of T 3 . 
     The second-adjusted trait score  1060  of each remaining trait is prorated to the aforementioned nominal community size to produce a prorated second-adjusted trait  1062 . Thus, a second-adjusted score S (2)   j  of trait Tj, 0≤j&lt;9, j≠6, j≠3, is prorated to 1000×(S (2)   j /Q j ), Q j  being the size of community W j . Trait T 5 , having the highest prorated second-adjusted trait  1062  of 24.3, is then the third-selected trait  1065 . 
     Thus, to determine a set of relevant traits, module  420  ( FIG. 4 ) acquires the size of each community of the superset of communities, initializes a set of relevant traits as an empty set, and determines for each trait of the superset of predefined traits a respective trait score as a number of clients of the set of prior clients determined to have the trait. Module  420  iteratively performs processes of:
         (i) prorating each trait score to a nominal community size to produce prorated initial scores;   (ii) transferring a particular trait of highest prorated score to the set of relevant traits; and   (iii) adjusting the score of each of the remaining traits of the superset of predefined traits to exclude users already included in the particular trait.       

     The processes of  FIG. 10  may continue until all predefined traits are ranked with respect to the specific commodity under consideration, or until the highest score of the remaining traits is below a predefined level. 
       FIG. 11  illustrates a method  1100  of determining significant traits for a selected commodity  1110 , labeled Φ 0  for the case of nine predefined traits (H=9). Initially, each of the nine traits is a candidate for selection as a first-stratum trait  1120 . A measure of relevance of each of the nine traits to the selected commodity is determined based on conjecture or based on analysis of tracked transaction data as described above with reference to  FIG. 10 . Only a measure of relevance above a predefined threshold is considered. The sum of the considered measures of relevance of all candidate traits to the selected commodity is normalized to unity. 
     In the example of  FIG. 11 , the measures  1130  of direct relevance of traits T 6 , T 3 , and T 5  to commodity Φ 0  are determined as 0.45, 0.30, and 0.25, respectively. With a predetermined threshold of direct relevance of 0.2, the measures of direct relevance of the remaining traits  1140  to the commodity Φ 0  are insignificant. The users belonging to communities W 6 , W 3 , and W 5 , corresponding to traits T 6 , T 3 , and T 5 , are treated as the primary users of interest with respect to commodity Φ 0 . 
     Each of the remaining traits {T 0 , T 1 , T 2 , T 4 , T 7 , T 8 } (reference  1140 ) is a candidate for selection as a second-stratum trait. A pairwise kinship value of each selected first-stratum trait to each of the remaining traits {T 0 , T 1 , T 2 , T 4 , T 7 , T 8 } is determined. Only candidate second-stratum traits each having pairwise kinship values above a predefined kinship threshold are considered. The sum of the kinship values of all considered candidate second-stratum traits with respect to a first-stratum trait is normalized to unity. As illustrated, first-stratum trait T 3  has a kinship value of 0.65 to T 2  and a kinship value of 0.35 to T 4 . First-stratum trait T 5  has a kinship value of 0.6 to T 2  and a kinship value of 0.4 to T 8 . First-stratum trait T 6  has a kinship value of 0.45 to T 1  and a kinship value of 0.55 to T 2 . 
     A compound relevance value θ j  of a candidate second-stratum trait T j , where T j  is one of candidate second-stratum traits {T 0 , T 1 , T 2 , T 4 , T 7 , T 8 } is determined according to the relevance measures of selected first-stratum traits {T 3 , T 5 , T 6 } and kinship values of candidate second-stratum trait T j  to respective first-stratum traits. As indicated in  FIG. 11 , the values of the compound relevance θ 2 , θ 4 , and θ 8 , for T 2 , T 4 , and T 8  are 0.2025, 0.6250, and 0.10, respectively. 
     Upon determining a set of Γ first-stratum traits, 0&lt;Γ&lt;H, a weighted aggregate kinship of each of the remaining (H-Γ) traits to the set of Γ first-stratum traits is determined. A remaining trait having an aggregate kinship exceeding a predefined threshold is qualified as a second-stratum trait. Table-II below illustrates the case of  FIG. 11  of three first-stratum traits (Γ=3) of indices 6, 3, and 5, having relevance coefficients of 0.45, 0.30, and 0.25, respectively, to commodity Φ 0 . 
     
       
         
           
               
             
               
                 TABLE II 
               
               
                   
               
               
                 Aggregate kinship of candidate second-stratum communities 
               
               
                   
               
             
            
               
                 First-stratum communities 
               
            
           
           
               
               
            
               
                   
                 Index j 
               
            
           
           
               
               
               
               
            
               
                   
                 6 
                 3 
                 5 
               
               
                   
               
               
                 η j   
                 0.45 
                 0.30 
                 0.25 
               
               
                   
               
            
           
           
               
               
            
               
                 Candidate second-stratum communities 
                   
               
            
           
           
               
               
               
            
               
                   
                 Pairwise kinship coefficient Λ j, k   
                 Aggregate 
               
               
                 Index k 
                 (type-1 kinship, for example) 
                 kinship: 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                   
                   
                   
                   
               
               
                 1 
                 0.45 
                   
                   
                 0.2025 
               
               
                 2 
                 0.55 
                 0.65 
                 0.6 
                 0.5925 
               
               
                 3 
                   
                   
                   
                   
               
               
                 4 
                   
                 0.35 
                   
                 0.105 
               
               
                 5 
                   
                   
                   
                   
               
               
                 6 
                   
                   
                   
                   
               
               
                 7 
                   
                   
                   
                   
               
               
                 8 
                   
                   
                 0.4 
                 0.10 
               
               
                   
               
            
           
         
       
     
     Setting a threshold of compound relevance to be 0.4, only trait T 2  would be accepted as second-stratum traits. According to the method of  FIG. 30 , the users belonging to communities W 3 , W 5 , W 6  and W 2 , corresponding to traits T 3 , T 5 , T 6 , and T 2 , are treated as communities of interest with respect to commodity Φ 0 . 
     With η j  denoting a relevance coefficient of a first-stratum community of index j, and Λ j ,k denoting pairwise kinship of a candidate community of index k to a first-stratum community of index j, a weighted aggregate kinship of the candidate of index k, to the set of first-stratum traits is determined as: 
     
       
         
           
             
               
                 Λ 
                 k 
               
               * 
             
             = 
             
               
                 
                   Σ 
                   j 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       η 
                       j 
                     
                     × 
                     
                       Λ 
                       
                         j 
                         . 
                         k 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 ( 
                 
                   
                     
                       η 
                       3 
                     
                     × 
                     
                       Λ 
                       
                         3. 
                         ⁢ 
                         k 
                       
                     
                   
                   + 
                   
                     
                       η 
                       5 
                     
                     × 
                     
                       Λ 
                       
                         5. 
                         ⁢ 
                         k 
                       
                     
                   
                   + 
                   
                     
                       η 
                       6 
                     
                     × 
                     
                       Λ 
                       
                         6. 
                         ⁢ 
                         k 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     With η 3 =0.30, η 5 =0.25, and η 6 =0.45, the weighted aggregate kinship of candidate traits T 1 , T 2 , T 4 , and T 8  (hence candidate communities W 1 , W 2 , W 4 , and W 8 ) are determined as: 
     
       
         
           
             
               
                 
                   Λ 
                   1 
                 
                 * 
               
               = 
               
                 
                   
                     η 
                     6 
                   
                   × 
                   
                     Λ 
                     6.1 
                   
                 
                 = 
                 
                   
                     0 
                     . 
                     4 
                   
                   ⁢ 
                   5 
                   × 
                   0.45 
                 
               
             
             ; 
           
         
       
       
         
           
             
               
                 
                   Λ 
                   2 
                 
                 * 
               
               = 
               
                 
                   ( 
                   
                     
                       
