Patent Publication Number: US-8538909-B2

Title: Temporal rule-based feature definition and extraction

Description:
BACKGROUND 
     Many types of data contain sequences. For example, the network packets sent on the network interface, the order of function calls made by an application, the order in which a user clicks on a website, all contain sequences. In each of these examples, mostly one event (such as clicking on a link or calling a particular function) occurs at a point in time. Thus, there is a clear temporal ordering between each event. 
     In this type of data each event has a temporal ordering. A sequence of events is known as a trace. One way to analyze a large data set for a particular purpose is to analyze the data based on the features that best describe the data in a manner that is relevant to the purpose. This can be achieved by transforming the data into a reduced representation set of features (called a features vector). The act of transforming the data into the set of features is known as feature extraction. Feature extraction involves simplifying the amount of resources used to describe a large set of data accurately. 
     Once the features are extracted they can be used to process the traces. This processing can involve classifying a trace (to determine whether a trace belongs to a certain group or class of traces), clustering similar traces, and fingerprinting the traces. Fingerprinting is a process that maps a large amount of data to a much smaller data string that uniquely identifies the large amount of data. 
     SUMMARY 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
     Embodiments of the temporal rule-based feature extraction system and method extract features from temporal-based rules satisfied by a trace. Embodiments of the system and method perform feature extraction that is based on the temporal relationship of events in a specific trace. When a temporal rule is found that is satisfied by the trace, then that rule is leveraged either as a feature or to extract additional features. The extracted feature then is used to process and characterize the trace. 
     Embodiments of the temporal rule-based feature extraction system include a feature definition module, which define features based on the temporal-based rules satisfied by a trace, and a similarity measure module, which defines a similarity measure for the defined feature. The feature definition module includes an extrinsic feature module, which defines extrinsic features by leveraging extrinsic properties of the rule that are independent of an internal structure of the rule, and an intrinsic feature module, which defines intrinsic features by leveraging intrinsic properties of the rule that are dependent on the internal structure of the rule. 
     The extrinsic features defined by embodiments of the temporal rule-based feature extraction system and method include a rule set feature and a rule frequency feature. The rule set feature is based on one or more temporal-based rules themselves. The rule frequency feature is defined using a normalized support for each rule in a set of temporal-based rules and then mapping each rule to their normalized supports. 
     The intrinsic features defined by embodiments of the temporal rule-based feature extraction system and method include a distance feature and a distance frequency feature. The distance feature is defined by computing a set of abstraction position pairs for a rule and computing a summary of distance measures of the pairs by using a summarizing function. An abstraction position pair is a pair of abstraction (or event) positions used to calculate distance statistics. For example, consider the ordering A→B→C. This ordering has three abstraction positions (namely, 1, 2, and 3) that are occupied by A, B, and C, respectively. In the context of a distance feature, pairs of these abstraction positions are considered for the purpose of calculating the distance statistics. For example, in the trace AXXXXXBYYYC that contains a witness for the ordering A→B→C, the&#39;distances for the abstraction position pairs (1,2), (2,3), and (1,3) are 5, 3, and 9, respectively. The distance feature then is generated as a mapping of each pair to the summary of distance measures given by the summarizing function. The distance frequency feature is defined by computing witness distances as a collection of distance between the abstraction position pair of each witness to the rule and then mapping the witness distances to a normalized frequency. 
     Embodiments of the similarity measure module include a rule set based similarity measure module, a rule frequency based similarity measure module, a distance based similarity measure module, and a distance frequency based similarity measure module. The rule set based similarity measure module generates a rule set based similarity measure module that depends both on a similarity and a dissimilarity between two traces. The rule frequency based similarity measure module generates a rule frequency based similarity measure that compares frequency distributions of rules between two traces. In essence, this similarity measure is used to determine a closeness between the two traces. 
     The distance based similarity measure module generates a distance based similarity measure that depends on distance between distance features of two traces. The distance computation performed can be based on a mean of a distance between abstraction position pairs or based on both the greatest and least distance between the abstraction position pairs. The distance frequency based similarity measure module generates a distance frequency based similarity measure that compares a frequency distribution of a temporal-based rule to other rule frequency distributions of other traces. 
     Embodiments of the temporal rule-based feature extraction system and method also include a comparison module processes traces, the defined features, and the similarity measures. In particular, based on the defined features, one or more traces can be compared using the similarity measures. This comparison can be used to classifying, cluster, or fingerprint one or more traces. 
     It should be noted that alternative embodiments are possible, and that steps and elements discussed herein may be changed, added, or eliminated, depending on the particular embodiment. These alternative embodiments include alternative steps and alternative elements that may be used, and structural changes that may be made, without departing from the scope of the invention. 
    
