JP2014146280A - Association calculation device, association calculation system, association calculation method, and association calculation program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a mechanism of association calculation including a technology which suppresses computational complexity of association calculation.SOLUTION: On a graph structure data which is a data model which expresses a relationship among data by a relationship between a node and edge, an association calculation device 10 calculates a propagation value from a node to an adjacent node for every edge using association of a node and weight of edge, and repeatedly calculates an association of each node to a set of node and using the propagation value of the edge. Then, the association calculation device 10 excludes a predetermined node from the node as a calculation object on the basis of the association of the node or the propagation value of the edge, every time an association of a node is calculated. Then, the association calculation device 10 calculates the association of the node of the calculation object in which the predetermined node is excluded.

Description

  The present invention relates to an association degree calculation device, an association degree calculation system, an association degree calculation method, and an association degree calculation program.

  Conventionally, graph structure data, which is a data model that expresses a relationship between data by a relationship between nodes and edges, is known. For example, when the computers and their connection relationships illustrated in FIG. 14 are given, the graph structure data is used to express these computers and their connection relationships in a data model as illustrated in FIG. be able to. In recent years, interest in the use of graph theory has increased due to the realization of advanced and high-quality search processing by applying graph theory to Personalized Search. In using this graph theory, the degree of association between nodes is one of the important attributes, and it is applied to applications in various fields, and various methods for calculating the degree of association have been proposed.

  As such a relevance calculation method, for example, a calculation method called Personalized Page Rank is one of the methods attracting attention as a relevance calculation method between nodes. Personalized Page Rank can calculate the degree of relevance based on the structural features of the graph, unlike the shortest distance between nodes that has been often used in graph theory.

  In this Personalized Page Rank, a random walk is started from the existence probability of each node based on the query distribution, and moves randomly to an adjacent node with a probability proportional to the edge weight. Furthermore, every time the node is reached, the node returns to the node with a probability based on the query distribution with a certain probability. As a result of recursively repeating this operation, a steady state probability at each node is obtained. In Personalized Page Rank, the obtained steady state probability is a method of using the degree of relevance.

  Here, with reference to FIG. 16, an example of an algorithm for calculating the degree of association in the Personalized Page Rank will be described. In the example of FIG. 16, in this algorithm, V and Cu are set as a set of all nodes in the graph and a set of adjacent nodes to which edges coming from the node u are connected. In addition, s ′ is a relevance degree after update calculated in repetition, and p is a propagation value of the relevance degree calculated between nodes. Here, the propagation value is obtained by multiplying the degree of relevance of the node and the weight of the edge.

  As shown in FIG. 16, first, the relevance distribution s is initialized to the inquiry distribution d (see the first line). Then, in the repetitive calculation, first, the degree of association after the update is initialized to 0 (see the third to fifth lines). After that, for all the nodes, the related values that the edges coming out of those nodes propagate to other nodes are calculated (see the 6th to 11th lines). Then, the updated degree of association is obtained from the propagated degree of association (see the 12th and 13th lines). Thereafter, the relevance calculation using the entire graph is recursively executed until a predetermined repetition condition is satisfied.

“A Survey on PageRank Computing”, Pavel Berkhin, Internet Mathematics Vol.2, 2005 “Fast and Exact Top-k Search for Random Walk with Restart”, Yasuhiro Fujiwara, Makoto Nakatsuji, Makoto Onizuka, Masaru Kitsuregawa, PVLDB Endowment, Vol.5, No.5 2012 “Network analysis (data science 8 learned with R)”, Tsutomu Suzuki, Satoshi Kimmei, Kyoritsu Publishing

  However, in the above-described conventional technique, since the calculation of the degree of association using the entire graph is repeatedly performed, there is a problem that the amount of calculation required for calculating the degree of association is large. For this reason, in order to effectively use relevance in practical applications such as realization of advanced and efficient search processing, the amount of calculation required to calculate relevance is reduced and relevance is efficiently calculated. It becomes a problem to do.

  Accordingly, the present invention has been made to solve the above-described problems of the related art, and an object of the present invention is to provide a relevance calculation mechanism having a technique for suppressing the calculation amount of relevance calculation.

  In order to solve the above-described problems and achieve the object, the relevance calculation apparatus according to the present invention is a graph structure data that is a data model that expresses a relationship between data as a relationship between a node and an edge. A relevance calculation unit for calculating a propagation value for each node using the relevance of the node and the weight of the edge, and repeatedly calculating the relevance of each node with respect to the aggregate of nodes using the propagation value of the edge; A deletion unit that excludes a predetermined node from a calculation target node based on the degree of association of the node or the propagation value of the edge each time the degree of association of the node is calculated by the degree of association calculation unit, The relevance calculation unit calculates the relevance of the calculation target node from which the predetermined node is excluded.

