Patent Publication Number: US-2021182329-A1

Title: Selecting balanced clusters of descriptive vectors

Description:
TECHNICAL FIELD 
     The subject matter disclosed herein generally relates to the technical field of special-purpose machines that perform or otherwise facilitate clustering of data items, including computerized variants of such special-purpose machines and improvements to such variants, and to the technologies by which such special-purpose machines become improved compared to other special-purpose machines that perform or otherwise facilitate clustering of data items. Specifically, the present disclosure addresses systems and methods that select balanced clusters of descriptive vectors. 
     BACKGROUND 
     In data processing, a machine may be configured to analyze data items and group them into clusters, which may be referred to as clustering the data items. Typically, data items are clustered according to various commonalities in their attributes. These attributes may be specified by the data items themselves, specified in corresponding metadata, or any suitable combination thereof. In some situations, a data item (e.g., a media item, such as a video file or an audio file, or an identifier of a media item) can be described by one or more attribute-value pairs, and a group of such attribute-value pairs can be represented (e.g., in a computer memory) as a multidimensional vector. As an example, for a data item describable by 100 attribute-value pairs, a 100-dimensional descriptive vector of the data item can be generated such that each of the 100 dimensions represents a different attribute and has a corresponding scalar value. Data items represented by such descriptive vectors thus can be clustered by clustering their descriptive vectors. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Some embodiments are illustrated by way of example and not limitation in the figures of the accompanying drawings. 
         FIG. 1  is a network diagram illustrating a network environment suitable for selecting balanced clusters of descriptive vectors, according to some example embodiments. 
         FIG. 2  is a block diagram illustrating components of a clustering machine suitable for selecting balanced clusters of descriptive vectors, according to some example embodiments. 
         FIG. 3  is a conceptual diagram illustrating a multi-tiered hierarchy of vector clusters, according to some example embodiments. 
         FIG. 4  is a conceptual diagram illustrating intra-cluster vector distances in a vector cluster in one of the tiers of the multi-tiered hierarchy, according to some example embodiments. 
         FIG. 5  is a conceptual diagram illustrating inter-cluster vector distances in one of the tiers of the multi-tiered hierarchy of vector clusters, according to some example embodiments. 
         FIG. 6  is a conceptual diagram illustrating a selected subset of the vector clusters in the hierarchy being defined by selecting a tier among multiple tiers of the hierarchy, according to some example embodiments. 
         FIGS. 7-10  are flowcharts illustrating operations of the clustering machine in performing a method of selecting balanced clusters of descriptive vectors, according to some example embodiments. 
         FIG. 11  is a block diagram illustrating components of a machine, according to some example embodiments, able to read instructions from a machine-readable medium and perform any one or more of the methodologies discussed herein. 
     
    
    