    
     
       DRAWINGS DESCRIPTION 
       Referring now to the drawings in which like reference numbers represent corresponding parts throughout: 
         FIG. 1  is a block diagram illustrating a general overview of embodiments of the temporal rule-based feature extraction system and method implemented on a computing device and in a computing environment. 
         FIG. 2  is a flow diagram illustrating the general operation of embodiments of the temporal rule-based feature extraction system and method shown in  FIG. 1 . 
         FIG. 3  is a flow diagram illustrating the operational details of embodiments of the feature definition module shown in  FIG. 1 . 
         FIG. 4  is a flow diagram illustrating the operational details of embodiments of the rule set based similarity measure module shown in  FIG. 1 . 
         FIG. 5  is a flow diagram illustrating the operational details of embodiments of the rule frequency based similarity measure module shown in  FIG. 1 . 
         FIG. 6  is a flow diagram illustrating the operational details of embodiments of the distance based similarity measure module shown in  FIG. 1 . 
         FIG. 7  is a flow diagram illustrating the operational details of embodiments of the distance frequency similarity measure module shown in  FIG. 1 . 
         FIG. 8  illustrates an example of a suitable computing system environment in which embodiments of the temporal rule-based feature extraction system and method shown in  FIGS. 1-7  may be implemented. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description of embodiments of a temporal rule-based feature extraction system and method reference is made to the accompanying drawings, which form a part thereof, and in which is shown by way of illustration a specific example whereby embodiments of the temporal rule-based feature extraction system and method may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the claimed subject matter. 
     I. Terminology 
     Before discussing an overview and the details of embodiments of the temporal rule-based feature extraction system and method, a terminology foundation will be set. Specifically, a trace t is defined as a sequence of events. An event type ô is a set of positions (names or fields). An event of type ô is a set of equality constraints relating all positions of ô to an atomic value. An atomic value is one that is not further divisible by any other value. In every event type, a set of positions are identified as a primary. Every non-empty subset of an event containing at least one equality constraint involving a primary position is designated as an abstraction of the event. 
     An abstraction with equality constraints that involve variables (instead of values) and a mapping from variables to values is called a quantified abstraction. An abstraction without variables is known as an unquantified abstraction. In this document it is assumed that there exists a general technique to generate abstractions of events and relate such abstractions by considering valuation mappings. 
     Between every two distinct events in a trace, embodiments of the temporal rule-based feature extraction system and method recognize two temporal orders captured by the operators. The first temporal order is ( ), which means “followed by.” The second temporal order is ( ), which means “preceded by.” In these operators, the first event is the trigger event and the second event is the effect event. Further, embodiments of the temporal rule-based feature extraction system and method also recognize a refinement of these operators that prohibits the recurrence of the trigger event between the trigger event and the effect event. These are essentially the operators supported by the database query language query by example in C (QBEC). Based on the relation between events and abstractions, the ordering and operators are applicable to abstractions as well. 
     A temporal ordering between abstractions is a sequence of abstraction with each consecutive pair of abstraction being related by a temporal operator. Orderings admit a grouping operator ( ) to indicate precedence of a sub-ordering over another sub-ordering. For example, the A (B C). Every ordering o is associated with a set of abstraction positions Pos(o) that is the index of the abstractions in o. 
     The support for an abstraction is the total number of events in the given trace set that are supersets of the abstraction. A subsequence of a trace is a witness to an ordering if the following are true. First, every event in the subsequence is represented by an abstraction in the ordering. Second, the order of the events in the sequence is identical to the order between the corresponding abstractions in the ordering. The support S(o) for an ordering o is the number of witnesses to the ordering in the given trace set. The confidence C(o) for an ordering is the ratio of the support for the ordering and the support for the trigger event of the ordering. 
     A trace t satisfies a rule r, if it contains a witness to the corresponding ordering. A set of rules satisfied by a trace t is denoted as R(t). Similarly, a set of rules satisfied by a trace set T is denoted as R(T). A temporal ordering with a witness is a temporal rule r. Given a support threshold S and confidence threshold C, an ordering with support equal to or greater than S is known as a candidate rule. A candidate rule with confidence equal to or greater than C is known as a significant rule. 
     II. System Overview 
       FIG. 1  is a block diagram illustrating a general overview of embodiments of the temporal rule-based feature extraction system  100  and method implemented on a computing device  110  and in a computing environment. Note that  FIG. 1  is merely one way in which embodiments of the embodiments of the temporal rule-based feature extraction system  100  and method may be implemented, and is shown merely for illustrative purposes. It should be noted that there are several other ways in which embodiments of the temporal rule-based feature extraction system  100  and method may be implemented, which will be apparent to those having ordinary skill in the art. 
     In general, embodiments of the temporal rule-based feature extraction system  100  and method extract features from temporal-based rules satisfied by a trace. This is performed by first defining features and then generating similarity measures to compute a similarity between traces. This similarity then is used to process and characterize the trace. 
     As shown in  FIG. 1 , embodiments of the temporal rule-based feature extraction system  100  and method are disposed on the computing device  110 . The input to embodiments of the temporal rule-based feature extraction system  100  are a trace  115  and a set of temporal-based rules that are satisfied by the trace  120 . Output of embodiments of the temporal rule-based feature extraction system  100  are extracted features based on the temporal rules  125 . 
     Embodiments of the temporal rule-based feature extraction system  100  include a feature definition module  130 , which define features based on the set of temporal-based rules that are satisfied by the trace  120 . In addition, embodiments of the temporal rule-based feature extraction system  100  include a similarity measure module  135 , which generate a similarity measure for the defined features, and a comparison module  140 , which use the defined features and similarity measures and use them to process and characterize traces. The comparison module  140  solves feature extraction problems by using the temporal rule-based feature and the corresponding similarity measure to compare traces. 
     The feature definition module  130  includes an extrinsic feature module  145 , which defines features using extrinsic properties of the temporal-based rules, and an intrinsic feature module  150 , which defines features using intrinsic properties of the temporal-based rules. The extrinsic feature module  145  generates a rule set feature  155 , which is based on using one rule or a set of rules as a feature, and a rule frequency feature  160 , which is based on how often a particular rule is satisfied by a trace. The intrinsic feature module  150  generates a distance feature  165 , which is based on a mapping of distances between abstraction position pairs, and a distance frequency feature  170 , which is based on a mapping of witness distance to a normalized frequency. 