  In addition, the relevance calculation system according to the present invention is a graph structure data that is a data model that expresses a relationship between data as a relationship between a node and an edge. And a relevance calculation unit that repeatedly calculates the relevance of each node to a set of nodes using the propagation value of the edge, and the relevance of the node is calculated by the relevance calculation unit. A deletion unit that excludes a predetermined node from a calculation target node based on the relevance level of the node or the propagation value of the edge each time the relevance calculation unit includes the predetermined node. The degree of association of the excluded nodes to be calculated is calculated.

  In addition, the relevance calculation method according to the present invention is a graph model data representing a data model that expresses a relationship between data as a relationship between a node and an edge. The relevance calculation step of calculating the relevance of each node with respect to the aggregate of nodes using the propagation value of the edge, and the relevance of the node is calculated by the relevance calculation step. Each step of deleting the predetermined node from the calculation target node based on the relevance of the node or the propagation value of the edge, and the relevance calculation step includes: The degree of association of the excluded nodes to be calculated is calculated.

  In addition, the relevance calculation program according to the present invention provides the propagation value from a node to an adjacent node using the relationship between the node and the edge weight in the graph structure data that is a data model expressing the relationship between the data by the relationship between the node and the edge. The relevance calculation step of repeatedly calculating the relevance of each node with respect to the aggregate of nodes using the propagation value of the edge, and calculating the relevance of the node by the relevance calculation step Each time, the computer executes a deletion step of excluding a predetermined node from the calculation target node based on the degree of association of the node or the propagation value of the edge. The relevance level of the calculation target node from which the node is excluded is calculated.

  According to the relevance calculation device, the relevance calculation system, the relevance calculation method, and the relevance calculation program according to the embodiment, it is possible to provide a relevance calculation mechanism having a technique for suppressing the calculation amount of relevance calculation. There is an effect that can be done.

FIG. 1 is a diagram for explaining the configuration of the relevance calculation apparatus according to the first embodiment. FIG. 2 is a diagram illustrating an example of an algorithm for calculating the degree of association. FIG. 3 is a diagram illustrating an example of a graph expressed by nodes and edges and an inquiry distribution value. FIG. 4 is a diagram illustrating an example of a graph expressed by nodes and edges, and values of relevance. FIG. 5 is a diagram illustrating an example of a graph expressed by nodes and edges after node pruning, and values of relevance. FIG. 6 is a flowchart illustrating the flow of the relevance calculation process performed by the relevance calculation apparatus according to the first embodiment. FIG. 7 is a diagram illustrating an example of a result when the relevance calculation is performed by the relevance calculation apparatus according to the first embodiment. FIG. 8 is a diagram for explaining the configuration of the relevance calculation apparatus according to the second embodiment. FIG. 9 is a diagram illustrating an example of edges rearranged in descending order of weight. FIG. 10 is a diagram illustrating an example of an algorithm for calculating the degree of association. FIG. 11 is a flowchart illustrating a relevance calculation process performed by the relevance calculation apparatus according to the second embodiment. FIG. 12 is a diagram illustrating an example of a result when the relevance calculation is performed by the relevance calculation apparatus according to the second embodiment. FIG. 13 is a diagram illustrating that the information processing by the relevance calculation apparatus program is specifically realized using a computer. FIG. 14 is a diagram illustrating an example of a computer connection relationship. FIG. 15 is a diagram illustrating an example of a connection relationship between computers expressed as a relationship between nodes and edges. FIG. 16 is a diagram illustrating an example of an algorithm for calculating the related degree of related art.

  Exemplary embodiments of an association degree calculation device, an association degree calculation system, an association degree calculation method, and an association degree calculation program according to the present invention will be described below in detail with reference to the accompanying drawings. Note that the present invention is not limited to the embodiments. For example, in the following explanation, an example of calculating the degree of relevance using Personalized Page Rank will be described, but the present invention is not limited to this. Methods other than Personalized Page Rank (for example, Page Rank and Random The present invention can also be applied to the case where the relevance is calculated using “walk with restart” or the like.

  In the following embodiments, the configuration of the relevance calculation device included in the relevance calculation system according to the first embodiment and the flow of processing will be described in order, and finally the effects of the first embodiment will be described.

[Configuration of relevance calculation device]
First, the relevance calculation device 10 included in the relevance calculation system according to the first embodiment will be described with reference to FIG. FIG. 1 is a diagram for explaining the configuration of the association degree calculation apparatus 10 according to the first embodiment. As shown in FIG. 1, the relevance calculation system according to the first embodiment includes a relevance calculation apparatus 10 and a user terminal 20. The relevance calculation system 10 and the user terminal 20 are connected via, for example, the Internet (not shown).