     DETAILED DESCRIPTION 
     Example methods (e.g., algorithms) facilitate selecting certain (e.g., balanced) clusters of vectors, and example systems (e.g., special-purpose machines) are configured to facilitate selecting such clusters of vectors. Examples merely typify possible variations. Unless explicitly stated otherwise, structures (e.g., structural components, such as modules) are optional and may be combined or subdivided, and operations (e.g., in a procedure, algorithm, or other function) may vary in sequence or be combined or subdivided. In the following description, for purposes of explanation, numerous specific details are set forth to provide a thorough understanding of various example embodiments. It will be evident to one skilled in the art, however, that the present subject matter may be practiced without these specific details. 
     A clustering machine is configured (e.g., by software modules) to access vectors (e.g., descriptive vectors that describe items, such as data items, physical items, or any suitable combination thereof) and automatically cluster them in a balanced manner, which may be referred to as automatic selecting of balanced clusters of vectors. After accessing the vectors (e.g., from a database), the clustering machine calculates distances (e.g., vector distances) between pairs (e.g., all pairs) of the accessed vectors and generates a hierarchy of clusters (e.g., vector clusters) based on the calculated distances. The hierarchy may have multiple tiers and may be referred to as a tiered hierarchy, a multi-tier hierarchy, or a multi-tiered hierarchy. The clustering machine also determines centroid vectors of the clusters (e.g., determines a separate centroid vector for each cluster), such that each cluster is represented by its corresponding centroid vector. 
     The clustering machine also calculates two sums, specifically, a sum (e.g., first sum) of inter-cluster vector distances between pairs of the centroid vectors for clusters (e.g., all clusters) in the hierarchy, and a sum (e.g., second sum) of intra-cluster vector distances between pairs of vectors in each of the clusters (e.g., all clusters) in the hierarchy. Having calculated these two sums, the clustering machine calculates multiple scores for the hierarchy by varying a scalar (e.g., selecting various values for the scalar) and calculating a separate score of the hierarchy for each separate scalar (e.g., each selected value of the scalar). For each selected scalar, this calculation is based on the two sums (e.g., first and second sums) previously calculated for the hierarchy. These calculated scores may be treated as representing granularity levels in the hierarchy (e.g., in the tiers of the hierarchy), and it may be helpful to select or otherwise identify a subset of the hierarchy (e.g., a particular tier) whose clusters are balanced between being excessively large and few (e.g., a couple of giant clusters) and being excessively small and numerous (e.g., too many tiny clusters). 
     Based on these calculated scores, the clustering machine selects a subset of the hierarchy (e.g., selects a tier from among the multiple tiers of the hierarchy). The calculated scores of the hierarchy each correspond to a different selected scalar, and the selecting of the subset may be based on a selected scalar (e.g., scalar value) that resulted in an extreme value (e.g., a minimum score or maximum score) for the calculated score the hierarchy. In some example embodiments, this may have the effect of determining that one of the tiers represents optimal balancing, and the clustering machine may accordingly choose that tier as a selected subset of the clusters in the hierarchy of clusters. With or without tier selection, the clustering machine automatically selects a subset of the clusters, based on the selected scalar value that resulted in extreme score, such that the clusters in the selected subset are balanced in their level of granularity. This may have the effect of automatically identifying a group of clusters that are balanced between being excessively large and few and being excessively small and numerous (e.g., for providing meaningful, pragmatic, helpful, or otherwise useful groupings of the accessed vectors (e.g., descriptive vectors of items, such as data items). 
     The clustering machine may also be configured to interact with one or more users by suggesting, recommending, or otherwise presenting the selected subset of the clusters, for example, in response to a user input that indicates a command or request to automatically group the vectors or the items described by the vectors. In some example embodiments, the clustering machine is configured to automatically generate labels for the selected subset of the clusters and present the automatically generated labels to a user (e.g., via a device of the user). In certain example embodiments, the clustering machine is also configured as a disambiguation machine that can use the selected subset of clusters to identify a source of the items described by the vectors (e.g., as an identifier of a recording artist that released songs described by the clustered vectors). 
       FIG. 1  is a network diagram illustrating a network environment  100  suitable for selecting balanced clusters of descriptive vectors, according to some example embodiments. The network environment  100  includes a clustering machine  110 , a database  115 , and devices  130  and  150 , all communicatively coupled to each other via a network  190 . The clustering machine  110 , with or without the database  115 , may form all or part of a cloud  118  (e.g., a geographically distributed set of multiple machines configured to function as a single server), which may form all or part of a network-based system  105  (e.g., a cloud-based server system configured to provide one or more network-based services to the devices  130  and  150 ). The clustering machine  110  and the devices  130  and  150  may each be implemented in a special-purpose (e.g., specialized) computer system, in whole or in part, as described below with respect to  FIG. 11 . 
     The database  115  may store descriptive vectors that describe items (e.g., data items or identifiers thereof). For example, the database  115  may store metadata (e.g., item profiles) that describe the items, and the metadata may include a descriptive vector for each item. Accordingly, each item represented in the database  115  may be represented by a separate descriptive vector (e.g., within a separate item profile for that item). According to various example embodiments, however, the descriptive vectors may be stored in the clustering machine  110  or in any of the devices  130  and  150 . The network  190  enables the descriptive vectors to be accessed from one or more of the clustering machine  110 , the database  115 , and the devices  130  and  150 . 
     Also shown in  FIG. 1  are users  132  and  152 . One or both of the users  132  and  152  may be a human user (e.g., a human being), a machine user (e.g., a computer configured by a software program to interact with the device  130  or  150 ), or any suitable combination thereof (e.g., a human assisted by a machine or a machine supervised by a human). The user  132  is associated with the device  130  and may be a user of the device  130 . For example, the device  130  may be a desktop computer, a vehicle computer, a tablet computer, a navigational device, a portable media device, a smart phone, or a wearable device (e.g., a smart watch, smart glasses, smart clothing, or smart jewelry) belonging to the user  132 . Likewise, the user  152  is associated with the device  150  and may be a user of the device  150 . As an example, the device  150  may be a desktop computer, a vehicle computer, a tablet computer, a navigational device, a portable media device, a smart phone, or a wearable device (e.g., a smart watch, smart glasses, smart clothing, or smart jewelry) belonging to the user  152 . 
     Any of the systems or machines (e.g., databases and devices) shown in  FIG. 1  may be, include, or otherwise be implemented in a special-purpose (e.g., specialized or otherwise non-generic) computer that has been modified (e.g., configured or programmed by software, such as one or more software modules of an application, operating system, firmware, middleware, or other program) to perform one or more of the functions described herein for that system or machine. For example, a special-purpose computer system able to implement any one or more of the methodologies described herein is discussed below with respect to  FIG. 11 , and such a special-purpose computer may accordingly be a means for performing any one or more of the methodologies discussed herein. Within the technical field of such special-purpose computers, a special-purpose computer that has been modified by the structures discussed herein to perform the functions discussed herein is technically improved compared to other special-purpose computers that lack the structures discussed herein or are otherwise unable to perform the functions discussed herein. Accordingly, a special-purpose machine configured according to the systems and methods discussed herein provides an improvement to the technology of similar special-purpose machines. 
     As used herein, a “database” is a data storage resource and may store data structured as a text file, a table, a spreadsheet, a relational database (e.g., an object-relational database), a triple store, a hierarchical data store, or any suitable combination thereof. Moreover, any two or more of the systems or machines illustrated in  FIG. 1  may be combined into a single machine, and the functions described herein for any single system or machine may be subdivided among multiple systems or machines. 
     The network  190  may be any network that enables communication between or among systems, machines, databases, and devices (e.g., between the machine  110  and the device  130 ). Accordingly, the network  190  may be a wired network, a wireless network (e.g., a mobile or cellular network), or any suitable combination thereof. The network  190  may include one or more portions that constitute a private network, a public network (e.g., the Internet), or any suitable combination thereof. Accordingly, the network  190  may include one or more portions that incorporate a local area network (LAN), a wide area network (WAN), the Internet, a mobile telephone network (e.g., a cellular network), a wired telephone network (e.g., a plain old telephone system (POTS) network), a wireless data network (e.g., a WiFi network or WiMax network), or any suitable combination thereof. Any one or more portions of the network  190  may communicate information via a transmission medium. As used herein, “transmission medium” refers to any intangible (e.g., transitory) medium that is capable of communicating (e.g., transmitting) instructions for execution by a machine (e.g., by one or more processors of such a machine), and includes digital or analog communication signals or other intangible media to facilitate communication of such software. 
       FIG. 2  is a block diagram illustrating components of the clustering machine  110 , according to some example embodiments. The clustering machine  110  is shown as including a vector distance calculator  210 , a cluster hierarchy generator  220 , a score calculator  230 , a subset selector  240 , a descriptive vector generator  250 , and a cluster subset handler  260 , all configured to communicate with each other (e.g., via a bus, shared memory, or a switch). 
     The vector distance calculator  210  may be or include a distance module or other computer code programmed to calculate vector distances between or among descriptive vectors. The cluster hierarchy generator  220  may be or include a generation module or other computer code programmed to cluster descriptive vectors based on vector distances calculated by the vector distance calculator  210  and generate a tiered hierarchy of vector clusters. The score calculator  230  (e.g., hierarchy score calculator) may be or include a score module or other computer code programmed to calculate scores of the hierarchy (e.g., based on various selected values of a scalar, as will be discussed below). 
     The subset selector  240  (e.g., a tier selector, a hierarchy truncator, or any suitable combination thereof) may be or include a selection module or other computer code programmed to select a subset of the hierarchy (e.g., a subset defined by a tier of the hierarchy) based on the scores calculated by the score calculator  230 . The descriptive vector generator  250  may be or include a description module or other computer code programmed to generate a descriptive vector (e.g., generate descriptive vectors of media items for subsequent access by the vector distance calculator  210 ). The cluster subset handler  260  may be or include a subset module or other computer code programmed to provide one or more interactive services based on the selected subset (e.g., selected tier) of the hierarchy (e.g., as selected by the subset selector  240 ). 
     As shown in  FIG. 2 , the vector distance calculator  210 , the cluster hierarchy generator  220 , the score calculator  230 , the subset selector  240 , the descriptive vector generator  250 , and the cluster subset handler  260  may form all or part of an application  200  (e.g., a software application, a web applet, or a mobile app) that is stored (e.g., installed) on the clustering machine  110 . Furthermore, one or more processors  299  (e.g., hardware processors, digital processors, or any suitable combination thereof) may be included (e.g., temporarily or permanently) in the application  200 , the vector distance calculator  210 , the cluster hierarchy generator  220 , the score calculator  230 , the subset selector  240 , the descriptive vector generator  250 , the cluster subset handler  260 , or any suitable combination thereof. In some example embodiments, the application  200  is stored and executed on one of the devices  130  or  150 . In certain example embodiments, the application  200  (e.g., modules thereof) is distributed across one or more of the clustering machine  110  and the devices  130  and  150 . 