     The similarity measure module  135  includes a rule set based similarity measure module  175 , a rule frequency based similarity measure module  180 , a distance based similarity measure module  185 , and a distance frequency based similarity measure module  190 . The rule set based similarity measure module  175  generates a similarity measure for the rule set feature  155 , the rule frequency based similarity measure module  180  generates a similarity measure for the rule frequency feature  160 , the distance based similarity measure module  185  generates a similarity measure for the distance feature  165 , and the distance frequency based similarity measure module  190  generates a similarity measure for the distance frequency feature  170 . The defined features and similarity measures then are used by the comparison module  140  to compare, characterize, and otherwise process traces. 
     III. Operational Overview 
       FIG. 2  is a flow diagram illustrating the general operation of embodiments of the temporal rule-based feature extraction system  100  and method shown in  FIG. 1 . In general, embodiments of the temporal rule-based feature extraction system  100  and method define and extract features using temporal-based rules satisfied by a trace. Referring to  FIG. 2 , the method begins by inputting a trace containing events (box  200 ). Next, embodiments of the temporal rule-based feature extraction method find a temporal-based rule that is satisfied by the trace (box  210 ). 
     Next, a feature is extracted from the trace based on the temporal-based rule (box  220 ). This extracted feature then is used to process the trace (box  230 ). As noted above and below, this processing can include classifying, clustering, and fingerprinting the trace. The extracted features based on the temporal-based rule then is output from embodiments of the temporal rule-based feature extraction method (box  240 ). 
     IV. Operational Details 
     The operational details of embodiments of the temporal rule-based feature extraction system  100  and method now will be discussed. These embodiments include embodiments of the feature definition module  130 , the rule set based similarity measure module  175 , the rule frequency based similarity measure module  180 , the distance based similarity measure module  185 , and the distance frequency based similarity measure module  190 . The operational details of each of these modules now will be discussed in detail. 
     IV.A. Feature Definition Module 
     The feature definition module  130  defines features based on the temporal-based rules satisfied by the trace.  FIG. 3  is a flow diagram illustrating the operational details of embodiments of the feature definition module  130  shown in  FIG. 1 . The operation of embodiments of the feature definition module  130  begins by inputting a set of temporal-based rules satisfied by a trace (box  300 ). Features then are extracted from the trace either by using extrinsic properties of the rules, intrinsic properties of the rules, or both. 
     In particular, embodiments of the feature definition module  130  extract features from the trace by leveraging extrinsic properties of the set of temporal-based rules (box  305 ). Next, one rule in the set of temporal-based rules is defined as a rule set feature (box  310 ). This means that the temporal-based rule itself is defined as a feature. In addition to a single rule being defined as a feature, the entire set of temporal-based rule may also be defined as a feature (box  315 ). 
     Embodiments of the feature definition module  130  then define a normalized support for each rule in the set of temporal-based rules (box  320 ). A rule frequency feature can be defined as a mapping of each rule in the set of temporal-based rules to their normalized supports (box  325 ). 
     Embodiments of the feature definition module  130  also extract features from the trace by leveraging intrinsic properties of the set of temporal-based rules (box  330 ). A set of abstraction position pairs then is computed for each rule in the set of temporal-based rules (box  335 ). Next, a summary of distance measures for the set of abstraction position pairs is computed using a summarizing function (box  340 ). A distance feature is defined by embodiments of the feature definition module  130  as a mapping of each abstraction position pair to the summary of distance measures given by the summarizing function (box  345 ). 
     A distance frequency feature is defined by embodiments of the feature definition module  130  as follows. Witness distances are computed as a collection of distances between each abstraction position pair of each witness to the set of temporal-based rules (box  350 ). Next, embodiments of the feature definition module  130  define the distance frequency feature as a mapping of witness distances to a normalized frequency (box  355 ). The output of embodiments of the feature definition module  130  are the defined features based on the set of temporal-based rules (box  360 ). These defined features include the rule set feature  155 , the rule frequency feature  160 , the distance feature  165 , and the distance frequency feature  170 . 
     IV.A.i. Extrinsic Feature Module 
     The extrinsic feature module  145  extracts features from the rules satisfied by the trace  115 . In general, this is performed by leveraging the extrinsic properties of rules. As noted above, extrinsic properties of rules are those properties that are independent of the internal structure of the rules. 
     IV.A.i.a. Rule Set Feature 
     One of the defined features based on the set of temporal-based rules satisfied by the trace  120  is the rule set feature  155 . Embodiments of the extrinsic feature module  145  include the rule set feature  155 . By construction, a sequence implicitly imposes an ordering between its elements. Therefore, these orderings can be perceived as describing the sequence and be considered as features of the sequence. Rules capturing the orderings between events of a trace can be considered as nominal features of the trace. Similarly, a set of rules can be considered as a feature as well. 
     Mathematically, the rule set feature  R (t) of t satisfying R(t) is R(t). 
     IV.A.i.b. Rule Frequency Feature 
     Another one of the defined features based on the set of temporal-based rules satisfied by the trace  120  is the rule frequency feature  160 . Embodiments of the extrinsic feature module  145  include the rule frequency feature  160 . For a given system, it is possible for two traces to satisfy the same set of rules while still capturing different behavior of the system. For example, an application that reads a database might do so with few failures in a good execution and with numerous failures in a bad execution. If the application programming interfaces (APIs) used in the application are traced, then traces of the above executions will satisfy the same set of rules about the ordering of APIs. However, the support for these rules in these traces will be different. Specifically, the trace of the good execution will have lower support for rules involving the database access API in comparison with the trace of the bad execution. In such cases, the support for the rules satisfied by a trace can be used as a feature of the trace. 
     While two traces capture the same behavior and satisfy the same set of rules, the support for the rules can be significantly different, depending on the length of the trace. Hence, the absolute rule support as a feature is too brittle in the context of comparative analysis. This shortcoming can be addressed by using the normalized support for the rules satisfied by a trace as ordinal feature of the trace. 
     Mathematically, given a set of rules R(t) for trace t, the normalized support  s (r) for a rule r is defined as,
 