  The degree-of-association calculation apparatus 10 includes a communication control unit 11 and a control unit 12, and is connected to the user terminal 20 via the Internet or the like. The processing of each of these units will be described below.

  The communication control unit 11 controls communication related to various information exchanged with the user terminal 20 connected via the Internet or the like. Specifically, the communication control unit 11 receives from the user terminal 20 the inquiry distribution d, the graph adjacency matrix W, the restart probability c, the number of iterations T, and the pruning threshold value θ. Further, the communication control unit 11 transmits the calculated relevance distribution to the user terminal 20.

  The control unit 12 controls various processes executed in the relevance calculation apparatus 10. Specifically, as shown in FIG. 1, the control unit 12 includes a relevance calculation unit 12a and a deletion unit 12b.

  The degree-of-association calculation unit 12a is configured to display a propagation value from a node to an adjacent node for each edge by using the degree of association of the node and the weight of the edge in the graph structure data that is a data model that expresses the relationship between the data by the relationship between the node and the edge. And the degree of relevance of each node to the set of nodes is repeatedly calculated using the propagation value of the edge. The relevance calculation unit 12a calculates the relevance of the calculation target node from which a predetermined node is excluded by the deletion unit 12b described later. In addition, the relevance calculation unit 12a repeatedly calculates the relevance of nodes according to a preset number of repetitions T.

  For example, the relevance calculation unit 12a calculates the relevance of each node using the algorithm illustrated in FIG. FIG. 2 is a diagram illustrating an example of an algorithm for calculating the degree of association. In the algorithm shown in FIG. 2, V and Cu are set as a set of all nodes in the graph and a set of adjacent nodes to which edges coming from the node u are connected. In addition, s ′ is the relevance degree after update calculated in repetition, and p is a propagation value of the relevance degree calculated between nodes. Further, the relevance value of a node after updating is calculated from the sum of propagation values from adjacent nodes connected to that node. V ′ is a set of nodes after pruning, and θ is a threshold for pruning.

  As shown in FIG. 2, the relevance calculation unit 12a first initializes the relevance distribution s to the query distribution d, and initializes the node set V ′ to the entire node set V (see the first and second lines). ). Further, the relevance calculation unit 12a sets the calculation count t to “1”. Then, the relevance calculation unit 12a selects the node u from the set V of all nodes, and initializes the relevance s ′ after the node update to 0 (see the 4th to 6th lines).

  Subsequently, in the repetitive calculation, the relevance calculation unit 12a calculates the propagation value p from each node not from the set V of all nodes but from the set V ′ of nodes after pruning narrowing down the propagation target. (See lines 7-12). Specifically, the relevance calculation unit 12a selects the node u from V ′ and the node v from Cu. Then, the relevance calculation unit 12a calculates the propagation value p by multiplying the adjacency matrix W of the graph indicating the relevance s of the node and the edge weight, that is, p = W [v, u] s [u] Calculate (see the ninth line), and use the calculated p to calculate s ′ [v] = s ′ [v] + p (see the tenth line). This process is repeated for all pairs of V 'and Cu nodes. Thereafter, the relevance calculation unit 12a calculates s ′ = (1-c) s ′ [v] + cd (see the 13th line), and sets the relevance distribution s as the relevance s ′ after update (14 See line). Then, the relevance calculation unit 12a outputs the calculated relevance distribution s to the deletion unit 12b, and stores the relevance distribution s in a storage unit (not shown) included in the deletion unit 12b.

  Thereafter, in the relevance calculation unit 12a, a storage unit (not shown) is stored in the deletion unit 12b described later, and V ′ including only nodes whose node relevance s ′ is equal to or greater than the pruning threshold θ, and the V ′ And the above relevance calculation process is repeated for a preset number of repetitions T. As described above, the relevance calculation unit 12a calculates the propagation value of the relevance only for the propagation from the node having a high relevance whose relevance is equal to or higher than the pruning threshold θ in the repetitive calculation, and results in high speed Calculate relevance. Then, the relevance calculation unit 12 a outputs the calculated relevance distribution s to the user terminal 20 when the relevance calculation process is repeated for the number of repetitions T.

  The deletion unit 12b excludes a predetermined node from the calculation target node every time the relevance level of the node is calculated by the relevance level calculation unit 12a. Specifically, the deletion unit 12b reads the degree of association of the node calculated by the degree of association calculation unit 12a from the storage unit, determines whether the degree of association of the node is less than a pruning threshold, Nodes whose node relevance is less than the pruning threshold are excluded from the nodes to be calculated.