     Any one or more of the components (e.g., modules) described herein may be implemented using hardware alone (e.g., one or more of the processors  299 ) or a combination of hardware and software. For example, any component described herein may physically include an arrangement of one or more of the processors  299  (e.g., a subset of or among the processors  299 ) configured to perform the operations described herein for that component. As another example, any component described herein may include software, hardware, or both, that configure an arrangement of one or more of the processors  299  to perform the operations described herein for that component. Accordingly, different components described herein may include and configure different arrangements of the processors  299  at different points in time or a single arrangement of the processors  299  at different points in time. Each component (e.g., module) described herein is an example of a means for performing the operations described herein for that component. Moreover, any two or more components described herein may be combined into a single component, and the functions described herein for a single component may be subdivided among multiple components. Furthermore, according to various example embodiments, components described herein as being implemented within a single system or machine (e.g., a single device) may be distributed across multiple systems or machines (e.g., multiple devices). 
       FIG. 3  is a conceptual diagram illustrating a hierarchy  300  (e.g., a multi-tiered nested hierarchy) of vector clusters  301 ,  311 ,  312 ,  321 ,  322 ,  323 ,  324 ,  325 ,  331 ,  332 ,  333 ,  334 ,  335 ,  341 ,  342 ,  343 ,  344 ,  345 , and  346 , according to some example embodiments. The hierarchy  300  may be generated by the cluster hierarchy generator  220 , for example, based on vector distances calculated by the vector distance calculator  210 . For illustrative purposes,  FIG. 3  shows the hierarchy  300  organized into multiple tiers, labeled Tier  1 , Tier  2 , Tier  3 , Tier  4 , and Tier  5 , which may or may not be present, depending on various example embodiments.. 
     As illustrated in  FIG. 3 , the hierarchy  300  has multiple tiers and is arranged so that each of the multiple tiers (e.g., Tier  3 ) is a subset of all vector clusters  301 - 346  represented in the hierarchy  300 . For example, in Tier  1  of the hierarchy  300 , the sole vector cluster  301  (e.g., the root node or root cluster) contains all descriptive vectors accessed by the vector distance calculator  210  and represented in the hierarchy  300 . As another example, in Tier  2  of the hierarchy  300 , the two vector clusters  311  and  312  subdivide (e.g., apportion) the descriptive vectors (e.g., contained in the vector cluster  301 ) into two groups. As a third example, in Tier  3  of the hierarchy  300 , the vector clusters  321  and  322  subdivide their parent vector cluster  311 , while the vector clusters  323 ,  324 , and  325  subdivide their parent vector cluster  312 . As a fourth example, in Tier  4  of the hierarchy  300 , the vector clusters  331 ,  332 , and  333  subdivide their parent vector cluster  322 , and the vector clusters  334  and  335  subdivide their parent cluster  325 . As a further example, in Tier  5  of the hierarchy  300 , the vector clusters  341  and  342  subdivide their parent vector cluster  331 ; the vector clusters  343  and  344  subdivide their parent vector cluster  332 ; and the vector clusters  345  and  346  subdivide their parent vector cluster  334 . As shown in  FIG. 3  by ellipses, additional tiers may be included in the hierarchy  300 , and any tier except Tier  1  (e.g., each of Tiers  2 - 5 ) can include additional vector clusters in hierarchy  300 . 
       FIG. 4  is a conceptual diagram illustrating intra-cluster vector distances in the vector cluster  321  (e.g., in Tier  3 ) of the hierarchy  300 , according to some example embodiments. Although only the vector cluster  321  is illustrated, other vector clusters (e.g., vector clusters  301 - 312  and  322 - 346 ) are similarly structured and can have similar vector distances between their constituent descriptive vectors. 
     As shown in  FIG. 4 , the vector cluster  321  groups multiple descriptive vectors (e.g., a plurality of descriptive vectors), each of these descriptive vectors is depicted as a small circle in  FIG. 4 . As used herein, an “intra-cluster vector distance” is a vector distance between two descriptive vectors that are both included (e.g., grouped or clustered) in the same vector cluster (e.g., vector cluster  321 ). For example, an intra-cluster vector distance can be calculated by taking a vector difference between a pair of descriptive vectors within the same vector cluster. As another example, an intra-cluster vector distance can be calculated by taking a square root of a sum of squared differences in each dimension represented by a pair of descriptive vectors from the same vector cluster. Other algorithms for calculating vector distances may be used to calculate an intra-cluster vector distance, according to various example embodiments. 
     In addition, any vector cluster (e.g., vector cluster  321 ) can be represented by a centroid vector, which can be calculated as or based on a mean vector that averages (e.g., with or without weighting) the descriptive vectors included in that vector cluster. As one example, a centroid vector of the vector cluster  321  may be calculated by calculating a mean vector of all descriptive vectors that are within the vector cluster  321 . As another example, the centroid vector of the vector cluster  321  may be calculated by weighting the descriptive vectors within the vector cluster  321  according to one or more of their constituent dimensions (e.g., values that signify presence or absence of a popular mood, such as “upbeat” or “danceable,” for descriptive vectors of media files) and then calculating a weighted mean vector of the descriptive vectors of the vector cluster  321 . 
       FIG. 5  is a conceptual diagram illustrating inter-cluster vector distances among the vector clusters  321 - 325  (e.g., in Tier  3 ) of the hierarchy  300 , according to some example embodiments. As noted above, each vector cluster (e.g., vector cluster  321 ) within the hierarchy  300  can be represented by a separate centroid vector. Accordingly, such centroid vectors can be used to calculate vector distances in between two vector clusters (e.g., between the vector clusters  321  and  322 ). An “inter-cluster vector distance,” as used herein, is a vector distance between two centroid vectors of different vector clusters in the same hierarchy (e.g., hierarchy  300 ) of vector clusters. As one example, the inter-cluster vector distance between two vector clusters can be calculated by taking a vector difference between their centroid vectors. As another example, the inter-cluster vector distance between a pair of vector clusters can be calculated by taking a square root of the sum of squared differences in each dimension represented by their centroid vectors. Other algorithms for calculating vector distances may be used to calculate an inter-cluster vector distance, according to various example embodiments. 
     As shown in  FIG. 5 , inter-cluster vector distances can be calculated between at least the following pairs of vector clusters (e.g., in Tier  3 ) of the hierarchy  300 : the vector clusters  321  and  322 , the vector clusters  321  and  323 , the vector clusters  321  and  324 , the vector clusters  321  and  325 , the vector clusters  322  and  323 , the vector clusters  322  and  324 , the vector clusters  322  and  325 , the vector clusters  323  and  324 , the vector clusters  323  and  325 , and the vector clusters  324  and  325 . Similar inter-cluster vector distances can be calculated throughout the hierarchy  300  (e.g., among all vector clusters, including the vector clusters  301 - 346 ). 
     For the purpose of selecting balanced clusters of descriptive vectors, it can be desirable to have the intra-cluster vector distances be relatively small or minimized and the inter-cluster vector distances be relatively large or maximized. This approach can result in identification of a clustering scheme (e.g., the specific clusters contained within a subset of vector clusters, which may be defined by a single tier, such as Tier  3 , within the hierarchy  300 ) that provides an optimal or otherwise desirable granularity level (e.g., between the root node and the leaf nodes of the hierarchy  300 ). Accordingly, the identified clustering scheme can be suggested, recommended, or otherwise used to group, categorize, classify, or otherwise subdivide the descriptive vectors in a manner that results in vector clusters (e.g., vector clusters  321 - 325 ) that are balanced and neither excessively large and few nor excessively small and numerous. 
       FIG. 6  is a conceptual diagram illustrating a selected subset  600  of the vector clusters (e.g., vector clusters  301 - 346 ) in the hierarchy  300 , according to some example embodiments. As shown in  FIG. 6 , Tier  3  of the hierarchy  300  may define the selected subset  600  of all vector clusters in the hierarchy  300 . In other words, the subset  600  may be defined by selection of a tier (e.g., Tier  3 ) among the multiple tiers of the hierarchy  300 , and such a selection may be based on analysis of the intra-cluster vector distances in the hierarchy  300  (e.g., as discussed above with respect to  FIG. 4 ) and the inter-cluster vector distances in the hierarchy  300  (e.g., as discussed above with respect to  FIG. 5 ). 
     Accordingly, the vector clusters (e.g., vector clusters  321 - 325 ) of the selected subset  600  of the hierarchy  300  can be suggested, recommended, or otherwise used to group the descriptive vectors represented in the hierarchy  300 . For example, the vector clusters (e.g., vector clusters  321 - 325 ) of the selected subset  600  of the hierarchy  300  can be presented in a user interface (e.g., a graphical user interface (GUI)) as a balanced or otherwise optimal clustering scheme (e.g., categorization scheme) for organizing, or otherwise managing the items (e.g., data items, such as media files) described by the descriptive vectors. 
     In some example embodiments, the selected subset  600  has clustered descriptive vectors that describe items (e.g., data items, such as media files) from multiple sources (e.g., a first source, such as a first recording artist, and a second source, such as a second recording artist). The vector clusters in the selected subset  600  (e.g., vector clusters  321 - 325 ) can themselves be clustered into multiple portions  601  and  602 . This may have the effect of subdividing the selected subset  600  of the hierarchy  300  in a manner that allows disambiguation of the multiple sources for the items described by the descriptive vectors. In other words, those items from the first source (e.g., first artist) may have descriptive vectors that are clustered in the portion  601  (e.g., first portion) of the subset  600 , while those items from the second source (e.g., second artist) may have descriptive vectors that are clustered in the portion  602  (e.g., second portion) of the subset  600 . 
       FIGS. 7-10  are flowcharts illustrating operations in a method  700  of selecting balanced clusters of descriptive vectors, according to some example embodiments. Operations in the method  700  may be performed by the clustering machine  110 , one or more the devices  130  and  150 , or any suitable combination thereof, using components (e.g., modules) described above with respect to  FIG. 2 , using one or more processors  299  (e.g., microprocessors or other hardware processors), or using any suitable combination thereof. As shown in  FIG. 7 , the method  700  includes operations  710 ,  720 ,  730 ,  740 ,  750 ,  760 ,  770 , and  780 . 
     In operation  710 , the vector distance calculator  210  accesses descriptive vectors to be analyzed and clustered. This may be performed by reading, retrieving, or otherwise accessing descriptive vectors stored in the database  115 . As noted above, each descriptive vector may have multiple different dimensions whose values indicate multiple different extents to which multiple different characteristics are present in a particular item (e.g., a data item, such as a media file) described by the descriptive vector. 
     In operation  720 , the cluster hierarchy generator  220  calculates vector distances between pairs (e.g., all pairs) of the descriptive vectors accessed in operation  710 . As one example, the vector distance between a pair of descriptive vectors may be calculated by taking a vector difference between the two descriptive vectors in the pair. As another example, the vector distance between two descriptive vectors may be calculated by taking the square root of the sum of squared differences in each dimension of the two descriptive vectors. Other algorithms for calculating a vector distance between two descriptive vectors may be used, according to various example embodiments. 
     In operation  730 , the cluster hierarchy generator  220  generates the hierarchy  300  of vector clusters (e.g., vector clusters  301 - 346 ). The hierarchy  300  may be generated in memory within the clustering machine  110 , in the database  115 , or any suitable combination thereof. Moreover, the hierarchy  300  may be generated by clustering the descriptive vectors into the vector clusters  301 - 346  based on the vector distances calculated in operation  720 . In some example embodiments, this clustering of the descriptive vectors may have the effect of organizing the descriptive vectors and the vector clusters (e.g., vector clusters  301 - 346 ) into multiple tiers of the hierarchy  300  (e.g., Tiers  1 - 5 ). In other example embodiments, the vector clusters (e.g., vector clusters  301 - 346 ) are formed without arranging them into any tiers within the hierarchy  300 . 
     In operation  740 , the score calculator  230  determines (e.g., by calculating or generating) centroid vectors of the vector clusters (e.g., all vector clusters, including the vector clusters  301 - 346 ) in the generated hierarchy  300  of vector clusters. As noted above, the centroid vectors may be determined by calculating weighted or unweighted mean vectors for the vector clusters (e.g., vector clusters  301 - 346 ) of the hierarchy  300 . Accordingly, each of the vector clusters in the hierarchy  300  can be represented by its corresponding centroid vector, as determined in operation  740 . 
     In operation  750 , the score calculator  230  sums the inter-cluster vector distances between pairs of the centroid vectors determined in operation  740 . That is, the score calculator  230  calculates inter-cluster vector distances between all pairs of the vector clusters (e.g., vector clusters  301 - 346 ) in the hierarchy  300 , and then adds these inter-cluster vector distances to obtain a sum (e.g., first sum) of the inter-cluster vector distances. 
     In operation  760 , the score calculator  230  sums the intra-cluster vector distances between descriptive vectors in each of the vector clusters (e.g., vector clusters  301 - 346 ) the hierarchy  300 . In other words, the score calculator  230  calculates intra-cluster vector distances between all descriptive vectors within a given vector cluster (e.g., vector cluster  311  or  321 ), and similar intra-cluster vector distances are calculated on a cluster-by-cluster basis for all other vector clusters (e.g., vector clusters  301 - 346 ) in the hierarchy  300 . All of these inter-cluster vector distances are then added together to obtain a sum (e.g., second sum) of the intra-cluster vector distances. 