 s ( r )/Σ r     i     εR ( t ) s ( r   i ),
 
and the rule frequency feature  160 ,
 
     s   ( t,R ( t ))
 
is defined as the mapping of all rules in R(t) to their normalized supports in t. In other words,
 
{( r,  s   ( r ))| rεR ( t )}.
 
Under a unique ordering of rules, the normalized frequency distribution of rules satisfied by a trace can also be used as a feature of the trace. Also, it should be noted that,      s    can be perceived as a random variable defined as the rules that describes some behavior. In addition, the normalized support can be perceived as the probability of the variable evaluating to any of the rule.
 
IV.B.i. Intrinsic Feature Module
 
     The intrinsic feature module  150  extracts features from the set of temporal-based rules satisfied by the trace  120  by leveraging the intrinsic properties of rules. As noted above, intrinsic properties are those properties that are dependent of the internal structure of the rules. 
     IV.B.i.a. Distance Feature 
     Another one of the defined features based on the set of temporal-based rules satisfied by the trace  120  is the distance feature  165 . Embodiments of the intrinsic feature module  150  include the distance feature  165 . Every temporal rule has an intrinsic property based on the involved events. In every witness to a rule, every pair of distinct events can be associated with distance measure. 
     Specifically, given a witness to a temporal rule in a trace, embodiments of the intrinsic feature module  150  measure the distance between any two events in the witness in terms of either elapsed time or intervening events. Thus, for every pair of abstraction positions of a rule, embodiments of the intrinsic feature module  150  collect the distance measures from each witness to the rule and calculate various summary statistics (such as Tukey&#39;s five numbers) of these measures. In different embodiments, various summary statistics of distance measures can be used as features of the corresponding rule. Consequently, these summary statistics can also be used as features of a satisfying trace. Depending on how the witness to a rule is constructed, distance can be sensitive to the length of the trace. To alleviate this issue, eager approaches can be used to construct the witnesses. 
     Mathematically, given a rule r, P(r) is the set of all pairs (i, j) of abstraction positions of r such that i&lt;j. Given a trace t that satisfies r, ç(p, r, t) is the summary of distance measures for,
 
 pεP ( r )
 
in t where ç is a summarizing function. The distance feature,
 
   η ( t,r )
 
of trace t satisfying rule r is defined as the mapping of all abstraction position pairs of r to their distance summary in t as provided by ç. This can be represented by the equation,
 
{( p ,η( p,r,t ))| pεP ( r )}.
 
IV.B.i.b. Distance Frequency Feature
 
     Another one of the defined features based on the set of temporal-based rules satisfied by the trace  120  is the distance frequency feature  170 . Embodiments of the intrinsic feature module  150  also include the distance frequency feature  170 . For a rule, each abstraction position pair can be associated with the frequency distribution of the distances between the abstraction positions in the witnesses to the rule. From this, embodiments of the intrinsic feature module  150  construct a feature that is similar to rule frequency feature. 
     Mathematically, given an abstraction position pair p=(i, j) of rule r satisfied by a trace t, the witness distances of p (denoted as Ä(p, r, t)) is the collection of distances between the i th  and j th  abstractions of all witnesses to r in t. The distance frequency feature  170 ,
 
   N ( t,r,p )
 
of trace t satisfying rule r with position pair p is the mapping of witness distances of p to their normalized frequency. In other words,
 
{(δ,    N   (δ))|δεΔ( p,r,t )},
 
where
 
   N   (δ)= N (δ)/|Δ( p,r,t )|
 
and N(δ) is the frequency of δ in Ä(p, r, t). As in the case of the rule frequency feature, the normalized frequency distribution of the distances for an abstraction position pair of a rule can be used as a feature of the rule. Consequently, it can be used a feature of the trace.
 
     IV.B. Similarity Measure Module 
     Embodiments of the similarity measure module  135  use a variety of similarity measures based on the features described above. Each of the modules that produce these similarity measures now will be discussed. 
     IV.B.i. Rule Set Based Similarity Measure Module 
     Embodiments of the rule set based similarity measure module  175  determine how similar two traces are based on the rule set feature  155 .  FIG. 4  is a flow diagram illustrating the operational details of embodiments of the rule set based similarity measure module  175  shown in  FIG. 1 . The operation begins by inputting a first trace and a second trace (box  400 ). In addition, a rule set feature  155  also is input (box  410 ). 
     Embodiments of the rule set based similarity measure module  175  then determine temporal-based rules that the first trace and the second trace have in common (box  420 ). This generates a similarity of the first trace and the second trace. In addition, embodiments of the rule set based similarity measure module  175  also determine temporal-based rules that the first trace and the second trace do not have in common (box  430 ). This generates a dissimilarity of the first trace and the second trace. A rule set based similarity measure then is computed that primarily depends on the similarity of the first trace and the second trace and secondarily depends on the dissimilarity of the first trace and the second trace (box  440 ). The output of embodiments of the rule set based similarity measure module  175  is the rule set based similarity measure (box  450 ). 
     Mathematically, let R(t 1 ) and R(t 2 ) the sets of rules satisfied by traces t 1  and t 2 , respectively. The set of rules R(t 1 )∩R(t 2 ) satisfied by both traces indicate the similarity between the traces and the number of such commonly satisfied rules is a measure of similarity. 
     By combining the rules from both sets and the rules common to both sets, an equation describing this similarity measure can be defined as: 
     