  If it demonstrates with reference to FIG. 2, the deletion part 12b calculates | requires the set of nodes after pruning from the relevance degree updated in each repetition calculation (refer 15th-20th line). Specifically, as illustrated in FIG. 2, the deletion unit 12b initializes the node set V ′ after pruning to 0 (see the 15th line), and then calculates each relevance calculation unit 12a. It is determined whether or not the node relevance s ′ of the node u is greater than or equal to the pruning threshold value θ (see the 17th line). As a result, the deletion unit 12b adds only nodes whose node relevance s ′ is equal to or greater than the pruning threshold θ to the V ′ (see the 18th line), and nodes whose node relevance s ′ is lower than the pruning threshold θ. Is deleted from the node for which relevance is calculated. Thereafter, the deletion unit 12b outputs the node set V ′ after pruning to the relevance calculation unit 12a, and stores the node set V ′ in a storage unit (not shown) included in the relevance calculation unit 12a.

  Here, the outline | summary of the relevance calculation process which the relevance degree calculation apparatus 10 performs is demonstrated using FIGS. FIG. 3 is a diagram illustrating an example of a graph expressed by nodes and edges and an inquiry distribution value. FIG. 4 is a diagram illustrating an example of a graph expressed by nodes and edges, and values of relevance. FIG. 5 is a diagram illustrating an example of a graph expressed by nodes and edges after node pruning, and values of relevance.

  In the example of FIGS. 3 to 5, there are a plurality of nodes A to H, and the nodes are connected by edges. First, as shown in FIG. 3, the existence probabilities determined from the query distribution are set for the nodes A to C. Further, as illustrated in FIG. 3, the existence probability of the node A is “0.5”, the existence probability of the node B is “0.25”, and the existence probability of the node C is “0.25”. is there. Here, the existence probability is a probability of each node at which the random walk is started. For example, the nodes A to C are sites bookmarked by the user, and the existence probability is the probability of each site that the user will access first.

  Next, as shown in FIG. 4, the relevance calculation device 10 calculates the relevance of the nodes A to H for all in the first relevance calculation. As illustrated in FIG. 4, the relevance of node A is “0.22”, the relevance of node B is “0.18”, the relevance of node C is “0.21”, and the relevance of node D is “0.18”, the relevance of node E is “0.11”, the relevance of node F is “0.05”, the relevance of node G is “0.02”, and the relevance of node H is “0”. .33 ". Here, the degree of association is the degree of importance that is individualized for the inquiry node. That is, a specific example will be described. For example, when the nodes A to C are news sites bookmarked by the user, the relevance of the nodes of the news sites that are not bookmarked is increased.

  Next, after calculating the relevance level, the relevance level calculation apparatus 10 determines whether each relevance level is lower than a pruning threshold before performing the next relevance level calculation process. For example, when the pruning threshold is “0.04”, in the example of FIG. 4, the degree of association between the node G and the node H is lower than the pruning threshold “0.04”. Therefore, as illustrated in FIG. 5, the node G and the node H lower than the pruning threshold “0.04” are deleted from the calculation target nodes, and the next relevance calculation process is performed.

  In this way, nodes with small relevance with updated relevance less than the threshold θ in the repeated calculation (nodes G and H in the examples of FIGS. 4 and 5) are deleted (pruned) from the calculation target nodes. To do. As a result, there is no need to calculate the propagation value from the pruned node, so the amount of propagation value calculation is reduced, and as a result, the relevance can be calculated at high speed. This method is based on the knowledge that “a node or an edge having a low degree of association does not greatly affect the value of the degree of association after update”. In other words, even if nodes or edges with low relevance are excluded, the relevance value after update is not greatly affected. Can be performed efficiently.

[Relevance calculation processing by relevance calculator]
Next, the flow of relevance calculation processing by the relevance calculation apparatus 10 will be described with reference to FIG. FIG. 6 is a flowchart illustrating the flow of the relevance calculation process performed by the relevance calculation apparatus according to the first embodiment. As illustrated in FIG. 6, when the relevance calculation unit 12a of the relevance calculation apparatus 10 receives a relevance calculation start instruction from the user terminal 20 (Yes in step S101), first, the relevance distribution s is initially set to the inquiry distribution d. The node set V ′ is initialized to the entire node set V (step S102). Then, the relevance calculation unit 12a sets the calculation count t to “1” (step S103).