                         η 
                         3 
                       
                       × 
                       
                         Λ 
                         
                           3 
                           . 
                           2 
                         
                       
                     
                     + 
                     
                       
                         η 
                         5 
                       
                       × 
                       
                         Λ 
                         
                           5 
                           . 
                           2 
                         
                       
                     
                     + 
                     
                       
                         η 
                         6 
                       
                       × 
                       
                         Λ 
                         6.2 
                       
                     
                   
                   ) 
                 
                 = 
                 
                   
                     
                       0 
                       . 
                       3 
                     
                     ⁢ 
                     0 
                     × 
                     
                       0 
                       . 
                       6 
                     
                     ⁢ 
                     5 
                   
                   + 
                   
                     
                       0 
                       . 
                       2 
                     
                     ⁢ 
                     5 
                     × 
                     
                       0 
                       . 
                       6 
                     
                   
                   + 
                   
                     
                       0 
                       . 
                       4 
                     
                     ⁢ 
                     5 
                     × 
                     0 
                     ⁢ 
                     .55 
                   
                 
               
             
             ; 
           
         
       
       
         
           
             
               
                 
                   Λ 
                   4 
                 
                 * 
               
               = 
               
                 
                   
                     η 
                     3 
                   
                   × 
                   
                     Λ 
                     3.4 
                   
                 
                 = 
                 
                   
                     0 
                     . 
                     3 
                   
                   × 
                   0.35 
                 
               
             
             ; 
             and 
           
         
       
       
         
           
             
               
                 Λ 
                 8 
               
               * 
             
             = 
             
               
                 
                   η 
                   5 
                 
                 × 
                 
                   Λ 
                   5.8 
                 
               
               = 
               
                 
                   0 
                   . 
                   2 
                 
                 ⁢ 
                 5 
                 × 
                 
                   0 
                   . 
                   4 
                   . 
                 
               
             
           
         
       
     
     Table-III below depicts aggregate kinship of candidate second-stratum communities for type-1 kinship, type-2 kinship, and type-3 kinship. 
     
       
         
           
               
             
               
                 TABLE III 
               
             
            
               
                   
               
               
                 Kinship values of candidate secondary traits to a set of primary traits 
               
            
           
           
               
               
               
               
            
               
                 Kinship 
                 Primary 
                   
                 Candidate secondary traits 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 type 
                 traits 
                 Relevance 
                 T 0   
                 T 1   
                 T 2   
                 T 4   
                 T 7   
                 T 8   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Type-1 
                 T3 
                 0.30 
                 — 
                 — 
                 0.65 
                 0.35 
                 — 
                 — 
               
               
                   
                 T5 
                 0.25 
                 — 
                 — 
                 0.60 
                 — 
                 — 
                 0.40 
               
               
                   
                 T6 
                 0.45 
                 — 
                 0.45 
                 0.55 
                 — 
                 — 
                 — 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Aggregate kinship 
                 — 
                 0.2025 
                 0.5925 
                 0.1050 
                 — 
                 0.1000 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Type-2 
                 T3 
                 0.30 
                 — 
                 — 
                 0.58 
                 0.42 
                 — 
                 — 
               
               
                   
                 T5 
                 0.25 
                 — 
                 — 
                 0.56 
                 — 
                 — 
                 0.44 
               
               
                   
                 T6 
                 0.45 
                 — 
                 0.50 
                 0.50 
                 — 
                 — 
                 — 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Aggregate kinship 
                 — 
                 0.225 
                 0.539 
                 0.126 
                 — 
                 0.110 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Type-3 
                 T3 
                 0.30 
                 — 
                 — 
                 0.62 
                 0.38 
                 — 
                 — 
               
               
                   
                 T5 
                 0.25 
                 — 
                 — 
                 0.59 
                 — 
                 — 
                 0.41 
               
               
                   
                 T6 
                 0.45 
                 — 
                 0.48 
                 0.52 
                 — 
                 — 
                 — 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Aggregate kinship 
                 — 
                 0.216 
                 0.5675 
                 0.114 
                 — 
                 0.1025 
               
               
                   
               
            
           
         
       
     
     A composite pairwise kinship level or a composite aggregate kinship level may be determined according to kinship values corresponding to type-1, type-2, and type-3 kinship levels as described below with reference to  FIG. 19 . 
       FIG. 12  illustrates a first measure  1200  of trait-pair kinship. Upon identifying a community  1210 , denoted W u , of N u  users of a first trait T u , and a community  1220 , denoted W v , of N v  users of a second trait T V , the number N c  of common members  1215  is determined. 
     The first measure of kinship is based on the intersection of communities W u , and W v , i.e., the number of users belonging to both communities. According to a first form r (1)   u,v  of the first measure, kinship is determined as the ratio of the number of common users of the two communities to the number of users of the union of the communities (reference  1230 ). According to a second form r (2)   u,v  of the first measure, kinship is determined as the ratio of the number of common users of the two communities to the arithmetic mean of the number of users of the first community and the number of users of the second community (reference  1240 ). According to a third form r (3)   u,v  of the first measure, kinship is determined as the ratio of the number of common users of the two communities to the geometric mean of the number of users of the first community and the number of users of the second community (reference  1250 ). The number of users of the union of the two communities is (N u +N v −N c ). The arithmetic mean is (N u +N v )/2. The geometric mean is (N u +N v ) 1/2 . Thus: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         
                           u 
                           , 
                           v 
                         
                       
                       = 
                       
                         
                           N 
                           c 
                         
                         / 
                         
                           ( 
                           
                             
                               N 
                               u 
                             
                             + 
                             
                               N 
                               v 
                             
                             - 
                             
                               N 
                               c 
                             
                           
                           ) 
                         
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         
                           u 
                           , 
                           v 
                         
                       
                       = 
                       
                         2 
                         × 
                         
                           
                             N 
                             c 
                           
                           / 
                           
                             ( 
                             
                               
                                 N 
                                 u 
                               
                               + 
                               
                                 N 
                                 v 
                               
                             
                             ) 
                           
                         
                       
                     
                     ; 
                     and 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         r 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       
                         u 
                         , 
                         v 
                       
                     
                     = 
                     
                       
                         N 
                         c 
                       
                       / 
                       
                         
                           
                             ( 
                             
                               
                                 N 
                                 u 
                               
                               + 
                               
                                 N 
                                 v 
                               
                             
                             ) 
                           
                           
                             1 
                             / 
                             2 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
       FIG. 13  illustrates examples  1300  of pairwise trait kinship according to the first measure of kinship with N u =924 and N v =416. 
     If all members of community W v  are also members of community W u , (reference  1310 ), with N u &gt;N v , then N c =N v  and: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         
                           u 
                           , 
                           v 
                         
                       
                       = 
                       
                         
                           
                             N 
                             c 
                           
                           / 
                           
                             ( 
                             
                               
                                 N 
                                 u 
                               
                               + 
                               
                                 N 
                                 v 
                               
                               - 
                               
                                 N 
                                 c 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           
                             
                               N 
                               c 
                             
                             / 
                             
                               N 
                               u 
                             
                           
                           = 
                           
                             0 
                             ⁢ 
                             .45 
                           
                         
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         
                           u 
                           , 
                           v 
                         
                       
                       = 
                       
                         
                           2 
                           × 
                           
                             
                               N 
                               c 
                             
                             / 
                             
                               ( 
                               
                                 
                                   N 
                                   u 
                                 
                                 + 
                                 
                                   N 
                                   v 
                                 
                               
                               ) 
                             
                           
                         
                         = 
                         0.621 
                       
                     
                     ; 
                     and 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         r 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       
                         u 
                         , 
                         v 
                       
                     
                     = 
                     
                       
                         