       
         
           
             
               
                 
                   
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     The above measure is undefined if the rule sets are empty. However, the measure can be extended to be zero when the rule sets for the traces are empty. 
     As  R(t)=R(t), Equation (1) above can be rewritten as: 
                     d   ⁡     (       t   1     ,     t   2       )       =     1   -                  ℵ   R     ⁡     (     t   1     )       ⋂       ℵ   R     ⁡     (     t   2     )                         ℵ   R     ⁡     (     t   1     )       ⋃       ℵ   R     ⁡     (     t   2     )                .               (   2   )               
IV.B.ii. Rule Frequency Based Similarity Measure Module
 
     Embodiments of the rule frequency based similarity measure module  180  determine how similar two traces are based on the rule frequency feature  160 . It is possible for two different traces to be deemed as similar by embodiments of the rule set based similarity measure module  175 . For example, consider an application that accesses a database over the network. The behavior of this application when the network connectivity is bad will differ from the behavior of the same application when the network connectivity is good. Specifically, the application may retry to establish connection to the database in the former case. Hence, the frequency of events that occur in both situations will differ in each situation. 
       FIG. 5  is a flow diagram illustrating the operational details of embodiments of the rule frequency based similarity measure module  180  shown in  FIG. 1 . The operation begins by inputting a first trace and a second trace (box  500 ). In addition, the rule frequency feature  160  is input (box  510 ). Next, embodiments of the rule frequency based similarity measure module  180  compute a first rule frequency distribution for a first set of temporal-based rules satisfied by the first trace (box  520 ). Embodiments of the rule frequency based similarity measure module  180  also compute a second rule frequency distribution for a second set of temporal-based rules satisfied by the second trace (box  530 ). 
     Embodiments of the rule frequency based similarity measure module  180  then compute a rule frequency based similarity measure (box  540 ). This is performed by comparing the first rule frequency distribution to the second rule frequency distribution. In some embodiments of the rule frequency based similarity measure module  180  the distributions are represented by a histogram. The output of embodiments of the rule frequency based similarity measure module  180  is the rule frequency based similarity measure (box  550 ). 
     Mathematically, embodiments of the rule frequency based similarity measure module  180  define t 1  and t 2  as two traces with,
 
     s   ( t   1   ,Q ) and      s (   t   2   ,Q )
 
rule frequency features, respectively, where Q is a set of rules satisfied by both t 1  and t 2 . Embodiments of the rule frequency based similarity measure module  180  define the similarity measure as follows:
 
     
       
         
           
             
               
                 
                   
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     It should be noted that alternatively the confidence of each rule r from Q in a trace t could be used instead of,
 
     s   ( t,Q )( r ),
 
to define the similarity measure. However, it is unclear how this similarity measure compares to the similarity measure defined in Equation (3) in terms of effectiveness. For example, in the above example scenario, it is possible that rules related database events will have high and similar confidence in both cases but the same rules will most likely differ in terms of support.
 
IV.B.iii. Distance Based Similarity Measure Module
 
     Embodiments of the distance based similarity measure module  185  determine how similar two traces are based on the distance feature  165 . It is possible for two different traces to be deemed as similar by embodiments of the rule frequency based similarity measure module  180 . For example, consider an application that accesses a database over the network. The behavior of this application in terms of the time duration between various database accessing actions and events is dependent on network latency. Thus, the application will observe larger latency under heavy network loads and consequently the time duration between various actions and events will be larger in such conditions. 
       FIG. 6  is a flow diagram illustrating the operational details of embodiments of the distance based similarity measure module  185  shown in  FIG. 1 . The operation begins by inputting a first trace and a second trace (box  600 ). In addition, the distance feature  165  is input (box  610 ). 
     Embodiments of the distance based similarity measure module  185  then define a temporal-based rule satisfied by the first trace as a first distance feature (box  620 ). In addition, distances between the first distance feature and distance features of a plurality of other traces are computed (box  630 ). The plurality of other traces also includes the second trace. 
     A determination then is made as to how the distance will be computed (box  640 ). A first way to compute distances is to use a mean of a distance between positions of abstraction position pairs across witnesses to the temporal-based rule (box  650 ). A second way to compute distances is to first find a greatest distance and a lowest distance between positions of the abstraction position pairs (box  660 ). Next, embodiments of the distance based similarity measure module  185  use the greatest distance and the lowest distance to compute the distances between the first distance feature and the distance features of the plurality of other traces (box  670 ). 
     Embodiments of the distance based similarity measure module  185  then compute a distance based similarity measure (box  680 ). This is achieved by finding a least distance between the first distance feature and the other distance features. The output from embodiments of the distance based similarity measure module  185  is the distance based similarity measure (box  690 ). 
     Mathematically, embodiments of the distance based similarity measure module  185  define t 1  and t 2  as two traces with,
 