  Subsequently, the relevance calculation unit 12a selects the nodes u one by one from the node set V (step S104), and initializes the relevance s ′ [u] after updating the node u to 0 (step S105). ). Then, the relevance calculation unit 12a determines whether or not all nodes have been selected from V (step S106), and if not all nodes have been selected from V (No in step S106), the process proceeds to step S104. Return. Further, when all the nodes are selected from V (Yes at Step S106), the relevance calculation unit 12a selects the nodes u one by one from the node set V ′ (Step S107), and selects one node v. Each node is selected from a set Cu of nodes (step S108).

  Then, the relevance calculation unit 12a calculates p = W [v, u] s [u], and calculates s ′ [v] = s ′ [v] + p using the calculated p (step S109). Subsequently, the relevance calculation unit 12a determines whether or not the relevance calculation unit 12a has selected all the nodes from Cu (step S110). If all the nodes have not been selected from Cu ( No at Step S110), the process returns to Step S108. Further, when all the nodes are selected from Cu (Yes at Step S110), the relevance calculation unit 12a determines whether all the nodes are selected from V ′ (Step S111), and all the nodes from V ′ are determined. If no node is selected (No at step S111), the process returns to step S107.

  Further, when all the nodes are selected from V ′ (Yes at Step S111), the relevance calculation unit 12a calculates s ′ = (1-c) s ′ [v] + cd, and the relevance distribution s Is the relevance s ′ after the update (step S112).

  Then, the deletion unit 12b of the relevance calculation apparatus 10 initializes the pruned node set V ′ to 0 (step S113), and then selects the nodes u one by one from the node set V (step S114). ). Then, the deletion unit 12b determines whether or not the node association degree s ′ of each node u calculated by the association degree calculation unit 12a is greater than or equal to the pruning threshold value θ (step S115). As a result, when the node relevance s ′ of the node u is greater than or equal to the pruning threshold θ (Yes in step S115), the deleting unit 12b adds the node u to the node set V ′ after pruning (step S115). S116), the process proceeds to step S117. When the node relevance s ′ of the node u is less than the pruning threshold θ (No in step S115), the deletion unit 12b determines that the node relevance s ′ is lower than the pruning threshold θ. The node is excluded from the calculation target nodes, and the process proceeds to step S117.

  In step S117, the deletion unit 12b determines whether all nodes have been selected from the node set V. If all nodes have not been selected from the node set V (No in step S117), the process proceeds to step S114. Return. If it is determined that the deletion unit 12b has selected all the nodes from the node set V (Yes at Step S117), the relevance calculation unit 12a adds 1 to the calculation count t (Step S118), and the calculation is performed. It is determined whether or not the number of times t has exceeded the number of repeated calculations T (step S119).

  As a result, when it is determined that the calculation count t does not exceed the repeat calculation count T (No at Step S119), the relevance calculation unit 12a returns to Step S104 to perform the relevance calculation processing. In the relevance level calculation process here, the relevance level is calculated from a set V ′ of nodes to be calculated from which nodes with low relevance levels are excluded. Also, when the relevance calculation unit 12a determines that the calculation count t has exceeded the repetitive calculation count T (Yes in step S119), the relevance distribution s is output to the user terminal 20 (step S120), and the relevance calculation The process ends.

[Experimental result of relevance calculation processing by relevance calculator]
Next, experimental results of the relevance calculation process performed by the relevance calculation apparatus according to the first embodiment will be described with reference to FIG. In addition, about an experimental result, it is an example to the last, and a structure or a process is not limited by this. FIG. 7 is a diagram illustrating an example of a result when the relevance calculation is performed by the relevance calculation apparatus according to the first embodiment. Note that “node pruning” illustrated in FIG. 7 indicates the experimental result of the relevance calculation processing by the relevance calculation apparatus according to the first embodiment, and “original” indicates the relevance calculation according to the conventional algorithm. Experimental results are shown.

In this experiment, the number of nodes was 265214 and the number of edges was 420045. In this experiment, c = 0.15, T = 100, and one random starting node is set at random. In the method of pruning nodes, the experiment was performed with the pruning threshold θ set to 10 ⁻³ and 10 ⁻⁷ .

FIG. 7 shows that the present invention can calculate the relevance at a higher speed than the conventional method. In the example of FIG. 7, the conventional calculation time is “1.01 [s]”, but in the method of the present invention, when the threshold θ is 10 ⁻³ , “0.05 [s] ] ”And the threshold θ is 10 ⁻⁷ , it is“ 0.46 [s] ”. It can also be seen that the higher the pruning threshold, the faster the relevance can be calculated. This is because a larger threshold value allows more nodes to be pruned.