                           N 
                           c 
                         
                         / 
                         
                           
                             ( 
                             
                               
                                 N 
                                 u 
                               
                               + 
                               
                                 N 
                                 v 
                               
                             
                             ) 
                           
                           
                             1 
                             / 
                             2 
                           
                         
                       
                       = 
                       
                         0.6 
                         ⁢ 
                         1 
                         ⁢ 
                         
                           1 
                           . 
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     With an intersection of 200 common members, i.e., N c =200, (reference  1312 ), then: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         
                           u 
                           , 
                           v 
                         
                       
                       = 
                       0.175 
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         
                           u 
                           , 
                           v 
                         
                       
                       = 
                       0.299 
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         r 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       
                         u 
                         , 
                         v 
                       
                     
                     = 
                     
                       0.323 
                       . 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     With an intersection of 70 common members, i.e., N c =70, (reference  1314 ), then: 
     
       
         
           
             
               
                 
                   r 
                   
                     ( 
                     1 
                     ) 
                   
                 
                 
                   u 
                   , 
                   v 
                 
               
               = 
               0.055 
             
             ; 
           
         
       
       
         
           
             
               
                 
                   r 
                   
                     ( 
                     2 
                     ) 
                   
                 
                 
                   u 
                   , 
                   v 
                 
               
               = 
               0.104 
             
             ; 
           
         
       
       
         
           
             
               
                 r 
                 
                   ( 
                   3 
                   ) 
                 
               
               
                 u 
                 , 
                 v 
               
             
             = 
             0113. 
           
         
       
     
       FIG. 14  illustrates examples  1400  of determination of kinship of each trait of a set of nine traits to a reference trait. The traits are indexed as (0) to (8), and corresponding communities are likewise indexed. The traits are denoted T 0  to T 8 , and corresponding communities are labeled W 0  to W 8 . The trait of index (2) is selected as a reference trait. The size of each community is determined and the intersection of each community with the reference community of index (2) is determined. The size of a community is the number of users determined to have a corresponding trait and the size of intersection of two communities is the number of users belonging to the two communities. The sizes of the nine communities and the intersection of each community with the reference community are determined. 
     The size of the community W 0  is 512, the size of the reference community W 2  is 560. The number of users belonging to communities W 0  and W 2  is 80. Thus, the size of the union of W 0  and W 2  is (512+560−80), which is 992. The arithmetic mean of the sizes of the two communities is 536 and the geometric mean of the sizes of the two communities is determined as (512+560) 1/2 , which is 535.5. Thus, 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         
                           0 
                           , 
                           2 
                         
                       
                       = 
                       
                         8 
                         ⁢ 
                         
                           0 
                           / 
                           9 
                         
                         ⁢ 
                         92 
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           r 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         
                           0 
                           , 
                           2 
                         
                       
                       = 
                       
                         8 
                         ⁢ 
                         
                           0 
                           / 
                           5 
                         
                         ⁢ 
                         36 
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         r 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       
                         0 
                         , 
                         2 
                       
                     
                     = 
                     
                       8 
                       ⁢ 
                       
                         0 
                         / 
                         5 
                       
                       ⁢ 
                       3 
                       ⁢ 
                       
                         5 
                         . 
                         5 
                         . 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Likewise, the values r (1)   j,2 , r (2)   j,2 , r (3)   j,2 , for j=1, 3, 4, 5, 6, 7, and 8 are determined. Only a kinship value above a prescribed lower bound are retained. In the example of  FIG. 14 , the lower bound is set to be 0.2. Accordingly, the retained values are: 
         r   (1)   1,2  and  r   (1)   3,2 ,(0.206 and 0.256,respectively), 
         r   (2)   1,2  and  r   (2)   3,2 ,(0.341 and 0.408,respectively), and 
         r   (3)   1,2   ,r   (3)   3,2 , and  r   (3)   5,2 ,(0.350, 0.415, and 0.202,respectively). 
     The sum of kinship measures is normalized to unity. Thus, the corresponding normalised kinship measures are: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           κ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         
                           1 
                           , 
                           2 
                         
                       
                       = 
                       
                         
                           
                             
                               r 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             
                               1 
                               , 
                               2 
                             
                           
                           / 
                           
                             ( 
                             
                               
                                 
                                   r 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 
                                   3 
                                   , 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                         0.446 
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           κ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         
                           3 
                           , 
                           2 
                         
                       
                       = 
                       
                         
                           
                             
                               r 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             
                               3 
                               , 
                               2 
                             
                           
                           / 
                           
                             ( 
                             
                               
                                 
                                   r 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 
                                   3 
                                   , 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                         0.554 
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           κ 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         
                           1 
                           , 
                           2 
                         
                       
                       = 
                       
                         
                           
                             
                               r 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                             
                               1 
                               , 
                               2 
                             
                           
                           / 
                           
                             ( 
                             
                               
                                 
                                   r 
                                   
                                     ( 
                                     2 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     2 
                                     ) 
                                   
                                 
                                 
                                   3 
                                   , 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                         0.455 
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           κ 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         
                           3 
                           , 
                           2 
                         
                       
                       = 
                       
                         
                           
                             
                               r 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                             
                               3 
                               , 
                               2 
                             
                           
                           / 
                           
                             ( 
                             
                               
                                 
                                   r 
                                   
                                     ( 
                                     2 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     2 
                                     ) 
                                   
                                 
                                 
                                   3 
                                   , 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                         0.545 
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           κ 
                           
                             ( 
                             3 
                             ) 
                           
                         
                         
                           1 
                           , 
                           2 
                         
                       
                       = 
                       
                         
                           
                             
                               r 
                               
                                 ( 
                                 3 
                                 ) 
                               
                             
                             
                               1 
                               , 
                               2 
                             
                           
                           / 
                           
                             ( 
                             
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   3 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   5 
                                   , 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                         0.362 
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           κ 
                           
                             ( 
                             3 
                             ) 
                           
                         
                         
                           3 
                           , 
                           2 
                         
                       
                       = 
                       
                         
                           
                             
                               r 
                               
                                 ( 
                                 3 
                                 ) 
                               
                             
                             
                               3 
                               , 
                               2 
                             
                           
                           / 
                           
                             ( 
                             
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   3 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   5 
                                   , 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                         0.429 
                       
                     
                     ; 
                     
                       
                         and 
                         ⁢ 
                         
                           
 
                         
                         ⁢ 
                         
                           
                             κ 
                             
                               ( 
                               3 
                               ) 
                             
                           
                           
                             5 
                             , 
                             2 
                           
                         
                       
                       = 
                       
                         
                           
                             
                               r 
                               
                                 ( 
                                 3 
                                 ) 
                               
                             
                             
                               5 
                               , 
                               2 
                             
                           
                           / 
                           
                             ( 
                             
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   3 
                                   , 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   r 
                                   
                                     ( 
                                     3 
                                     ) 
                                   
                                 
                                 
                                   5 
                                   , 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           0 
                           ⁢ 
                           
                             .209 
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     If the lower bound is set to be 0.4 instead of 0.20, then the retained values of the third form of type-kinship would be r (3)   1,2  and r (3)   3,2 , (0.350 and 0.415, respectively), with corresponding normalised kinship measures of: 
     
       
         
           
             
               
                 
                   κ 
                   
                     ( 
                     3 
                     ) 
                   
                 
                 
                   1 
                   , 
                   2 
                 
               
               = 
               
                 
                   
                     
                       r 
                       
                         ( 
                         3 
                         ) 
                       
                     
                     
                       1 
                       , 
                       2 
                     
                   
                   / 
                   
                     ( 
                     
                       
                         
                           r 
                           
                             ( 
                             3 
                             ) 
                           
                         
                         
                           1 
                           , 
                           2 
                         
                       
                       + 
                       
                         
                           r 
                           
                             ( 
                             3 
                             ) 
                           
                         
                         
                           3 
                           , 
                           2 
                         
                       
                     
                     ) 
                   
                 
                 = 
                 0.458 
               
             
             ; 
             and 
           
         
       
       
         
           
             
               
                 κ 
                 
                   ( 
                   3 
                   ) 
                 
               
               
                 3 
                 , 
                 2 
               
             
             = 
             
               
                 
                   
                     r 
                     
                       ( 
                       3 
                       ) 
                     
                   
                   
                     3 
                     , 
                     2 
                   
                 
                 / 
                 
                   ( 
                   
                     
                       
                         r 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       
                         1 
                         , 
                         2 
                       
                     
                     + 
                     
                       
                         r 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       
                         3 
                         , 
                         2 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 0.542 
                 . 
               