     In operation  770 , the score calculator  230  calculates scores (e.g., granularity scores, suitability scores, optimization scores, or any suitable combination thereof) of the hierarchy  300 . The scores are calculated based on the results of operations  750  and  760 . Specifically, the scores are calculated based on the summed inter-cluster vector distances (e.g., the first sum, as calculated in operation  750 ) and based on the summed intra-cluster vector distances (e.g., the second sum, as calculated in operation  760 ). Furthermore, the scores are calculated based on various values of a scalar, which may be selected by score calculator  230  from a range of scalar values (e.g., between zero and one (unity)), such that each calculated score corresponds to a different selected scalar value (e.g., results from a different selected scalar value). For example, the score calculator  230  may vary the scalar within a predetermined range of values (e.g., between zero and one) and perform a calculation of a score of the hierarchy  300  for each separately selected value of the scalar. Accordingly, a distribution of calculated scores of the hierarchy  300  may be obtained from the various scalars selected. A particular scalar (e.g., a particular scalar value) among the selected scalars (e.g., within the range of scalar values) corresponds to (e.g., results in) an extreme score (e.g., a minimum score or maximum score) among the calculated scores. Additional details of operation  770  are discussed below with respect to  FIG. 9 , according to various example embodiments. 
     In operation  780 , the subset selector  240  selects (e.g., identifies, chooses, or otherwise designates as being selected) the subset  600  of the hierarchy  300 . In particular, the subset  600  may be selected based on the particular scalar that corresponds to (e.g., resulting in) the extreme score (e.g., the minimum score or the maximum score) among the calculated scores from operation  770 . Accordingly, operation  780  may include determining which calculated score among the calculated scores of the hierarchy  300  is the extreme score (e.g., the minimum score for the maximum score). 
     As shown in  FIG. 8 , in addition to any one or more of the operations previously described, the method  700  may include one or more of operations  801 ,  802 ,  810 ,  820 ,  821 ,  830 , and  831 . Any one or more of operations  801 ,  802 , and  803  may be performed prior operation  710 , in which the vector distance calculator  210  accesses the descriptive vectors to be analyzed. 
     In operation  801 , the descriptive vector generator  250  accesses data items (e.g., media files, each containing different media content) that are describable by descriptive vectors (e.g., descriptive vectors to be generated in operation  802 ). According to various example embodiments, the accessed data items may be or include media items (e.g., media files), identifiers of media items, identifiers of physical items, or any suitable combination thereof. For example, the descriptive vector generator  250  may access a library (e.g., catalog) of media files (e.g., audio files that each contain a different song) stored by the database  115  or by one of the devices  130  or  150 . 
     In operation  802 , the descriptive vector generator  250  normalizes the data items accessed in operation  801 . This normalization process may include omitting duplicate data items (e.g., media items), omitting non-original data items, omitting data items included in data compilations (e.g., media items released on compilation albums), omitting data items recorded at live performances, retaining data items recorded in studios, or any suitable combination thereof. 
     In operation  803 , the descriptive vector generator  250  determines descriptive vectors for the data items accessed in operation  801  (e.g., and normalized in operation  802 ). In some cases, existing descriptive vectors (e.g., stored in the database  115 ) are overwritten or updated. In other cases, new descriptive vectors are freshly generated (e.g., and stored in the database  115 ). Accordingly, performance of operation  803  generates a different descriptive vector for each of the data items accessed in operation  801 . In certain example embodiments in which the accessed data items are media files, the generating of each different descriptive vector includes analyzing media content in the corresponding media file and generating the descriptive vector for that media file based on the analyzed media content. The descriptive vectors generated in operation  803  may accordingly be accessed by the vector distance calculator  210  in performing operation  710 . 
     Operation  820  may be performed as part (e.g., a precursor task, a subroutine, or a portion) of operation  720 , in which the cluster hierarchy generator  220  calculates vector distances between pairs of descriptive vectors. In operation  820 , the cluster hierarchy generator  220  calculates one or more of the vector distances based on correlations (e.g., calculated statistical correlations) among the descriptive vectors. Accordingly, performance of operation  820  may include performing calculations of statistical correlation between pairs of descriptive vectors (e.g., based on scalar values for their dimensions). 
     In some example embodiments, operation  821  is performed as part of operation  820 . In operation  821 , as part of calculating one or more of the vector distances based on correlations among the descriptive vectors, the cluster hierarchy generator  220  calculates one or more quadratic-chi histogram distances between the pairs of descriptive vectors. Accordingly, the calculation of the vector distances between the pairs of descriptive vectors in operation  720  may be based on these calculated quadratic-chi histogram distances resultant from operation  821 . 
     Operation  830  may be performed as part of operation  730 , in which the cluster hierarchy generator  220  generates the hierarchy  300  of vector clusters (e.g., vector clusters  301 - 346 ). In operation  830 , the cluster hierarchy generator  220  applies agglomerative hierarchical clustering to the descriptive vectors accessed in operation  710 . Thus, the clustering of the descriptive vectors into the vector clusters  301 - 346  in operation  730  may be performed according to, or otherwise based on, an agglomerative hierarchical clustering algorithm. This may have the effect of causing the hierarchy  300  to be generated as a nested and agglomeratively clustered hierarchy of vector clusters. 
     In some example embodiments, operation  831  is performed as part of operation  830 . In operation  831 , as part of applying the agglomerative hierarchical clustering algorithm, the cluster hierarchy generator  220  applies complete-linkage clustering to the descriptive vectors accessed in operation  710 . Thus, the clustering of the descriptive vectors into the vector clusters  301 - 346  in operation  730  may be performed according to, or otherwise based on, a complete-linkage clustering algorithm. This may have the effect of causing the hierarchy  300  to be generated as a nested, agglomeratively clustered, and complete-linkage clustered hierarchy of vector clusters. 
     As shown in  FIG. 9 , in addition to any one or more of the operations previously described, the method  700  may include one or more of operations  970 ,  971 ,  972 ,  973 ,  990 ,  991 ,  992 ,  993 ,  994 , and  995 . Operations  970 ,  971 ,  972 , and  973  may be performed as part of operation  770 , in which the score calculator  230  calculates scores of the hierarchy  300 . As noted above, the calculated scores may correspond to different values of a scalar. 
     In operation  970 , the score calculator  230  selects (e.g., automatically chooses) a scalar between zero and one (unity). This scalar is a numerical value that may represent a candidate level of granularity for selecting the subset  600  as a balanced subset of the vector clusters (e.g., vector clusters  321 - 325 ) in the hierarchy  300 . In some example embodiments, a scalar value of zero corresponds to maximum granularity (e.g., every descriptive vector by itself is its own vector cluster, while a scalar value of one (unity) corresponds to minimum granularity (e.g., all descriptive vectors are clustered into a single vector cluster, such as the vector cluster  301 ). In certain example embodiments, this selected scalar may correspond to a tier (e.g., Tier  3 ) among the multiple tiers of the hierarchy  300 , though in alternative example embodiments, the selected scalar is independent of any of the multiple tiers of the hierarchy  300 . 
     According to some example embodiments, the selection of the scalar is preconfigured (e.g., programmed or hard-coded), while in other example embodiments, the selection of the scalar is based on user input (e.g., submitted by the user  132  via the device  130  and received by the clustering machine  110  via the network  190 ). In certain example embodiments, the selection of the scalar is based on metadata (e.g., stored in the database  115  and accessed therefrom) regarding some or all of the descriptive vectors accessed in operation  710  (e.g., a count of albums by a same single artist that recorded media files described by the descriptive vectors). Thus, in such example embodiments, the scalar (e.g., the value of the scalar) may be selected based on the size of an artist&#39;s catalog (e.g., number of albums). 
     In operation  971 , the score calculator  230  multiplies the scalar selected in operation  970  by the sum of the intra-cluster vector distances (e.g., the second sum) calculated in operation  760 . The result (e.g., product) of this multiplication can be referred to as a first multiplicative product. 
     In operation  972 , the score calculator  230  subtracts the scalar selected in operation  970  from one (unity) to obtain an intermediate result and multiplies this intermediate result by the sum of inter-cluster vector distances (e.g., the first sum) calculated in operation  750 . The result (e.g., product) of this multiplication can be referred to as a second multiplicative product. 
     In operation  973 , the score calculator  230  adds the result of operation  971  to the results of operation  972 , thus calculating a sum (e.g., third sum) of the first multiplicative product and the second multiplicative product. This calculated sum may be treated as a calculated score of the hierarchy  300  (e.g., among multiple calculated scores of the hierarchy  300 ), and this calculated score may correspond to the selected scalar, at least in the sense that the selected scalar resulted in this calculated score. 
     Operations  970 - 973  may be repeated for multiple values of the scalar to obtain a set (e.g., distribution) of calculated scores for the hierarchy  300 . As noted above, performance of operation  780  may include determining that one of the calculated scores is an extreme score (e.g., minimum score or maximum score), such that the scalar (e.g., scalar value) that corresponds to the extreme score (e.g., that resulted in the minimum or maximum score) is identified for use in operation  780  (e.g., for use in selecting the subset  600  of the hierarchy  300 ). 
     Operation  990  may be performed after operation  780 , in which the subset selector  240  selects the subset  600  of the hierarchy  300  based on the scalar that corresponds to the extreme score among the calculated scores from operation  770 . In operation  990 , the selected subset  600  of vector clusters is modified by the cluster subset handler  260 . Such modification of the subset  600  can include removal of one or more vector clusters (e.g., vector cluster  325 ) from the subset  600 . For this purpose, operations  991  and  995  may be performed as part of operation  990 . 
     In operation  991 , the cluster subset handler  260  calculates weights of the vector clusters (e.g., vector clusters  321 - 325 ) in the selected subset  600  of vector clusters. According to various example embodiments, this calculation of weights may be performed by executing one or more of operations  992 ,  993 , and  994 , which may be performed as part of operation  991 . Accordingly, a separate weight is calculated for each vector cluster in the subset  600 , for example, such that the first weight corresponds to a first vector cluster (e.g., vector cluster  321 ) in the selected subset  600 , a second weight corresponds to a second vector cluster (e.g., vector cluster  322 ) in the selected subset  600 , and so on. 
     In some example embodiments, the weights of the vector clusters are calculated based on sizes of the vector clusters. Hence, in operation  992 , the cluster subset handler  260  determines the sizes of the vector clusters in the selected subset  600  (e.g., counts of descriptive vectors in the vector clusters  321 - 325 ) and calculates the weights of these vector clusters based on their determined sizes (e.g., counts of descriptive vectors). 
     In certain example embodiments, the weights of the vector clusters are calculated based on average popularity scores of the vector clusters. Hence, in operation  993 , the cluster subset handler  260  calculates popularity scores for a group of items (e.g., data items, such as media items) described by at least some of the descriptive vectors in a vector cluster (e.g., vector cluster  321 ) from the selected subset  600  of vector clusters. The cluster subset handler  260  then calculates an average (e.g., arithmetic mean) of these popularity scores, and the weight of the vector cluster (e.g., vector cluster  321 ) is then calculated based on this average popularity score. This process may be repeated for each vector cluster (e.g., vector clusters  322 - 325 ) in the selected subset  600 . 
     In various example embodiments, the weights of the vector clusters are calculated based on extents to which the vector clusters are dominated by their primary moods. Hence, in operation  994 , the cluster subset handler  260  calculates the weights of the vector clusters based on values of the most dominant dimensions in their encompassed descriptive vectors. For example, in calculating a weight of a vector cluster (e.g., vector cluster  321 ) represented by a centroid vector, the cluster subset handler  260  may calculate a ratio between a most dominant value of the most dominant dimension in the centroid vector and a sum of less dominant values of less dominant dimensions in the centroid vector. This ratio represents a degree of dominance by the most dominant dimension, and where the most dominant dimension represents a primary mood, the ratio represents an extent to which the primary mood dominates the vector cluster (e.g., vector cluster  321 ). This calculation may be repeated for each vector cluster (e.g., vector clusters  322 - 325 ) in the selected subset  600 ). 