It can also be seen from FIG. 7 that the relevance error in the present invention is a very small value. As shown in FIG. 7, in the method of the present invention, when the threshold θ is 10 ⁻³ , the average error is “3.15 · 10 ⁻⁸ ” compared to the conventional method, and the threshold θ is 10 ^When it is ⁻⁷ , it is “4.81 · 10 ⁻¹¹ ”. This is because the method of the present invention prunes the node, but the threshold value is set so as not to affect the relevance value as much as possible. FIG. 7 also shows that the present invention can calculate the degree of relevance with higher accuracy when the threshold value is smaller. This is because the calculation accuracy of the relevance is improved because more nodes or edges are to be calculated when the threshold value is smaller. From these results, it can be seen that in the present invention, the threshold value should be increased if high-speed calculation is desired, and the threshold value should be decreased if high-precision calculation is desired.

[Effect of Example 1]
As described above, the degree-of-association calculation apparatus 10 according to the first embodiment uses a graph structure data, which is a data model that expresses a relationship between data as a relationship between a node and an edge. Calculation is performed for each edge using the degree of association and the weight of the edge, and the degree of association of each node with respect to the aggregate of nodes is repeatedly calculated using the propagation value of the edge. Then, each time the degree of association of the node is calculated, the degree-of-association calculation apparatus 10 excludes a predetermined node from the calculation target node based on the degree of association of the node or the propagation value of the edge. Then, the relevance calculation device 10 calculates the relevance of the calculation target node from which a predetermined node is excluded. As a result, nodes with low relevance can be excluded from the nodes to be calculated. As a result, it is possible to provide a relevance calculation mechanism having a technique for suppressing the calculation amount of relevance. In addition, it is possible to adjust the accuracy of the calculation speed in the relevance calculation by adjusting the threshold.

  Further, the relevance calculation apparatus 10 according to the first embodiment determines whether or not the calculated relevance of the node is less than a predetermined threshold, and determines the node having the relevance of the node less than the threshold as a calculation target. Exclude from the node. For this reason, pruning can be performed by excluding nodes with low relevance from the nodes to be calculated, and in the calculation process after pruning, relevance is calculated from the narrowed down nodes. It is possible to suppress the calculation amount of the relevance calculation.

  In addition, the relevance calculation apparatus 10 according to the first embodiment repeatedly calculates the relevance of nodes according to a preset number of repetitive calculations. For this reason, it is possible to easily change the number of repetitions of relevance calculation.

  By the way, in the above-described first embodiment, a case where a node having a low degree of association is excluded from a calculation target node has been described. However, the present invention is not limited to this. For example, the calculation of an edge having a low degree of association is stopped, You may make it exclude the node connected to the edge from calculation object. Thus, in a second embodiment described below, a case will be described in which calculation of an edge having a low degree of association is stopped and a node connected to the edge is excluded from the calculation target.

  First, the configuration of the relevance calculation apparatus 10A according to the second embodiment will be described with reference to FIG. FIG. 8 is a diagram for explaining the configuration of the relevance calculation apparatus according to the second embodiment. In addition, description is abbreviate | omitted about the structure similar to the relevance calculation apparatus 10 which concerns on Example 1. FIG.

  As illustrated in FIG. 8, the relevance calculation apparatus 10A according to the second embodiment further includes a rearrangement unit 1c2 as compared with the relevance calculation apparatus 10 according to the first embodiment. The rearrangement unit 12c sets the weight value of the edge connected to the node for each node, and rearranges the edges in descending order of the weight value. Here, to explain using the example of FIG. 3, the rearrangement unit 12 c has an edge connected to the node B (here, an edge with the edge ID “1”) and an edge connected to the node C (here In this case, it is connected to two edges having an edge ID “2”.

  Here, as illustrated in FIG. 9, for the edge of edge ID1 that connects node A and node B, the weight value is “0.6”, and for the edge of edge ID2 that connects node A and node C, When the weight value is “0.4”, the rearrangement unit 12c rearranges in order of edge ID1 and edge ID2 in descending order of the weight value. FIG. 9 is a diagram illustrating an example of edges rearranged in descending order of weight.

  Further, the relevance calculation unit 12a of the relevance calculation apparatus 10A according to the second embodiment calculates edge propagation values in the order rearranged by the rearrangement unit 12c, and calculates the relevance of each node. Specifically, the relevance calculation unit 12a calculates a relevance distribution using the algorithm illustrated in FIG. In the algorithm in FIG. 10, V and Cu are set as a set of all nodes in the graph and a set of adjacent nodes to which edges coming from the node u are connected. In addition, s ′ is the relevance degree after update calculated in repetition, and p is a propagation value of the relevance degree calculated between nodes. Further, the relevance value of a node after updating is calculated from the sum of propagation values from adjacent nodes connected to that node. V ′ is a set of nodes after pruning, and θ is a threshold for pruning.