             
           
         
       
     
       FIG. 15  illustrates a number of communities  1500  of users of the universe  430  of tracked users formed according to a number, H, of predefined significant traits of individual users. Nine communities  1520 ( 0 ) to  1520 ( 8 ) corresponding to nine traits (H=9) of interest, denoted T 0  to T 8 , are defined. The communities are labeled W 0  to W 8 . Each community corresponds to a single trait. A user may have more than one trait. Thus, a community may intersect other communities. 
       FIG. 16  illustrates a universe  1620  of tracked users segmented into K clusters  1600  based on characteristics of individual users, K&gt;1. Five clusters (K=5) labeled C 0 , C 1 , C 2 , C 3 , and C 4  are defined in the example of  FIG. 16  with each user of the universe of tracked users belonging to only one cluster. 
       FIG. 17  illustrates superposition  1700  of communities W 0  to W 8  onto clusters C 0  to C 4  indicating saturation of the communities within the clusters. As illustrated, some members of community W 1  belong to cluster C 3  while the remaining members community W 1  belong to cluster C 0 . Community W 2  includes members belonging to cluster C 0 , members belonging to cluster C 1 , and members belonging to cluster C 3 . Table-IV below indicates saturation vectors of communities W 0  to W 8  within the set of clusters. 
     
       
         
           
               
             
               
                 TABLE IV 
               
             
            
               
                   
               
               
                 Saturation vectors of the communities of FIG. 15 
               
               
                 within the clusters of FIG. 16 
               
            
           
           
               
               
               
            
               
                   
                   
                 Clusters 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Community 
                 C 0   
                 C 1   
                 C 2   
                 C 3   
                 C 4   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Saturation 
                 W 0   
                 0.0 
                 1.0 
                 0.0 
                 0.0 
                 0.0 
               
               
                 vectors 
                 W 1   
                 0.08 
                 0.0 
                 0.0 
                 0.92 
                 0.0 
               
               
                 → 
                 W 2   
                 0.14 
                 0.52 
                 0.0 
                 0.34 
                 0.0 
               
               
                   
                 W 3   
                 0.0 
                 0.0 
                 0.32 
                 0.68 
                 0.0 
               
               
                   
                 W 4   
                 0.0 
                 0.0 
                 1.0 
                 0.0 
                 0.0 
               
               
                   
                 W 5   
                 0.0 
                 0.0 
                 0.0.05 
                 0.63 
                 0.32 
               
               
                   
                 W 6   
                 0.12 
                 0.0 
                 0.0 
                 0.84 
                 0.04 
               
               
                   
                 W 7   
                 0.65 
                 0.35 
                 0.0 
                 0.0 
                 0.0 
               
               
                   
                 W 8   
                 0.0 
                 0.0 
                 0.0 
                 0.0 
                 1.0 
               
               
                   
               
            
           
         
       
     
       FIG. 18  illustrates determining first-stratum communities  1800  of users corresponding to a specific commodity. Prior transaction data  1810  is analysed to determine a number Γ of significant traits,  1820 ( 0 ) to  1820 (Γ−1), Γ&gt;0, corresponding to the specific commodity. The significant traits are labeled T* 0  to T* (Γ−1) . Corresponding communities  1830 ( 0 ) to  1830 ((Γ−1), labeled W* 0  to W* (Γ−1) , are determined from the superset of communities W 0  to W H−1  determined in module  430 . For example, with Γ=2, W* 0  may correspond to W 2  and W* 1  may correspond to W5. 
     After determining the primary communities, the primary communities may be indexed as 0 to (Γ−1) and the remaining communities of the superset of communities may be indexed as Γ to (H−1). 
     Determining Aggregate Kinship and Composite Kinship 
     Table-V below indicates pairwise kinship levels (also called pairwise kinship coefficients) of a specific candidate community of index k, Γ≤k&lt;H, to each primary community of a set of Γ primary communities for each kinship type. 
     
       
         
           
               
             
               
                 TABLE V 
               
             
            
               
                   
               
               
                 Pairwise type-specific kinship levels 
               
            
           
           
               
               
               
            
               
                   
                   
                 Relevance of each of primary communities  
               
               
                 Kinship 
                 Kinship 
                 to candidate community 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 ↓ 
                 weight ↓  
                 p 0   
                 p 1   
                 . . . 
                 p (Γ-2)   
                 p (Γ-1)   
               
               
                   
               
               
                 Type-1 
                 q 1   
                 g 1, 0, k   
                 g 1, 1, k   
                 . . . 
                 g 1, (Γ-2), k   
                 g 1, (Γ-1), k   
               
               
                 Type-2 
                 q 2   
                 g 2, 0, k   
                 g 2, 1, k   
                 . . . 
                 g 2, (Γ-2), k   
                 g 2, (Γ-1), k   
               
               
                 Type-3 
                 q 3   
                 g 3, 0, k   
                 g 3, 1, k   
                 . . . 
                 g 3, (Γ-2), k   
                 g 3, (Γ-1), k   
               
               
                   
               
            
           
         
       
     
     The relevance level, denoted p j , p j ≥0.0, of a primary community of index j, 0≤j&lt;Γ, to a commodity under consideration is conjectured or determined from prior-consumers&#39; data as illustrated in  FIG. 10 . The sum of the Γ relevance levels p 0  to p (Γ−1)  is normalized to unity. Thus: 
     
       
         
           
             
               
                 p 
                 0 
               
               + 
               
                 p 
                 1 
               
               + 
               
                 … 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   p 
                   
                     ( 
                     
                       Γ 
                       - 
                       2 
                     
                     ) 
                   
                 
               
               + 
               
                 p 
                 
                   ( 
                   
                     Γ 
                     - 
                     1 
                   
                   ) 
                 
               
             
             = 
             
               1 
               . 
               0 
               . 
             
           
         
       
     
     Different weights (positive real numbers), denoted q 1 , q 2 , and q 3  may be assigned to the kinship types. Preferably, the weights are normalized to a sum of unity. Thus, q 1 +q 2 +q 3=1.0.    
     An aggregate type-t kinship, denoted ξ (t)   k , the index t being 1, 2, or 3, of a candidate community of index k, Γ≤k&lt;H, to the set of Γ primary communities, indexed as 0 to (Γ−1), is determined as: 
     
       
         
           
             
               ξ 
               k 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 
                   p 
                   0 
                 
                 × 
                 
                   g 
                   
                     t 
                     , 
                     0 
                     , 
                     k 
                   
                 
               
               + 
               
                 
                   p 
                   1 
                 
                 × 
                 
                   g 
                   
                     t 
                     , 
                     1 
                     , 
                     k 
                   
                 
               
               + 
               … 
               + 
               
                 
                   p 
                   
                     ( 
                     
                       Γ 
                       - 
                       2 
                     
                     ) 
                   
                 
                 × 
                 
                   g 
                   
                     
                       t 
                       ⁡ 
                       
                         ( 
                         
                           Γ 
                           - 
                           2 
                         
                         ) 
                       
                     
                     , 
                     k 
                   
                 
               
               + 
               
                 
                   p 
                   
                     ( 
                     
                       Γ 
                       - 
                       1 
                     
                     ) 
                   
                 
                 × 
                 
                   
                     g 
                     
                       t 
                       , 
                       
                         ( 
                         
                           Γ 
                           - 
                           1 
                         
                         ) 
                       
                       , 
                       k 
                     
                   
                   . 
                 