     In operation  995 , the cluster subset handler  260  removes (e.g., deletes or otherwise omits) any vector clusters that fail to transgress a predetermined threshold percentile of the weights calculated in operation  991 . This may include determining a range of the weights calculated in operation  991 , calculating a threshold weight based on the predetermined threshold percentile, and comparing each of the calculated weights from operation  991  to the threshold weight, to determine which vector clusters have weights that transgress the threshold weight and which vector clusters have weights that fail to transgress the threshold weight. 
     As shown in  FIG. 10 , in addition to any one or more of the operations previously described, the method  700  may include one or more of operations  1000 ,  1001 ,  1002 ,  1003 ,  1010 ,  1020 , and  1021 . One or more of these operations may be performed after operation  780 , in which the subset selector  240  selects the subset  600  of the hierarchy  300  of vector clusters, or performed after operation  990 , in which the cluster subset handler  260  modifies the selected subset  600  of the hierarchy  300 , or performed after both. 
     In some example embodiments, the application  200  is configured to perform automatic cluster labeling, and accordingly, in operation  1000 , the cluster subset handler  260  generates labels (e.g., single-word or multi-word text descriptors) for one or more vector clusters in the subset  600  (e.g., modified or unmodified). For example, a first vector cluster (e.g., vector cluster  321 ) in the selected tier (e.g., Tier  3 ) of the hierarchy  300  may be labeled by a first label, a second vector cluster (e.g., vector cluster  322 ) in the same tier may be labeled with a second label, and so on. Each of these labels may be generated based on the centroid vector of the corresponding vector cluster (e.g., with the first label being generated based on the centroid vector of vector cluster  321 ). Furthermore, generation of a label (e.g., first label) for a vector cluster (e.g., first vector cluster, such as vector cluster  321 ) may be accomplished by performing one or more of operations  1001 ,  1002 , and  1003 , each of which may be performed as part of operation  1000 . Operations  1001 - 1003  may be repeated for additional vector clusters (e.g., vector clusters  322 - 325 ). 
     In operation  1001 , for a first centroid vector of the first vector cluster (e.g., vector cluster  321 ), the cluster subset handler  260  determines a set of most dominant dimensions (e.g., top one, top two, or top five most dominant moods represented by dimensions) in the first centroid vector. As noted above, most dominant dimensions have the most dominant (e.g., highest) values in a given centroid vector. 
     In operation  1002 , for the first vector cluster (e.g., vector cluster  321 ), the cluster subset handler  260  accesses the database  115 , which in such example embodiments stores a correspondence relationship between the set of most dominant dimensions and one or more corresponding textual descriptors. That is, the database  115  maps the set of most dominant dimensions to textual descriptors of those dimensions. In some example embodiments, each dimension (e.g., representing a mood, such as “aggressive”) is mapped to a separate textual descriptor (e.g., a word, such as “aggressive,” or a phrase, such as “mean-sounding” or “in your face”). Accordingly, the cluster subset handler  260  can obtain one or more textual descriptors that correspond to the determined set of most dominant dimensions from operation  1001 . 
     In operation  1003 , for the first vector cluster (e.g., vector cluster  321 ), the cluster subset handler  260  incorporates the accessed textual descriptors into the first label to be applied to the first vector cluster, thus fully or partially generating the first label of the first vector cluster. As noted above, the process described with respect operations  1001 - 1003  may be repeated for additional vector clusters to be labeled (e.g., vector clusters  322 - 325 ). 
     In certain example embodiments, the application  200  is configured to perform tracking or other analysis of musical moods by a recording artist over time. According to such example embodiments, the descriptive vectors accessed in operation  710  are already known to describe the items recorded by a single same artist. For example, operation  710  may have been performed by accessing only descriptive vectors of media files in a library of works by that artist. 
     Accordingly, in operation  1010 , the cluster subset handler  260  makes a record of the selected subset  600  (e.g., in the database  115 ). This may be accomplished by storing the centroid vectors of the selected subset  600  (e.g., modified or unmodified) or identifiers of the centroid vectors in the database  115 . Moreover, the centroid vectors or identifiers thereof may be stored with a timestamp (e.g., current date, current time, or both). 
     Performance of operation  1010  may have the effect of taking a contemporary “snapshot” of the centroid vectors, which may form all or part of an evolutionary history of works by the artist. That is, the centroid vectors or identifiers thereof can indicate primary or dominant moods evoked by the artist&#39;s works (e.g., media files), as analyzed by the clustering machine  110 . Over time, as the artist releases additional works, and as additional “snapshots” of these primary or dominant moods are recorded in the database  115 , the network-based system  105  can provide mood tracking services or other mood analysis services to the users  132  and  152 , in regard to how the artist&#39;s musical moods have evolved over time (e.g., during the artist&#39;s career). 
     In various example embodiments, the application  200  is configured to disambiguate sources (e.g., recording artists) of items (e.g., media files), even though the sources have similar names or have the same name, based on analysis of descriptive vectors for the items (e.g., descriptive vectors describing musical moods). For example, to disambiguate recording artists, the application  200  is configured to detect differences in the dominant or primary moods evoked by works released by the artists or otherwise sourced from the artists. According to such example embodiments, the descriptive vectors accessed in operation  710  are already known to describe a collection of items (e.g., media files) sourced from (e.g., released by) more than one source (e.g., more than one artist). As an example, the descriptive vectors accessed in operation  710  may describe all media files aggregated from multiple libraries of media files by multiple artists who have the same name or who have similar names (e.g., a flamenco guitarist named “Freddo” and a death metal band named “F.R.E.D.D.O.,” whose name sometimes is written as “FREDDO”). In accordance with various example embodiments, artist disambiguation may be accomplished by performing operations  1020  and  1021 . 
     In operation  1020 , the cluster subset handler  260  determines that a first source (e.g., first artist) of items (e.g., media items) is distinct from a second source (e.g., second artist) of items. As noted above, this may be performed by grouping the vector clusters of the selected tier (e.g., vector clusters  321 - 325  in Tier  3 ) of the hierarchy  300  into multiple portions (e.g., portions  601  and  602 ) of the selected subset  600  of the hierarchy  300 . For example, the cluster subset handler  260  may calculate vector distances between centroid vectors of the vector clusters  321 - 325  and use these vector distances to subdivide the subset  600  into the portion  601  (e.g., first portion) and the portion  602  (e.g., second portion). 
     In operation  1021 , the cluster subset handler  260  causes presentation of a notification (e.g., an alert or other message within a GUI) that the first and second sources are distinct. The notification may be presented to one of the users  132  or  152  via the network  190  and their respective devices  130  or  150 . This may be performed in response or fulfillment of a request to analyze the items (e.g., media files) represented by the descriptive vectors accessed in operation  710 . For example, the notification may indicate that the items likely come from at least two different sources, provide labels (e.g., generated in operation  1000 ) of vector clusters (e.g., vector clusters  321  and  322 ) in each of the portions  601  and  602 , or both. According to certain example embodiments, the cluster subset handler  260  generates the notification (e.g., including generating labels for the portions  601  and  602 , such as by concatenating or otherwise combining text descriptors accessed in operation  1002 ). 
     According to various example embodiments, one or more of the methodologies described herein may facilitate automatic selection of balanced clusters of descriptive vectors. Moreover, one or more of the methodologies described herein may facilitate identification, selection, and recommendation of a balanced or otherwise optimal clustering scheme (e.g., categorization scheme) for organizing, or otherwise managing items (e.g., data items, such as media files) described by descriptive vectors. Hence, one or more of the methodologies described herein may facilitate faster, more convenient, and more meaningful understanding of items described by descriptive vectors, as well as similarly improved applications for exploring, suggesting, recommending, choosing, purchasing, deleting, or omitting such items. 
     When these effects are considered in aggregate, one or more of the methodologies described herein may obviate a need for certain efforts or resources that otherwise would be involved in automatic selection of balance clusters of descriptive vectors. Efforts expended by a user in creating and maintaining a catalog of items may be reduced by use of (e.g., reliance upon) a special-purpose machine that implements one or more of the methodologies described herein. Computing resources used by one or more systems or machines (e.g., within the network environment  100 ) may similarly be reduced (e.g., compared to systems or machines that lack the structures discussed herein or are otherwise unable to perform the functions discussed herein). Examples of such computing resources include processor cycles, network traffic, computational capacity, main memory usage, graphics rendering capacity, graphics memory usage, data storage capacity, power consumption, and cooling capacity. 
       FIG. 11  is a block diagram illustrating components of a machine  1100 , according to some example embodiments, able to read instructions  1124  from a machine-readable medium  1122  (e.g., a non-transitory machine-readable medium, a machine-readable storage medium, a computer-readable storage medium, or any suitable combination thereof) and perform any one or more of the methodologies discussed herein, in whole or in part. Specifically,  FIG. 11  shows the machine  1100  in the example form of a computer system (e.g., a computer) within which the instructions  1124  (e.g., software, a program, an application, an applet, an app, or other executable code) for causing the machine  1100  to perform any one or more of the methodologies discussed herein may be executed, in whole or in part. 
     In alternative embodiments, the machine  1100  operates as a standalone device or may be communicatively coupled (e.g., networked) to other machines. In a networked deployment, the machine  1100  may operate in the capacity of a server machine or a client machine in a server-client network environment, or as a peer machine in a distributed (e.g., peer-to-peer) network environment. The machine  1100  may be a server computer, a client computer, a personal computer (PC), a tablet computer, a laptop computer, a netbook, a cellular telephone, a smart phone, a set-top box (STB), a personal digital assistant (PDA), a web appliance, a network router, a network switch, a network bridge, or any machine capable of executing the instructions  1124 , sequentially or otherwise, that specify actions to be taken by that machine. Further, while only a single machine is illustrated, the term “machine” shall also be taken to include any collection of machines that individually or jointly execute the instructions  1124  to perform all or part of any one or more of the methodologies discussed herein. 
     The machine  1100  includes a processor  1102  (e.g., one or more central processing units (CPUs), one or more graphics processing units (GPUs), one or more digital signal processors (DSPs), one or more application specific integrated circuits (ASICs), one or more radio-frequency integrated circuits (RFICs), or any suitable combination thereof), a main memory  1104 , and a static memory  1106 , which are configured to communicate with each other via a bus  1108 . The processor  1102  contains solid-state digital microcircuits (e.g., electronic, optical, or both) that are configurable, temporarily or permanently, by some or all of the instructions  1124  such that the processor  1102  is configurable to perform any one or more of the methodologies described herein, in whole or in part. For example, a set of one or more microcircuits of the processor  1102  may be configurable to execute one or more modules (e.g., software modules) described herein. In some example embodiments, the processor  1102  is a multicore CPU (e.g., a dual-core CPU, a quad-core CPU, an 8-core CPU, or a 128-core CPU) within which each of multiple cores behaves as a separate processor that is able to perform any one or more of the methodologies discussed herein, in whole or in part. Although the beneficial effects described herein may be provided by the machine  1100  with at least the processor  1102 , these same beneficial effects may be provided by a different kind of machine that contains no processors (e.g., a purely mechanical system, a purely hydraulic system, or a hybrid mechanical-hydraulic system), if such a processor-less machine is configured to perform one or more of the methodologies described herein. 
     The machine  1100  may further include a graphics display  1110  (e.g., a plasma display panel (PDP), a light emitting diode (LED) display, a liquid crystal display (LCD), a projector, a cathode ray tube (CRT), or any other display capable of displaying graphics or video). The machine  1100  may also include an alphanumeric input device  1112  (e.g., a keyboard or keypad), a pointer input device  1114  (e.g., a mouse, a touchpad, a touchscreen, a trackball, a joystick, a stylus, a motion sensor, an eye tracking device, a data glove, or other pointing instrument), a data storage  1116 , an audio generation device  1118  (e.g., a sound card, an amplifier, a speaker, a headphone jack, or any suitable combination thereof), and a network interface device  1120 . 