  As shown in FIG. 10, the relevance calculation unit 12a first initializes the relevance distribution s to the inquiry distribution (see the first line). And in order to perform efficient calculation pruning in repeated calculations, the edge that comes out of each node is assigned to the edge weight (corresponding to the size of the non-zero element of the adjacency matrix of the graph) Sort in descending order (see lines 2-4).

  Then, the relevance calculation unit 12a calculates a propagation value p from each node to another adjacent node in the repeated calculation (see the 11th line).

  The deletion unit 12b determines whether the propagation value of the edge calculated by the relevance calculation unit 12a is less than the pruning threshold. If the propagation value of the edge is less than the pruning threshold, the deletion unit 12b The calculation of the propagation value of the edge having a weight value smaller than the weight value is stopped, and the node connected by the edge is excluded from the calculation target nodes.

  That is, at each node, in the process of calculating the propagation value to the adjacent node adjacent to the node using the set of edges, the propagation value to the other adjacent node calculated thereafter from the propagation value to a certain adjacent node is When it is found that the value is smaller than the pruning threshold value θ, the calculation of the propagation value for the remaining uncalculated adjacent nodes including the other adjacent nodes is stopped (pruning the calculation), and as a result, the relevance is high. Perform the calculation.

  Specifically, as shown in FIG. 10, if the calculated propagation value is smaller than the pruning threshold θ, the deletion unit 12b applies to the remaining uncalculated adjacent nodes having the following edge weights from the node. The calculation of the propagation value is pruned (see the 13th to 15th lines). This is because the edges are rearranged in the descending order of weight, so that the propagation value to the remaining adjacent node scheduled to be calculated thereafter does not become larger than θ. Since this method can efficiently prun the calculation of the propagation value to the node connected with the edge whose propagation value is smaller than the predetermined threshold value, the relevance can be calculated at high speed.

[Relevance calculation processing by relevance calculator]
Next, the flow of relevance calculation processing by the relevance calculation apparatus 10A will be described with reference to FIG. FIG. 11 is a flowchart illustrating a relevance calculation process performed by the relevance calculation apparatus according to the second embodiment. As illustrated in FIG. 11, when the reordering unit 12c of the relevance calculation apparatus 10A receives a relevance calculation start instruction from the user terminal 20 (Yes in step S201), first, the relevance distribution s is initialized to the inquiry distribution d. (Step S202).

  Subsequently, the rearrangement unit 12c selects nodes u one by one from the node set V (step S203), and sorts the node set Cu in descending order of edge weights (step S204). Then, the rearrangement unit 12c determines whether or not all nodes have been selected from V (step S205). If not all nodes have been selected from V (No in step S205), the process returns to step S203. . If the reordering unit 12c determines that all nodes have been selected from V (Yes at Step S205), the relevance calculation unit 12a sets the calculation count t to “1” (Step S206).

  Subsequently, the relevance calculation unit 12a selects the nodes u one by one from the node set V (step S207), and initializes the relevance s ′ [u] after updating the node u to 0 (step S208). ). Then, the degree-of-association calculation unit 12a determines whether or not all nodes have been selected from V (step S209). If all nodes have not been selected from V (No in step S209), the process proceeds to step S207. Return. Further, when all the nodes are selected from V (Yes at Step S209), the relevance calculation unit 12a selects the nodes u one by one from the node set V ′ (Step S210), and selects one node v. Each node is selected from the node set Cu (step S211). Here, the nodes v are selected one by one from the node set Cu in the order sorted in step S203.

  Then, the relevance calculation unit 12a calculates p = W [v, u] s [u], and calculates s ′ [v] = s ′ [v] + p using the calculated p (step S212). Then, the deletion unit 12b determines whether or not the calculated propagation value p is less than the pruning threshold value θ (step S213). As a result, when the propagation value p calculated by the deletion unit 12b is not less than the pruning threshold θ (No in step S213), the relevance calculation unit 12a determines whether all nodes have been selected from Cu. If not all nodes are selected from Cu (step S214 negative), the process returns to step S211. If all nodes are selected from Cu (Yes at step S214), the process proceeds to step S215. When the propagation value p calculated by the deletion unit 12b is less than the pruning threshold value θ (Yes in step S213), the process proceeds to step S215.

  In step S215, the relevance calculation unit 12a determines whether all nodes have been selected from the node set V. If all nodes have not been selected from the node set V (No in step S215), step S215 is performed. Return to S210. If the relevance calculation unit 12a determines that all nodes have been selected from the node set V (Yes in step S215), the relevance calculation unit 12a calculates s '= (1-c) s' [v] + cd. The relevance degree distribution s is set as the relevance degree s ′ after update (step S216).