               
             
           
         
       
     
     Determining the aggregate type-specific kinship ξ (t)   k  is of interest because, for some applications, it may be desired to rely on only one type of kinship. 
     A composite aggregate kinship, denoted E k , of a candidate community of index k, Γ≤k&lt;H, to the set of Γprimary communities is determined as: 
     
       
         
           
             
               
                 
                   
                     E 
                     k 
                   
                   = 
                   
                     
                       
                         q 
                         1 
                       
                       × 
                       
                         
                           ξ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         k 
                       
                     
                     + 
                     
                       
                         q 
                         2 
                       
                       × 
                       
                         
                           ξ 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         k 
                       
                     
                     + 
                     
                       
                         q 
                         3 
                       
                       × 
                       
                         
                           
                             ξ 
                             
                               ( 
                               2 
                               ) 
                             
                           
                           k 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     A composite pairwise kinship, denoted e j,k , of a candidate community of index k, Γ≤k&lt;H, to primary community of index j, 0≤j&lt;Γ, is determined as: 
     
       
         
           
             
               e 
               
                 j 
                 , 
                 k 
               
             
             = 
             
               
                 
                   q 
                   1 
                 
                 × 
                 
                   g 
                   
                     1 
                     , 
                     j 
                     , 
                     k 
                   
                 
               
               + 
               
                 
                   q 
                   2 
                 
                 × 
                 
                   g 
                   
                     2 
                     , 
                     j 
                     , 
                     k 
                   
                 
               
               + 
               
                 
                   q 
                   3 
                 
                 × 
                 
                   
                     g 
                     
                       3 
                       , 
                       j 
                       , 
                       k 
                     
                   
                   . 
                 
               
             
           
         
       
     
     Determining the composite pair-wise kinship, e j,k , is of interest because, for some applications, it may be desired to rely on kinship of a candidate community to a single primary community rather than the set of Γ primary communities. 
     A composite aggregate kinship, denoted E* k , of a candidate community of index k, 0≤k&lt;H, to the set of Γprimary communities is determined as: 
     
       
         
           
             
               
                 
                   E 
                   * 
                 
                 k 
               
               = 
               
                 
                   
                     p 
                     0 
                   
                   × 
                   
                     e 
                     
                       0 
                       , 
                       k 
                     
                   
                 
                 + 
                 
                   
                     p 
                     1 
                   
                   × 
                   
                     e 
                     
                       1 
                       , 
                       k 
                     
                   
                 
                 + 
                 … 
                 + 
                 
                   
                     p 
                     
                       ( 
                       
                         Γ 
                         - 
                         2 
                       
                       ) 
                     
                   
                   × 
                   
                     e 
                     
                       
                         ( 
                         
                           Γ 
                           - 
                           2 
                         
                         ) 
                       
                       , 
                       , 
                       k 
                     
                   
                 
                 + 
                 
                   
                     p 
                     
                       ( 
                       
                         Γ 
                         - 
                         1 
                       
                       ) 
                     
                   
                   × 
                   
                     
                       e 
                       
                         
                           ( 
                           
                             Γ 
                             - 
                             1 
                           
                           ) 
                         
                         , 
                         , 
                         k 
                       
                     
                     . 
                     
                       
 
                     
                     ⁢ 
                     Notably 
                   
                 
               
             
             , 
             
               
                 
                   E 
                   * 
                 
                 k 
               
               ≡ 
               
                 
                   E 
                   k 
                 
                 . 
               
             
           
         
       
     
     The composite aggregate kinship E k  is a robust measure of kinship of a candidate community to a set of primary communities. 
     Normalized Kinship Levels 
     The type-1 kinship coefficient g 1,j,k  (based on overlap of communities) of a candidate community (candidate trait) of index k to a primary community (primary trait) of index j varies between 0.0 and 1.0. Each of type-2 and type-3 kinship coefficients g 2,j,k  and g 3,j,k  (based on proximity and cross-correlation, respectively, of saturation vectors) varies between −1.0 and 1.0. 
     An aggregate kinship level or a composite kinship level is determined as a respective function of pairwise kinship levels. A pairwise kinship of a candidate community to a primary community is taken into account only if the corresponding kinship coefficient at least equals a predetermined positive threshold (of 0.20, for example). Thus, a pairwise kinship level determined to be below the threshold is set to 0.0. In the example of  FIG. 11 , all pairwise kinship levels considered in computing an aggregate kinship level are above a corresponding threshold. 
       FIG. 19  illustrates determining a pairwise composite kinship as a weighted sum of corresponding type-1, type-2, and type-3 kinship levels. 
     Tables  1910 ,  1920 , and  1930  hold pairwise type-1, type-2, and type-3 kinship values of each candidate community to each primary community. Table  1940  indicates a pairwise composite kinship for each pair of a candidate community and a primary community. Each entry in Table  1940  is determined as a weighted sum of corresponding entries in Tables  1910 ,  1920 , and  1930 . With H denoting the total number of communities of the superset of communities determined in module  430 , and Γ denoting the number primary communities determined in module  450 , the H communities of the superset of communities may be indexed so that the primary communities are indexed (reference  1950 ) as 0 to (Γ−1) and the remaining (H−Γ) communities are indexed (reference  1960 ) as Γ to (H−1). In the example of  FIGS. 19 , H=12 and Γ=4. A composite pairwise kinship level determined as: 
     
       
         
           
             
               
                 e 
                 
                   j 
                   , 
                   k 
                 
               
               = 
               
                 
                   
                     q 
                     1 
                   
                   × 
                   
                     g 
                     
                       1 
                       , 
                       j 
                       , 
                       k 
                     
                   
                 
                 + 
                 
                   
                     q 
                     2 
                   
                   × 
                   
                     g 
                     
                       2 
                       , 
                       j 
                       , 
                       k 
                     
                   
                 
                 + 
                 
                   
                     q 
                     3 
                   
                   × 
                   
                     g 
                     
                       3 
                       , 
                       j 
                       , 
                       k 
                     
                   
                 
               
             
             ; 
           
         
       