     The data storage  1116  (e.g., a data storage device) includes the machine-readable medium  1122  (e.g., a tangible and non-transitory machine-readable storage medium) on which are stored the instructions  1124  embodying any one or more of the methodologies or functions described herein. The instructions  1124  may also reside, completely or at least partially, within the main memory  1104 , within the static memory  1106 , within the processor  1102  (e.g., within the processor&#39;s cache memory), or any suitable combination thereof, before or during execution thereof by the machine  1100 . Accordingly, the main memory  1104 , the static memory  1506 , and the processor  1102  may be considered machine-readable media (e.g., tangible and non-transitory machine-readable media). The instructions  1124  may be transmitted or received over the network  190  via the network interface device  1120 . For example, the network interface device  1120  may communicate the instructions  1124  using any one or more transfer protocols (e.g., hypertext transfer protocol (HTTP)). 
     In some example embodiments, the machine  1100  may be a portable computing device (e.g., a smart phone, a tablet computer, or a wearable device), and may have one or more additional input components  1130  (e.g., sensors or gauges). Examples of such input components  1130  include an image input component (e.g., one or more cameras), an audio input component (e.g., one or more microphones), a direction input component (e.g., a compass), a location input component (e.g., a global positioning system (GPS) receiver), an orientation component (e.g., a gyroscope), a motion detection component (e.g., one or more accelerometers), an altitude detection component (e.g., an altimeter), a biometric input component (e.g., a heartrate detector or a blood pressure detector), and a gas detection component (e.g., a gas sensor). Input data gathered by any one or more of these input components may be accessible and available for use by any of the modules described herein. 
     As used herein, the term “memory” refers to a machine-readable medium able to store data temporarily or permanently and may be taken to include, but not be limited to, random-access memory (RAM), read-only memory (ROM), buffer memory, flash memory, and cache memory. While the machine-readable medium  1122  is shown in an example embodiment to be a single medium, the term “machine-readable medium” should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, or associated caches and servers) able to store instructions. The term “machine-readable medium” shall also be taken to include any medium, or combination of multiple media, that is capable of storing the instructions  1124  for execution by the machine  1100 , such that the instructions  1124 , when executed by one or more processors of the machine  1100  (e.g., processor  1102 ), cause the machine  1100  to perform any one or more of the methodologies described herein, in whole or in part. Accordingly, a “machine-readable medium” refers to a single storage apparatus or device, as well as cloud-based storage systems or storage networks that include multiple storage apparatus or devices. The term “machine-readable medium” shall accordingly be taken to include, but not be limited to, one or more tangible and non-transitory data repositories (e.g., data volumes) in the example form of a solid-state memory chip, an optical disc, a magnetic disc, or any suitable combination thereof. A “non-transitory” machine-readable medium, as used herein, specifically does not include propagating signals per se. In some example embodiments, the instructions  1124  for execution by the machine  1100  may be communicated by a carrier medium. Examples of such a carrier medium include a storage medium (e.g., a non-transitory machine-readable storage medium, such as a solid-state memory, being physically moved from one place to another place) and a transient medium (e.g., a propagating signal that communicates the instructions  1124 ). 
     Certain example embodiments are described herein as including modules. Modules may constitute software modules (e.g., code stored or otherwise embodied in a machine-readable medium or in a transmission medium), hardware modules, or any suitable combination thereof. A “hardware module” is a tangible (e.g., non-transitory) physical component (e.g., a set of one or more processors) capable of performing certain operations and may be configured or arranged in a certain physical manner. In various example embodiments, one or more computer systems or one or more hardware modules thereof may be configured by software (e.g., an application or portion thereof) as a hardware module that operates to perform operations described herein for that module. 
     In some example embodiments, a hardware module may be implemented mechanically, electronically, hydraulically, or any suitable combination thereof. For example, a hardware module may include dedicated circuitry or logic that is permanently configured to perform certain operations. A hardware module may be or include a special-purpose processor, such as a field programmable gate array (FPGA) or an ASIC. A hardware module may also include programmable logic or circuitry that is temporarily configured by software to perform certain operations. As an example, a hardware module may include software encompassed within a CPU or other programmable processor. It will be appreciated that the decision to implement a hardware module mechanically, hydraulically, in dedicated and permanently configured circuitry, or in temporarily configured circuitry (e.g., configured by software) may be driven by cost and time considerations. 
     Accordingly, the phrase “hardware module” should be understood to encompass a tangible entity that may be physically constructed, permanently configured (e.g., hardwired), or temporarily configured (e.g., programmed) to operate in a certain manner or to perform certain operations described herein. Furthermore, as used herein, the phrase “hardware-implemented module” refers to a hardware module. Considering example embodiments in which hardware modules are temporarily configured (e.g., programmed), each of the hardware modules need not be configured or instantiated at any one instance in time. For example, where a hardware module includes a CPU configured by software to become a special-purpose processor, the CPU may be configured as respectively different special-purpose processors (e.g., each included in a different hardware module) at different times. Software (e.g., a software module) may accordingly configure one or more processors, for example, to become or otherwise constitute a particular hardware module at one instance of time and to become or otherwise constitute a different hardware module at a different instance of time. 
     Hardware modules can provide information to, and receive information from, other hardware modules. Accordingly, the described hardware modules may be regarded as being communicatively coupled. Where multiple hardware modules exist contemporaneously, communications may be achieved through signal transmission (e.g., over circuits and buses) between or among two or more of the hardware modules. In embodiments in which multiple hardware modules are configured or instantiated at different times, communications between such hardware modules may be achieved, for example, through the storage and retrieval of information in memory structures to which the multiple hardware modules have access. For example, one hardware module may perform an operation and store the output of that operation in a memory (e.g., a memory device) to which it is communicatively coupled. A further hardware module may then, at a later time, access the memory to retrieve and process the stored output. Hardware modules may also initiate communications with input or output devices, and can operate on a resource (e.g., a collection of information from a computing resource). 
     The various operations of example methods described herein may be performed, at least partially, by one or more processors that are temporarily configured (e.g., by software) or permanently configured to perform the relevant operations. Whether temporarily or permanently configured, such processors may constitute processor-implemented modules that operate to perform one or more operations or functions described herein. As used herein, “processor-implemented module” refers to a hardware module in which the hardware includes one or more processors. Accordingly, the operations described herein may be at least partially processor-implemented, hardware-implemented, or both, since a processor is an example of hardware, and at least some operations within any one or more of the methods discussed herein may be performed by one or more processor-implemented modules, hardware-implemented modules, or any suitable combination thereof. 
     Moreover, such one or more processors may perform operations in a “cloud computing” environment or as a service (e.g., within a “software as a service” (SaaS) implementation). For example, at least some operations within any one or more of the methods discussed herein may be performed by a group of computers (e.g., as examples of machines that include processors), with these operations being accessible via a network (e.g., the Internet) and via one or more appropriate interfaces (e.g., an application program interface (API)). The performance of certain operations may be distributed among the one or more processors, whether residing only within a single machine or deployed across a number of machines. In some example embodiments, the one or more processors or hardware modules (e.g., processor-implemented modules) may be located in a single geographic location (e.g., within a home environment, an office environment, or a server farm). In other example embodiments, the one or more processors or hardware modules may be distributed across a number of geographic locations. 
     Throughout this specification, plural instances may implement components, operations, or structures described as a single instance. Although individual operations of one or more methods are illustrated and described as separate operations, one or more of the individual operations may be performed concurrently, and nothing requires that the operations be performed in the order illustrated. Structures and their functionality presented as separate components and functions in example configurations may be implemented as a combined structure or component with combined functions. Similarly, structures and functionality presented as a single component may be implemented as separate components and functions. These and other variations, modifications, additions, and improvements fall within the scope of the subject matter herein. 
     Some portions of the subject matter discussed herein may be presented in terms of algorithms or symbolic representations of operations on data stored as bits or binary digital signals within a memory (e.g., a computer memory or other machine memory). Such algorithms or symbolic representations are examples of techniques used by those of ordinary skill in the data processing arts to convey the substance of their work to others skilled in the art. As used herein, an “algorithm” is a self-consistent sequence of operations or similar processing leading to a desired result. In this context, algorithms and operations involve physical manipulation of physical quantities. Typically, but not necessarily, such quantities may take the form of electrical, magnetic, or optical signals capable of being stored, accessed, transferred, combined, compared, or otherwise manipulated by a machine. It is convenient at times, principally for reasons of common usage, to refer to such signals using words such as “data,” “content,” “bits,” “values,” “elements,” “symbols,” “characters,” “terms,” “numbers,” “numerals,” or the like. These words, however, are merely convenient labels and are to be associated with appropriate physical quantities. 
     Unless specifically stated otherwise, discussions herein using words such as “accessing,” “processing,” “detecting,” “computing,” “calculating,” “determining,” “generating,” “presenting,” “displaying,” or the like refer to actions or processes performable by a machine (e.g., a computer) that manipulates or transforms data represented as physical (e.g., electronic, magnetic, or optical) quantities within one or more memories (e.g., volatile memory, non-volatile memory, or any suitable combination thereof), registers, or other machine components that receive, store, transmit, or display information. Furthermore, unless specifically stated otherwise, the terms “a” or “an” are herein used, as is common in patent documents, to include one or more than one instance. Finally, as used herein, the conjunction “or” refers to a non-exclusive “or,” unless specifically stated otherwise. 
     The following enumerated embodiments describe various example embodiments of methods, machine-readable media, and systems (e.g., machines, devices, or other apparatus) discussed herein. 
     A first embodiment provides a method comprising:
     accessing, by one or more processors, descriptive vectors that describe items, each descriptive vector having multiple dimensions whose values indicate extents to which multiple characteristics are present in a different item among the items;   calculating, by the one or more processors, vector distances between pairs of the descriptive vectors;   generating, by the one or more processors, a hierarchy of vector clusters by clustering the descriptive vectors into the vector clusters based on the calculated vector distances;   determining, by the one or more processors, centroid vectors of the vector clusters in the hierarchy by calculating mean vectors of the vector clusters, each mean vector and each centroid vector representing a different vector cluster in the hierarchy;   summing, by the one or more processors, inter-cluster vector distances between pairs of the centroid vectors;   summing, by the one or more processors, intra-cluster vector distances between pairs of descriptive vectors in each of the vector clusters;   calculating, by the one or more processors, scores of the hierarchy based on the summed inter-cluster vector distances and on the summed intra-cluster vector distances, each of the scores being calculated based on a different scalar among a plurality of scalars among which a scalar corresponds to an extreme score among the calculated scores; and   selecting, by the one or more processors, a subset of the vector clusters in the hierarchy based on the scalar that corresponds to the extreme score.   