   η ( t   1   ,r ) and    η ( t   2   ,r ),
 
distance features, respectively. Note that r is a rule satisfied by both t 1  and t 2 . Embodiments of the distance based similarity measure module  185  define the similarity measure as follows:
 
     
       
         
           
             
               
                 
                   
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     The effectiveness of this similarity measure depends on the choice of summary statistics provided by ç. For example, suppose ç provides the mean of the distance between positions of an abstraction position pair across all witnesses to the rule. While mean can be sensitive to outliers occurring at one end of the distribution, it can also be insensitive to outliers when they occur at both ends of the distribution. Thus, the similarity measure of Equation (4) can be ineffective. On the other hand, the width of the interval defined by the lowest and highest distance between positions of an abstraction position pair is sensitive to outliers. Thus, it can be used as an alternative summary statistics. 
     IV.B.iv. Distance Frequency Based Similarity Measure Module 
     Embodiments of the distance frequency based similarity measure module  190  determine how similar two traces are based on the distance frequency feature  170 . Similar to embodiments of the rule frequency based similarity measure module  180 , embodiments of the distance frequency based similarity measure module  190  leverage the normalized frequency of various distances between positions of an abstraction position pair as exhibited in various witnesses to a rule to define a distance frequency based similarity measure. 
       FIG. 7  is a flow diagram illustrating the operational details of embodiments of the distance frequency similarity measure module  190  shown in  FIG. 1 . Embodiments of the distance frequency similarity measure module  190  input a first trace and a second trace (box  700 ), and also input the distance frequency feature  170  (box  710 ). Next, distances between positions of abstraction position pairs as exhibited in witnesses to the temporal-based rule satisfied by the first trace are determined (box  720 ). 
     Embodiments of the distance frequency similarity measure module  190  the normalize the distances to obtain normalized distances between positions of the abstraction position pairs (box  730 ). Next, a first rule frequency distribution is computed for a first set of temporal-based rules satisfied by the first trace (box  740 ). Embodiments of the distance frequency similarity measure module  190  then compute the distance frequency based similarity measure by comparing the first rule frequency distribution to other rule frequency distributions of other traces (box  750 ). The output from embodiments of the distance frequency similarity measure module  190  is the rule frequency based similarity measure (box  760 ). 
     Mathematically, embodiments of the distance frequency based similarity measure module  190  define t 1  and t 2  as two traces with,
 
   η ( t   1   ,r,p ) and    N ( t   2   ,r,p ),
 
distance frequency features, respectively. Note that r is a rule satisfied by both t 1  and t 2  and p is a abstraction position pair of r. Embodiments of the distance frequency based similarity measure module  190  define the distance frequency based similarity measure as follows:
 
                       d   ⁡     (       t   1     ,     t   2     ,   r     )       =       ∑     p   ∈     P   ⁡     (   r   )           ⁢       ∑     i   ∈     I   p         ⁢       (         ℵ   N     ⁡     (       t   1     ,   r   ,   p     )       ⊥       (   i   )     -       ℵ   N     ⁡     (       t   2     ,   r   ,   p     )         ⊥     (   i   )       )     2           ,     
     ⁢   where   ,     
     ⁢       I   p     =       dom   ⁡     (       ℵ   N     ⁡     (       t   1     ,   r   ,   p     )       )       ⋃       dom   ⁡     (       ℵ   N     ⁡     (       t   2     ,   r   ,   p     )       )       ⁢           ⁢   and         ,     
     ⁢           ℵ   N     ⁡     (     t   ,   r   ,   p     )       ⊥     (   x   )       =     {               ℵ   N     ⁡     (     t   ,   r   ,   p     )       ⁢     (   x   )           :         x   ∈     dom   ⁡     (       ℵ   N     ⁡     (     t   ,   r   ,   p     )       )                 0       :         otherwise   .                       (   5   )               
V. Applications
 