     
     where 0≤j&lt;Γ, Γ≤k&lt;H. The weighting factors q 1 , q 2 , and q 3  of the kinship coefficients g 2,j,k , and g 3,j,k ; are prescribed, with q 1 +q 2 +q 3 =1.0. 
     The type-1 kinship coefficient, g 1,j,k , is based on a number of users belonging to the candidate community, a number of users belonging to the specific primary community, and a number of common users belonging to both the candidate community and the specific primary community. The type-2 kinship coefficient, g 2,j,k , is based on proximity of the K-dimensional saturation vector of the candidate community to a K-dimensional saturation vector of the specific primary community. The type-3 kinship coefficient, g 3,j,k , is based on cross-correlation of the K-dimensional saturation vector of the candidate community to the K-dimensional saturation vector of the specific primary community. 
       FIG. 20  illustrates a first method  2000  of determining prospective clients for a specific commodity. Step  2010  selects a commodity from a list of commodities of interest. Process  2020  acquires a set of tracked clients of the specific commodity. Process  2030  determines a set of significant first-stratum traits of the tracked clients. Process  2050  determines a union of communities of the significant first-stratum traits. Process  2060  communicates with users of the union of communities of the significant first-stratum traits. 
       FIG. 21  illustrates trait-defined users  2100  of a significant trait determined from a set of specific tracked users. A set  2110  of tracked users is analyzed to determine a dominant trait from a set of predefined traits of interest. A community  2120  of users of the dominant trait is considered a first-stratum community. The set  2130  of users of community  2120  are considered to be compatible with the commodity under consideration. 
     Communities  2140 ,  2141 ,  2142 ,  2143 , and  2144  of varying levels of kinship to first-stratum community  2120  are determined using the method of  FIG. 28 . 
     Community  2140  of users is determined to have a considerable kinship to community  2120  while communities  2141 ,  2142 ,  2143 , and  2144  are determined to have insignificant kinship to first-stratum community  2120 . Thus, only the users within the union  2150  of communities  2120  and  2140  are considered to be compatible with the commodity under consideration. 
       FIG. 22  illustrates associating at least two communities of users with two user traits determined from a set of specific tracked users. Consider the case  2200  of two significant traits of clients of a specific commodity. A set  2210  of tracked users of a first trait and a set  2212  of tracked users of a second trait are determined from known transactions data. A community  2220  of users of the first trait and a community  2222  of users of the second trait are then determined from a database of the superset of communities determined in module  430 . The union  2230  of communities  2220  and  2222  constitutes a set of first-stratum users of the first and second traits. 
     Communities  2240  and  2241  of kinship to first-stratum community  2220  and communities  2242  and  2243  of kinship to first-stratum community  2222  are determined using the method of  FIG. 28 . 
     Community  2240  of users is determined to have a considerable kinship to community  2220  while community  2241  is determined to have insignificant kinship to first-stratum community  2220 . Community  2242  of users is determined to have a considerable kinship to community  2222  while community  2243  is determined to have slight kinship to first-stratum community  2222 . Thus, only the users within the union  2250  of communities  2220 ,  2222 ,  2240 , and  2242  are considered to be compatible with the commodity under consideration. 
       FIG. 23  illustrates an example  2300  of four communities of users associated with two user traits determined from a set of specific tracked users. A set  2310  of tracked users of a first trait and a set  2312  of tracked users of a second trait are determined from known transactions data. A community  2320  of users of the first trait and a community  2330  of users of the second trait are then determined from a database of the superset of communities determined in module  430  ( FIG. 4 ). A community  2340  of users of considerable kinship to community  2320  and a community  2350  of users of considerable kinship to community  2330  are determined ( FIG. 28 ). The users within the union  2360  of communities  2320 ,  2330 ,  2340 , and  2350  are considered to be compatible with the commodity under consideration. 
       FIG. 24  illustrates another example  2400  of four communities of users associated with two user traits determined from a set of specific tracked users. A community  2450  of users of considerable kinship to community  2330  is determined. The users within the union  2460  of communities  2320 ,  2330 ,  2340 , and  2450  are considered to be compatible with the commodity under consideration. 
       FIG. 25  illustrates an alternate indication  2500  of traits&#39; kinship based on saturation levels of communities of users within a set of clusters. Saturation levels of nine communities W 0  to W 8  within five clusters  2510  of users denoted C 0  to C 4 , are indicated. Segments  2520  of a community W j , 0≤j≤H, denoted {Ω j,0 , Ω j,1 , . . . Ω j,K−1 } belonging to clusters C 0  to C K−1 , respectively, define a saturation pattern of community W j  within the K clusters of the universe  1620  of tracked users. A saturation-score vector of community W j  within the K clusters is defined as {ν j,0 , ν j,1 , . . . ν j,K−1 }, where ν j,k  denotes the number of users within a segment Ω j,k , 0≤j&lt;H, 0≤k&lt;K. A normalized saturation-level vector is determined as {ρ j,0 , ρ j,1 , . . . , ρ j,K−1 } where ρ j,k =(ν j,k /N j ), N j  being the total number of users of community W j .  FIG. 25  illustrates segments  2520  of each of communities W 0 , W 1 , and W 8  within clusters C 0  to C 4 . 
       FIG. 26  illustrates a method  2600  of determining a second measure of kinship of traits T u  and T v  based on proximity of trait saturation levels within K clusters, K&gt;1. N* denotes the number of users belonging to community W u  of trait T u , M* denotes the number of users belonging to community W v  of trait T v , η j , denotes saturation score of trait T u  within cluster j, and m j  denotes saturation score of trait T v  within cluster j, 0≤j&lt;K. 
     A normalized saturation level α j  of trait T u  within cluster j is determined as α j =x j /X*, where x j  is a real number equal to integer η j  and X* is a real number equal to N*. Likewise, a normalized saturation level β j  of trait T v  within cluster j is determined as β j =y j /Y*, where y j  is a real number equal to integer m j  and Y* is a real number equal to M*. The absolute value  2610  of a difference of normalized saturation levels of traits Tu and Tv within a cluster j is determined as |α j −β j |. The second measure g 2,u,v  of kinship of traits T u  and T v  is determined as: 
     
       
         
           
             
               g 
               
                 2 
                 , 
                 u 
                 , 
                 v 
               
             
             = 
             
               
                 1.0 
                 - 
                 
                   Σ 
                   
                     0 
                     ≤ 
                     j 
                     &lt; 
                     K 
                   
                 
               
               | 
               
                 
                   α 
                   j 
                 
                 - 
                 
                   β 
                   j 
                 
               
               | 
               . 
             
           
         
       
     
       FIG. 27  illustrates a method  2700  of determining a third measure of kinship of traits T u  and T v  based on cross-correlation of trait saturation patterns  2710  and  2720  within K clusters, K&gt;1. 
     The third measure g 3,u,v  of kinship of traits T u  and T v  is determined as: 
     
       
         
           
             
               
                 g 
                 
                   3 
                   , 
                   u 
                   , 
                   v 
                 
               
               = 
               
                 
                   ( 
                   
                     
                       
                         Σ 
                         
                           0 
                           ≤ 
                           j 
                           &lt; 
                           K 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             n 
                             j 
                           
                           × 
                           
                             m 
                             j 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       K 
                       × 
                       
                         &lt; 
                         n 
                         &gt; 
                       
                       × 
                       
                         &lt; 
                       
                       ⁢ 
                       m 
                       ⁢ 
                       
                         &gt; 
                       
                     
                   
                   ) 
                 
                 / 
                 
                   ( 
                   
                     K 
                     × 
                     
                       σ 
                       0 
                     
                     × 
                     
                       σ 
                       m 
                     
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     which may be computed as: 
     
       
         
           
             
               g 
               
                 3 
                 , 
                 u 
                 , 
                 v 
               
             
             = 
             
               
                 ( 
                 
                   
                     K 
                     × 
                     
                       
                         Σ 
                         
                           0 
                           ≤ 
                           j 
                           &lt; 
                           K 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             n 
                             j 
                           
                           × 
                           
                             m 
                             j 
                           
                         
                         ) 
                       
                     
                   
                   - 
                   
                     
                       N 
                       * 
                     
                     × 
                     
                       M 
                       * 
                     
                   
                 
                 ) 
               
               / 
               
                 
                   ( 
                   
                     
                       ( 
                       
                         
                           K 
                           × 
                           
                             Σ 
                             
                               0 
                               ≤ 
                               j 
                               &lt; 
                               K 
                             
                           
                           ⁢ 
                           
                             
                               n 
                               j 
                             
                             2 
                           
                         
                         - 
                         
                           N 
                           
                             * 
                             2 
                           
                         
                       
                       ) 
                     
                     × 
                     
                       ( 
                       
                         
                           K 
                           × 
                           
                             Σ 
                             
                               0 
                               ≤ 
                               j 
                               &lt; 
                               K 
                             
                           
                           ⁢ 
                           
                             
                               m 
                               j 
                             
                             2 
                           
                         
                         - 
                         
                           M 
                           
                             * 
                             2 
                           
                         
                       
                       ) 
                     
                   
                   ) 
                 
                 
                   1 
                   / 
                   2 
                 
               
             