     A second embodiment provides a method according to the first embodiment, further comprising:
     accessing the items prior to the accessing of the descriptive vectors, each of the items including different media content; and   determining the descriptive vectors by generating a different descriptive vector for each of the items, the generating of each different descriptive vector including analyzing the media content in the corresponding item to be described.   

     A third embodiment provides a method according to the second embodiment, wherein:
     the accessed items are media items;   the method further comprises normalizing the media items by at least one of: omitting duplicate media items, omitting non-original media items, omitting media items released on compilation albums, omitting media items recorded at live performances, or retaining media items recorded in studios; and   the determining of the descriptive vectors is performed by generating a different descriptive vector for each of the normalized media items.   

     A fourth embodiment provides a method according to any of the first through third embodiments, wherein:
     the calculating of the vector distances between the pairs of the descriptive vectors is based on correlations among the descriptive vectors.   

     A fifth embodiment provides a method according to any of the first through fourth embodiments, wherein:
     the calculating of the vector distances between the pairs of the descriptive vectors includes calculating quadratic-chi histogram distances between the pairs of the descriptive vectors.   

     A sixth embodiment provides a method according to any of the first through fifth embodiments, wherein:
     the clustering of the descriptive vectors is performed according to an agglomerative hierarchical clustering algorithm.   