     Embodiments of the temporal rule-based feature extraction system  100  and method extract features that can be used to classify, cluster, and fingerprint traces. In addition, the features extracted by embodiments of the temporal rule-based feature extraction system  100  and method can be used to identify differences between two traces. The details of how the extracted features are used to solve these problems will be discussed in detail. 
     V.A. Clustering Problem 
     Embodiments of the temporal rule-based feature extraction system  100  and method can address the problem of given a set of traces, create clusters of traces that capture the same behavior. Under the assumption that the temporal rules satisfied by a trace can be used either directly or indirectly (as features) to capture the behavior of a system captured in the trace, embodiments of the temporal rule-based feature extraction system  100  and method are used to extract features of traces, define a distance metric based on the extracted feature, and use it with existing clustering algorithms to cluster traces. 
     For example, a divisive clustering algorithm can be trivially adapted to use the rules satisfied by a trace as a feature. Specifically, rules can be mined from the given trace set and then used to iteratively partition the trace set based on the rules satisfied by a trace. In alternate embodiments, the trace set can be partitioned based on trace specific support for a rule. In each iteration, the rule can be chosen in the decreasing order of the support of the rules. In alternate embodiments, rules can be chosen in the order of the number of traces satisfying the rules. 
     To admit local changes in each partition, embodiments of the temporal rule-based feature extraction system  100  and method apply the algorithm to each trace partition separately by mining the rules for each partition and using them to create a sub-partition. Similarly, embodiments of the temporal rule-based feature extraction system  100  and method can devise rule-based agglomerative clustering algorithms. 
     Embodiments of the temporal rule-based feature extraction system  100  and method use the above strategies either alone or in any combination. In other words, different features may be used in different iterations such that any one or a combination of the four features extracted by embodiments of the system  100  and method can be used in these algorithms. 
     V.B. Classification Problem 
     Embodiments of the temporal rule-based feature extraction system  100  and method can address the problem that from a set of trace sets (or classes) such that all traces in a trace set capture the same behavior of the system, identify a trace set (if one exists) that captures the same behavior as a given trace. 
     One solution that embodiments of the temporal rule-based feature extraction system  100  and method use is to mine rules from the given trace and then use any of the features described above to define a distance metric to identify the closest trace set (or class). One trivial solution is to collapse the trace sets into a single set, add the given trace to this set, and cluster the traces in this set using techniques set forth above. Using this solution means that clustering will result in the same initial trace sets, with the exception of one trace set containing an additional element. Further, it will most likely be inefficient due to repetition of redundant classifications. 
     When comparing traces using the rules they satisfy, it is most likely that that rules may be similar but not identical. For example, the arguments to the same set of functions in call traces will be different. If such arguments are data bits owing between functions, then quantified rules will enforce identicalness. On the other hand, if the arguments are context-specific (such as a location of a configuration file, a non-zero value to indicate success), then some elements of the abstractions involved in a rule are dropped to establish similarity between rules. Embodiments of the temporal rule-based feature extraction system  100  and method considered rules to be similar if the difference in abstractions at the corresponding non-primary positions was no more than a given threshold. 
     V.C. Fingerprinting Problem 
     A fingerprint of an object or of data is a comparatively small piece of data that can uniquely identify the original object or data. Trivially, a subset of features of an object or data can be perceived as a fingerprint of the object or data. Hence, there can be numerous fingerprints for an object. Applications often are interested in only certain aspects of objects. Consequently, only fingerprints that help identify and distinguish objects along such aspects are relevant. 
     A trace captures the behavior of a system as observed or exhibited in terms of an specific alphabet (such as APIs and logging or tracing statements). Hence, a fingerprint of a trace can be perceived as representing the behavior of a system as captured in the trace. So, a fingerprint can be perceived as a signature of a specific behavior of the system. 
     Embodiments of the temporal rule-based feature extraction system  100  and method can address the problem that given a trace, generate a (behavioral) fingerprint of the trace based on the behavior of the system captured by the trace. Since temporal rules abstract the behavior of the system captured by the trace, these rules can be used to extract features of a trace. Consequently, a collection of features extracted from the temporal rules satisfied by a trace can be used as a fingerprint of the trace. 
     Such fingerprint can be softened (against outliers) by considering a subset of the rules. Of course, this will raise the issue of how to identify such a subset. Similarly, collections of other features extracted from temporal rules satisfied by a trace can be used as fingerprints of a trace. 
     V.D. Trace Diffing Problem 
     Embodiments of the temporal rule-based feature extraction system  100  and method can address the problem of identifying differences between two traces. In particular, given two traces, t 1  and t 2 , along with the sets of rules satisfied by these traces, embodiments of the temporal rule-based feature extraction system and method can leverage the above defined features and measures to help identify the differences between the traces. 
     First, for every rule that is not satisfied by a trace, the occurrences (if any) of the trigger event of the rule can be considered as the differences between the traces with respect to the rule. As every occurrence of the trigger event qualifies as a difference, such differences could be overwhelming when the frequency of the triggering event in the trace is high. 
     Second, let Q be the set of rules satisfied by traces, t 1  and t 2 . For every rule,
 
 rεQ,  
 
then,
 
(     s   ( t   1   ,Q )( r )−     s   ( t   2   ,Q )( r )) 2  
 
can be used to rank the rules in terms of the extent of deviation between traces as captured by a rule. With such ranking, a user can sift through the differences pertaining to the rules in order of the rank of the rules.
 
     Third, let r be a rule that is satisfied by traces, t 1  and t 2 . Then,
 
(   η ( t   1   ,r )( p )−   η ( t   2   ,r )( p )) 2  
 
can be used to rank the position pairs in the rule in terms of extent of deviation between traces as captured by a rule. This differentiating aspect can be used to merely suggest that the user should focus her attention on a specific position pair of witnesses to the rule while trying to identify the difference.
 
     Fourth, let p be an abstraction position pair in a rule r satisfied by traces, t 1  and t 2 . Let E p  be the set of all distances in,
 
 dom (Δ( t   1   ,r,p ))
 
that differ in terms of frequency in traces, t 1  and t 2 . Now, every witness with distances from E p  for p describes a difference between the traces, t 1  and t 2 .
 