           
         
       
     
     The notations n j , m j , α j , and β j , 0≤j&lt;K, are defined above with respect to the second measure of kinship. The remaining notations are defined below. 
     &lt;n&gt;: mean value of saturation scores of trait T u ,
 
&lt;m&gt;: mean value of saturation scores of trait T v ,
 
σ n : standard deviation of the saturation score of trait T u ,
 
σ m : standard deviation of the saturation score of trait T v ,
 
σ α : standard deviation of the normalized saturation level of trait T u ,
 
σ β : standard deviation of the normalized saturation level of trait T v ,
 
     The measure of kinship, Λ u,v  may be selected to be any of the measures g 1,u,v , g 2,u,v , or g 3,u,v . The measure of kinship may also be a function of g 1,u,v , g 2,u,v , and g 3,u,v , such as a weighted sum of the three measures. 
       FIG. 28  illustrates a method  2800  for determining trait-pair kinship for use in determining second-stratum communities of consumers of a specific commodity. Selecting a community W j , 0≤j&lt;H, as a reference first-stratum community  2810 , each other community W k , 0≤k&lt;H, k≠j, may be considered as a candidate second-stratum community  2812 . 
     A process  2820  selects at least one of three kinship criteria. A first criterion, criterion- 1 , is based on common memberships of the reference community and a candidate community as described with reference to  FIG. 12  and  FIG. 13 . A second criterion, criterion- 2 , is based on proximity of trait-saturation patterns of the reference community and a candidate community within the K clusters as described with reference to  FIG. 26 . A third criterion, criterion- 3 , is based on cross-correlation of trait-saturation patterns of the reference community and a candidate community within the K clusters as described with reference to  FIG. 27 . 
     Process  2830  determines a count of the common membership of the reference community and the candidate community. Process  2832  evaluates a first kinship measure g 1,r,c  of the reference and candidate communities based on common memberships of the reference community and the candidate community. 
     Process  2840  determines saturation patterns (saturation vectors) of the reference community and candidate community within the K clusters. Process  2842  evaluates a second kinship measure g 2,r,c  of the reference and candidate communities based on proximity of the saturation patterns of the reference community and the candidate community. Process  2844  evaluates a third kinship measure g 3,r,c  of the reference and candidate communities based on cross-correlation of the saturation patterns of the reference community and the candidate community. Process  2850  decides whether to include the candidate community in a set of second-stratum communities of users relevant to the reference community. The decision to include the candidate community may be based on a kinship value determined in any of processes  2832 ,  2842 , or  2844 . The decision may also be based on a predefined function of g 1,r,c , g 2,r,c , and g 3,r,c . 
       FIG. 29  illustrates a method  2900  of determining a kinship measure of two traits. Process  2930  acquires a (pre-computed) community of users of a first trait  2920 , denoted T a , and determines a corresponding community W a . Process  2940  acquires a (pre-computed) community of users of a second trait  2921 , denoted T b , and determines a corresponding community W b . Process  2950  determines kinship of the first and second traits using the method of  FIG. 28 . Processes  2930 ,  2940 , and  2950  rely on input data  2910 , comprising user clusters  1600  and trait communities  1500 . 
       FIG. 30  illustrates a second method  3000  of determining prospective clients for the specific commodity. Step  2010 , process  2020 , and process  2030  perform the same functions described above with reference to  FIG. 20 . Process  3040  determines a set of significant second-stratum traits relevant to the set of first-stratum traits ( FIG. 28 ). Process  3050  determines a union of communities of the significant traits. Process  3060  communicates with users of the union of communities of the significant traits. 
       FIG. 31  illustrates a table  3100  of inter-trait kinships for a set of 9 traits (H=9). For each pair of traits {T j , T k }, 0≤j&lt;H, j&lt;k&lt;H, H=9, a respective kinship value  3130  is determined according to the method of  FIG. 28 . The kinship value for a trait pair {T j , T k } equals the kinship value of trait pair {T k , T j }, thus, it suffices to determine the kinship values for k&gt;j. 
       FIG. 32  illustrates a pre-processing stage  3200  for determining clusters of users based on characteristics of users and communities of users corresponding to traits of users. A preprocessing module  3270  acquires values of individual user characteristics (predefined user characteristics  415 ) of a population of users from database  414  of tracked users. The module also extracts values of individual user traits of interest (predefined superset of traits  413 ) from database  414 . 
     Module  3270  may comprise module  430  and module  440  ( FIG. 4 ). Module  430  identifies communities  1500  of users corresponding to the predefined user traits  413 . Module  440  sorts the population of users into a number of clusters  1600  of users according to the predefined user characteristics. A user may possess multiple distinctive traits while a community is associated with only one trait. Thus, a community may overlap other communities. 
       FIG. 33  illustrates trait kinship patterns  3300  of exemplary traits T 0 , T 1 , and T 2 , indicating normalized (0.0 to 1.0) trait-saturation values  3330  of each trait within each of five clusters denoted cluster- 0  to cluster- 4 . Trait-pair kinship values are determined according to the second measure of  FIG. 26  and the third measure of  FIG. 27 . For a trait pair {T j , T k }, 0≤j≤2, 0≤k≤2, k&gt;j, the kinship value determined according the second measure (trait-patterns proximity) is denoted g 2,j,k  while the kinship value determined according to the third measure (trait-patterns cross correlation) is denoted g 3,j,k . 
     Table-VI indicates normalized trait-saturation levels for each of traits T 0 , T 1 , and T 2  within clusters of indices 0 to 4. Table-VI indicates proximity of the saturation levels of each of traits T 0  and T 2  to corresponding saturation levels of trait T 1 . Table-V-II indicates kinship values of pairs of traits T 0 , T 1 , and T 2  based on the second measure and third measure. 
     As indicated in Table-VII, the sum of absolute values of saturation-level deviation of T 0  from T 1  equals the sum of absolute values of saturation-level deviation of T 2  from T 1 . The kinship measure according to the second measure ( FIG. 26 ) is determined as 1.0 minus the sum of absolute values of saturation-level deviation. 
     
       
         
           
               
             
               
                 TABLE VI 
               
             
            
               
                   
               
               
                 Normalized trait-saturation levels 
               
            
           
           
               
               
               
            
               
                   
                 Trait  
                 Cluster index 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 identifier 
                 0 
                 1 
                 2 
                 3 
                 4 
               
               
                   
                   
               
               
                   
                 T 0   
                 0.12 
                 0.24 
                 0.28 
                 0.16 
                 0.20 
               
               
                   
                 T 1   
                 0.32 
                 0.20 
                 0.16 
                 0.32 
                 0.00 
               
               
                   
                 T 2   
                 0.48 
                 0.32 
                 0.00 
                 0.12 
                 0.08 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE VII 
               
             
            
               
                   
               
               
                 Deviation from T1 saturation levels 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Sum of  
               
               
                   
                   
                   
                   
                   
                   
                 absolute values 
               
            
           
           
               
               
               
            
               
                 Trait 
                 Cluster index 
                 of saturation- 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 identifier ↓ 
                 0 
                 1 
                 2 
                 3 
                 4 
                 level differences 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 T 0   
                 −0.20 
                 0.04 
                 0.12 
                 −0.16 
                 0.20 
                 0.72 
               
               
                 T 2   
                 0.16 
                 0.12 
                 −0.16 
                 −0.20 
                 0.08 
                 0.72 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE VIII 
               
             
            
               
                   
               
               
                 Trait-pair kinship 
               
            
           
           
               
               
               
            
               
                   
                 Proximity-based  
                 Cross-correlation-based  
               
               
                 Trait pair 
                 kinship 
                 kinship 
               
               
                   
               
            
           
           
               
               
               
            