     A seventh embodiment provides a method according to the fifth embodiment, wherein:
     the agglomerative hierarchical clustering algorithm includes a complete-linkage clustering algorithm.   

     An eighth embodiment provides a method according to any of the first through seventh embodiments, wherein:
     the calculating of each score of the hierarchy includes:   selecting a scalar between zero and unity;   multiplying the scalar by the summed intra-cluster vector distances to obtain a first multiplicative product;   multiplying the summed inter-cluster vector distances by the scalar subtracted from unity to obtain a second multiplicative product; and   adding the first multiplicative product to the second multiplicative product to obtain the score of the hierarchy.   

     A ninth embodiment provides a method according to the eighth embodiment, wherein:
     the items are media items released in a set of albums by a same artist; and   the selecting of the scalar is based on a count of albums in the set of albums by the same artist.   

     A tenth embodiment provides a method according to any of the first through ninth embodiments, further comprising:
     modifying the selected subset of the vector clusters in the hierarchy, the modifying of the selected subset including:   calculating weights of vector clusters in the selected subset, a first calculated weight corresponding to a first vector cluster in the selected subset;   removing a first vector cluster from the selected subset based on the first calculated weight failing to transgress a threshold percentile of the calculated weights of the vector clusters in the selected subset.   

     An eleventh embodiment provides a method according to the tenth embodiment, wherein:
     the calculating of the weights of vector clusters in the selected subset is based on sizes of vector clusters in the selected subset, the first calculated weight being calculated based on a count of descriptive vectors in the first vector cluster within the selected subset.   

     A twelfth embodiment provides a method according to the tenth embodiment or the eleventh embodiment, wherein:
     the calculating of the weights of vector clusters in the selected subset is based on average popularity scores of vector clusters in the selected subset, the first calculated weight being calculated based on an average of a group of popularity scores that correspond to a group of items described by at least some descriptive vectors in the first vector cluster within the selected subset.   

     A thirteenth embodiment provides a method according to any of the tenth through twelfth embodiments, wherein:
     the calculating of the weights of vector clusters in the selected subset is based on values of most dominant dimensions of descriptive vectors in vector clusters in the selected subset,   the first vector cluster having a first centroid vector among the centroid vectors,   the first calculated weight being calculated based on a ratio of a most dominant value of a most dominant dimension in the first centroid vector of the first vector cluster to a sum of less dominant values of less dominant dimensions in the first centroid vector of the first vector cluster.   

     A fourteenth embodiment provides a method according to any of the first through thirteenth embodiments, further comprising:
     generating labels that identify vector clusters in the selected subset of the hierarchy,   a first label identifying a first vector cluster in the selected subset,   the first vector cluster having a first centroid vector among the centroid vectors, the first label being generated by:   determining a set of most dominant dimensions in the first centroid vector of the first vector cluster, the set of most dominant dimensions having most dominant values in the first centroid vector;   accessing a database that maps the set of most dominant dimensions to corresponding textual descriptors; and   incorporating the textual descriptors into the first label.   

     A fifteenth embodiment provides a method according to the first through fourteenth embodiments, wherein:
     the descriptive vectors that describe the items are mood vectors that describe media items all recorded by a same artist, each mood vector indicating extents to which multiple emotions are perceivable in a different media item among the media items;   the hierarchy of vector clusters is a nested hierarchy of mood clusters that group the mood vectors; and   the selected subset of the mood clusters represents a tier among multiple tiers of the nested hierarchy, the centroid vectors of the selected mood clusters describing and representing the same artist.   

     A sixteenth embodiment provides a method according to any of the first through fifteenth embodiments, wherein:
     the items described by the descriptive vectors have a common source;   the selected subset of the vector clusters is representative of the common source of the items; and the method further comprises:   storing identifiers of centroid vectors of vector clusters in the selected subset, the identifiers being stored with a contemporary timestamp in an evolutionary history of items attributed to the common source.   

     A seventeenth embodiment provides a method according to any of the first to sixteenth embodiments, wherein:
     the items described by the descriptive vectors are sourced from multiple sources that include a first source and a second source;   the selected subset of the vector clusters has a first portion that is representative of the first source of the items and has a second portion that is representative of the second source of the items; and the method further comprises:   determining that the first source represented by the first portion of the selected subset is distinct from the second source; and   causing presentation of a notification that the first and second sources are different.   

     An eighteenth embodiment provides a machine-readable medium (e.g., a non-transitory machine-readable storage medium) comprising instructions that, when executed by one or more processors of a machine, cause the machine to perform operations comprising:
     accessing descriptive vectors that describe items, each descriptive vector having multiple dimensions whose values indicate extents to which multiple characteristics are present in a different item among the items;   calculating vector distances between pairs of the descriptive vectors;   generating a hierarchy of vector clusters by clustering the descriptive vectors into the vector clusters based on the calculated vector distances;   determining centroid vectors of the vector clusters in the hierarchy by calculating mean vectors of the vector clusters, each mean vector and each centroid vector representing a different vector cluster in the hierarchy;   summing inter-cluster vector distances between pairs of the centroid vectors;   summing intra-cluster vector distances between pairs of descriptive vectors in each of the vector clusters;   calculating scores of the hierarchy based on the summed inter-cluster vector distances and on the summed intra-cluster vector distances, each of the scores being calculated based on a different scalar among a plurality of scalars among which a scalar corresponds to an extreme score among the calculated scores; and   selecting a subset of the vector clusters in the hierarchy based on the scalar that corresponds to the extreme score.   

     A nineteenth embodiment provides a machine-readable medium according to the eighteenth embodiment, wherein:
     the selecting of the subset of the vector clusters in a hierarchy includes determining that the scalar that corresponds to the extreme score corresponds to a minimum score among the calculated scores; and   the selected subset of the mood clusters represents a tier among multiple tiers of the hierarchy.   

     A twentieth embodiment provides a system (e.g., machine) comprising:
     one or more processors; and   a memory storing instructions that, when executed by at least one processor among the one or more processors, cause the system to perform operations comprising:   accessing descriptive vectors that describe items, each descriptive vector having multiple dimensions whose values indicate extents to which multiple characteristics are present in a different item among the items;   calculating vector distances between pairs of the descriptive vectors;   generating a hierarchy of vector clusters by clustering the descriptive vectors into the vector clusters based on the calculated vector distances;   determining centroid vectors of the vector clusters in the hierarchy by calculating mean vectors of the vector clusters, each mean vector and each centroid vector representing a different vector cluster in the hierarchy;   summing inter-cluster vector distances between pairs of the centroid vectors;   summing intra-cluster vector distances between pairs of descriptive vectors in each of the vector clusters;   calculating scores of the hierarchy based on the summed inter-cluster vector distances and on the summed intra-cluster vector distances, each of the scores being   calculated based on a different scalar among a plurality of scalars among which a scalar corresponds to an extreme score among the calculated scores; and   selecting a subset of the vector clusters in the hierarchy based on the scalar that corresponds to the extreme score.   

     A twenty first embodiment provides a carrier medium carrying machine-readable instructions for controlling a machine to carry out the method of any one of the previously described embodiments.