VI. Exemplary Operating Environment
 
     Embodiments of the temporal rule-based feature extraction system  100  and method are designed to operate in a computing environment. The following discussion is intended to provide a brief, general description of a suitable computing environment in which embodiments of the temporal rule-based feature extraction system  100  and method may be implemented. 
       FIG. 8  illustrates an example of a suitable computing system environment in which embodiments of the temporal rule-based feature extraction system  100  and method shown in  FIGS. 1-7  may be implemented. The computing system environment  800  is only one example of a suitable computing environment and is not intended to suggest any limitation as to the scope of use or functionality of the invention. Neither should the computing environment  800  be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in the exemplary operating environment. 
     Embodiments of the temporal rule-based feature extraction system  100  and method are operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well known computing systems, environments, and/or configurations that may be suitable for use with embodiments of the temporal rule-based feature extraction system  100  and method include, but are not limited to, personal computers, server computers, hand-held (including smartphones), laptop or mobile computer or communications devices such as cell phones and PDA&#39;s, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like. 
     Embodiments of the temporal rule-based feature extraction system  100  and method may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Embodiments of the temporal rule-based feature extraction system  100  and method may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices. Still further, the aforementioned instructions could be implemented, in part or in whole, as hardware logic circuits, which may or may not include a processor. With reference to  FIG. 8 , an exemplary system for embodiments of the temporal rule-based feature extraction system  100  and method includes a general-purpose computing device in the form of a computer  810 . 
     Components of the computer  810  may include, but are not limited to, a processing unit  820  (such as a central processing unit, CPU), a system memory  830 , and a system bus  821  that couples various system components including the system memory to the processing unit  820 . The system bus  821  may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus also known as Mezzanine bus. 
     The computer  810  typically includes a variety of computer readable media. Computer readable media can be any available media that can be accessed by the computer  810  and includes both volatile and nonvolatile media, removable and non-removable media. By way of example, and not limitation, computer readable media may comprise computer storage media and communication media. Computer storage media includes volatile and nonvolatile removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. 
     Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computer  810 . By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of any of the above should also be included within the scope of computer readable media. 
     The system memory  830  includes computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM)  831  and random access memory (RAM)  832 . A basic input/output system  833  (BIOS), containing the basic routines that help to transfer information between elements within the computer  810 , such as during start-up, is typically stored in ROM  831 . RAM  832  typically contains data and/or program modules that are immediately accessible to and/or presently being operated on by processing unit  820 . By way of example, and not limitation,  FIG. 8  illustrates operating system  834 , application programs  835 , other program modules  836 , and program data  837 . 
     The computer  810  may also include other removable/non-removable, volatile/nonvolatile computer storage media. By way of example only,  FIG. 8  illustrates a hard disk drive  841  that reads from or writes to non-removable, nonvolatile magnetic media, a magnetic disk drive  851  that reads from or writes to a removable, nonvolatile magnetic disk  852 , and an optical disk drive  855  that reads from or writes to a removable, nonvolatile optical disk  856  such as a CD ROM or other optical media. 
     Other removable/non-removable, volatile/nonvolatile computer storage media that can be used in the exemplary operating environment include, but are not limited to, magnetic tape cassettes, flash memory cards, digital versatile disks, digital video tape, solid state RAM, solid state ROM, and the like. The hard disk drive  841  is typically connected to the system bus  821  through a non-removable memory interface such as interface  840 , and magnetic disk drive  851  and optical disk drive  855  are typically connected to the system bus  821  by a removable memory interface, such as interface  850 . 
     The drives and their associated computer storage media discussed above and illustrated in  FIG. 8 , provide storage of computer readable instructions, data structures, program modules and other data for the computer  810 . In  FIG. 8 , for example, hard disk drive  841  is illustrated as storing operating system  844 , application programs  845 , other program modules  846 , and program data  847 . Note that these components can either be the same as or different from operating system  834 , application programs  835 , other program modules  836 , and program data  837 . Operating system  844 , application programs  845 , other program modules  846 , and program data  847  are given different numbers here to illustrate that, at a minimum, they are different copies. A user may enter commands and information (or data) into the computer  810  through input devices such as a keyboard  862 , pointing device  861 , commonly referred to as a mouse, trackball or touch pad, and a touch panel or touch screen (not shown). 
     Other input devices (not shown) may include a microphone, joystick, game pad, satellite dish, scanner, radio receiver, or a television or broadcast video receiver, or the like. These and other input devices are often connected to the processing unit  820  through a user input interface  860  that is coupled to the system bus  821 , but may be connected by other interface and bus structures, such as, for example, a parallel port, game port or a universal serial bus (USB). A monitor  891  or other type of display device is also connected to the system bus  821  via an interface, such as a video interface  890 . In addition to the monitor, computers may also include other peripheral output devices such as speakers  897  and printer  896 , which may be connected through an output peripheral interface  895 . 
     The computer  810  may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer  880 . The remote computer  880  may be a personal computer, a server, a router, a network PC, a peer device or other common network node, and typically includes many or all of the elements described above relative to the computer  810 , although only a memory storage device  881  has been illustrated in  FIG. 8 . The logical connections depicted in  FIG. 8  include a local area network (LAN)  871  and a wide area network (WAN)  873 , but may also include other networks. Such networking environments are commonplace in offices, enterprise-wide computer networks, intranets and the Internet. 
     When used in a LAN networking environment, the computer  810  is connected to the LAN  871  through a network interface or adapter  870 . When used in a WAN networking environment, the computer  810  typically includes a modem  872  or other means for establishing communications over the WAN  873 , such as the Internet. The modem  872 , which may be internal or external, may be connected to the system bus  821  via the user input interface  860 , or other appropriate mechanism. In a networked environment, program modules depicted relative to the computer  810 , or portions thereof, may be stored in the remote memory storage device. By way of example, and not limitation,  FIG. 8  illustrates remote application programs  885  as residing on memory device  881 . It will be appreciated that the network connections shown are exemplary and other means of establishing a communications link between the computers may be used. 
     The foregoing Detailed Description has been presented for the purposes of illustration and description. Many modifications and variations are possible in light of the above teaching. It is not intended to be exhaustive or to limit the subject matter described herein to the precise form disclosed. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims appended hereto.