               
                 {T 0 , T 1 } 
                 0.28 
                 −0.5244 
               
               
                 {T 0 , T 2 } 
                 0.12 
                 −0.6132 
               
               
                 {T 1 , T 2 } 
                 0.28 
                 0.5385 
               
               
                   
               
            
           
         
       
     
       FIG. 34  illustrates exemplary trait-saturation scores  3400  of four traits denoted traits T 0 , T 1 , T 2 , and T 3  within five clusters of indices 0 to 4. The patterns of trait-saturation scores for the individual traits are identified as  3430 ( 0 ) to  3430 ( 3 ). 
       FIG. 35  illustrates normalized trait-saturation levels  3500  corresponding to the trait-saturation scores of  FIG. 34 . The patterns of normalized trait-saturation levels for the individual traits are identified as  3430 ( 0 ) to  3430 ( 3 ). 
       FIG. 36  illustrates a table  3600  of trait-saturation scores  3630  and a table  3620  of normalized trait-saturation levels  3640  corresponding to  FIG. 34  and  FIG. 35 , respectively 
       FIG. 37  illustrates a set  2710  of pairwise trait-kinship values  2712  determined according to the second measure of  FIG. 26  and a set  3720  of pairwise trait-kinship values  3722  determined according to the third measure of  FIG. 27 . 
       FIG. 38  compares kinship levels  3810  based on proximity of trait-saturation patterns and kinship levels  2820  based on cross correlation of trait-saturation patterns as indicated in  FIG. 37 . 
       FIG. 39  illustrates pattern  3430 ( 0 ) of the trait-saturation scores of a trait T 0  and pattern  3430 ( 1 ) of trait-saturation scores of a trait T 1  of  FIG. 34 . As indicated in  FIG. 37 , the proximity-based kinship measure g 2,0,1  is determined as 0.2 while the kinship measure g 3,0,1  based on cross-correlation of patterns  3430 ( 0 ) and  3430 ( 1 ) is determined as −0.97. The kinship measure g 3,0,1  reveals the strong negative correlation of the two patterns. 
       FIG. 40  illustrates pattern  3430 ( 0 ) of the trait-saturation scores of a trait T 0  and pattern  3430 ( 2 ) of trait-saturation scores of a trait T 2  of  FIG. 34 . As indicated in  FIG. 37 , the proximity-based kinship measure g 2,0,2  is determined as 0.32 while the kinship measure g 3,0,2  based on cross-correlation of patterns  3430 ( 0 ) and  3430 ( 2 ) is determined as 0.036. The insignificant kinship measure g 3,0,2  of 0.036 is indicative of a weak correlation of the two patterns. 
       FIG. 41  illustrates pattern  3430 ( 0 ) of the trait-saturation scores of a trait T 0  and pattern  3430 ( 3 ) of trait-saturation scores of a trait T 3  of  FIG. 34 . As indicated in  FIG. 37 , the proximity-based kinship measure g 2,0,3  is determined as 0.0 while the kinship measure g 2,0,3  based on cross-correlation of patterns  3430 ( 0 ) and  3430 ( 3 ) is determined as −0.808. The kinship value g 2,0,3  of −0.808 is indicative of a strong negative correlation of the two patterns. 
       FIG. 42  illustrates pattern  3430 ( 1 ) of the trait-saturation scores of a trait T 1  and pattern  3430 ( 3 ) of trait-saturation scores of a trait T 3  of  FIG. 24 . As indicated in  FIG. 37 , the proximity-based kinship value g 2,1,3  is determined as 0.733 while the kinship value g 3,1,3  based on cross-correlation of patterns  3430 ( 1 ) and  3430 ( 3 ) is determined as 0.853. The kinship value g 2,1,3  of 0.733 is indicative of close proximity of the two patterns. The kinship value g 3,1,3  of 0.853 is indicative of a strong positive correlation of the two patterns. 
     As illustrated in  FIG. 26  and  FIG. 27 , the second and third kinship measures of two communities are based on saturation scores (or saturation levels) of communities within a number K of clusters, K&gt;1. The saturation score of a community within a cluster is determined as a count of the number of users of the community within the cluster. 
     Alternatively, the users of a cluster may be given different weights according to proximity to a centroid of the cluster. The saturation score of a community within a cluster may then be determined as a sum of weights of common users of the community and the cluster. 
     As described above, the process of selecting a candidate community as a second-stratum community may be based on: 
     a first kinship measure determined according to common membership with the first-stratum communities; 
     a second kinship measure based on proximity of a saturation-level vector of a candidate community to saturation-level vectors of first-stratum communities; and/or 
     a third kinship measure based on cross-correlation of the saturation-level vector of the candidate community to saturation-level vectors of the first-stratum communities. 
     The candidate community qualifies as a second-stratum community based on one of the three kinship measures or based on a function of the three kinship measures. A set of prospective clients is determined as a union of the first stratum communities and resulting second-stratum communities. 
     Alternatively: 
     a first set of second-stratum communities may be determined based on the first kinship measure only; 
     a second set of second-stratum communities may be determined based on the second kinship measure only; 
     a third set of second-stratum communities may be determined based on the third kinship measure only; and 
     a set of prospective clients may be determined as a union of the first-stratum communities and the three sets of second-stratum communities. 
     The three sets of second-stratum communities may include common users, or may even be identical. 
     The three sets of secondary communities may intersect, i.e., include common users, or may even be identical. Users belonging to two or more primary or secondary communities may be considered distinct prospective clients. 
     The methods of the present invention have numerous advantages over the prior art. At least some of the advantages include:
         (1) comprehensive thorough analysis of massive data to appropriately determine prospective clients for a product or a service;   (2) novel approaches that consider factors that enable intelligent marketing, such as traits of potential consumers for specific commodities and pairwise trait kinship;   (3) multi-stratum classification of prospective clients which is of paramount importance to strategic marketing;   (4) computationally efficient algorithms for handling massive data, which operate faster than the prior art algorithms;   (5) ease of expansion to add new features as exemplified in  FIGS. 4 to 9 ; and   (6) ease of implementation in a flexible modular hardware structure.       

     Methods of the embodiments of the invention may be performed using at least one hardware processor, executing processor-executable instructions causing the at least one hardware processor to implement the processes described above. Computer executable instructions may be stored in processor-readable storage media such as floppy disks, hard disks, optical disks, Flash ROMs (read only memories), non-volatile ROM, and RAM (random access memory). A variety of processors, such as microprocessors, digital signal processors, and gate arrays, may be employed. 
     Systems of the embodiments of the invention may be implemented as any of a variety of suitable circuitry, such as one or more microprocessors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), discrete logic, software, hardware, firmware or any combinations thereof. When modules of the systems of the embodiments of the invention are implemented partially or entirely in software, the modules contain a memory device for storing software instructions in a suitable, non-transitory computer-readable storage medium, and software instructions are executed in hardware using one or more processors to perform the methods of this disclosure. 
     It should be noted that methods and systems of the embodiments of the invention and data described above are not, in any sense, abstract or intangible. Instead, the data is necessarily presented in a digital form and stored in a physical data-storage computer-readable medium, such as an electronic memory, mass-storage device, or other physical, tangible, data-storage device and medium. It should also be noted that the currently described data-processing and data-storage methods cannot be carried out manually by a human analyst due the complexity and vast numbers of intermediate results generated for processing and analysis of even quite modest amounts of data. Instead, the methods described herein are necessarily carried out by electronic computing systems having processors on electronically or magnetically stored data, with the results of the data processing and data analysis digitally stored in one or more tangible, physical, data-storage devices and media. 
     Although specific embodiments of the invention have been described in detail, it should be understood that the described embodiments are intended to be illustrative and not restrictive. Various changes and modifications of the embodiments shown in the drawings and described in the specification may be made within the scope of the following claims without departing from the scope of the invention in its broader aspect.