  Then, the degree-of-association calculation unit 12a adds 1 to the number of calculations t (step S217), and determines whether the number of calculations t exceeds the number of repetitions T (step S218).

  As a result, when it is determined that the calculation count t does not exceed the repeated calculation count T (No at Step S218), the relevance calculation unit 12a returns to Step S207 to perform the relevance calculation processing. If the relevance calculation unit 12a determines that the calculation count t has exceeded the repetitive calculation count T (Yes in step S218), the relevance distribution s is output to the user terminal 20 (step S219), and the relevance calculation is performed. The process ends.

[Experimental result of relevance calculation processing by relevance calculator]
Next, the experiment result of the relevance calculation process performed by the relevance calculation apparatus according to the second embodiment will be described with reference to FIG. In addition, about an experimental result, it is an example to the last, and a structure or a process is not limited by this. FIG. 12 is a diagram illustrating an example of a result when the relevance calculation is performed by the relevance calculation apparatus according to the second embodiment. Note that “edge pruning” illustrated in FIG. 12 indicates an experimental result of the relevance calculation processing by the relevance calculation apparatus according to the second embodiment, and “original” indicates a relevance calculation according to a conventional algorithm. Experimental results are shown.

In this experiment, the number of nodes was 265214 and the number of edges was 420045. In this experiment, c = 0.15, T = 100, and one random starting node is set at random. In the method of edge pruning, experiments were performed with the pruning threshold θ set to 10 ⁻³ and 10 ⁻⁷ .

FIG. 12 shows that the present invention can calculate the relevance at a higher speed than the conventional method. In the example of FIG. 12, the conventional calculation time is “1.01 [s]”, whereas in the method of the present invention, when the threshold θ is 10 ⁻³ , “0.93 [s] ] ”And the threshold θ is 10 ⁻⁷ , it is“ 0.96 [s] ”. It can also be seen that the higher the pruning threshold, the faster the relevance can be calculated. This is because a larger threshold value allows more nodes or edges to be pruned.

It can also be seen from FIG. 12 that the relevance error in the present invention is a very small value. As shown in FIG. 12, in the method of the present invention, when the threshold θ is 10 ⁻³ , the average error is “3.54 · 10 ⁻⁸ ” compared to the conventional method, and the threshold θ is 10 ^In the case of ⁻⁷ , it is “3.17 · 10 ⁻¹⁰ ”. This is because the present invention prunes a node or an edge, but the threshold is set so that the relevance value is not affected as much as possible. Further, FIG. 12 shows that the present invention can calculate the degree of association with higher accuracy when the threshold value is smaller. This is because the calculation accuracy of the relevance is improved because more nodes or edges are to be calculated when the threshold value is smaller. From these results, it can be seen that in the present invention, the threshold value should be increased if high-speed calculation is desired, and the threshold value should be decreased if high-precision calculation is desired.

[Effect of Example 2]
As described above, the relevance calculation apparatus 10A according to the second embodiment sets the weight value of the edge connected to the node for each node, and rearranges the edges in descending order of the weight value. Then, the relevance calculation device 10A calculates edge propagation values in the rearranged order, determines whether the calculated edge propagation value is less than the threshold value, and the edge propagation value is less than the threshold value. In such a case, the calculation of the propagation value of the edge having a weight value smaller than the weight value of the edge is stopped, and the node connected by the edge is excluded from the calculation target nodes. As a result, it is possible to exclude edges with low relevance from the calculation target. As a result, it is possible to provide a relevance calculation mechanism including a technique for suppressing the calculation amount of relevance. In addition, it is possible to adjust the accuracy of the calculation speed in the relevance calculation by adjusting the threshold.

  By the way, the relevance calculation apparatus in the said Example 1, 2 may be implemented with a various different form other than the Example mentioned above. Therefore, in a third embodiment, another embodiment of the above relevance calculation system will be described.

[Repetition calculation]
The relevance calculation devices of the first and second embodiments have been described with respect to the case where the number of iterations is set in advance as the convergence condition for iterations. However, the present invention is not limited to this, and the convergence threshold is set in advance. You may make it set. For example, in the relevance calculation performed repeatedly, the relevance calculation device calculates a difference between the relevance calculated this time and the relevance calculated last time, and the difference is smaller than a preset convergence threshold. In such a case, the calculation of the degree of association may be terminated, and if it is large, the calculation of the degree of association may be repeated.

[System configuration]
Of the processes described in this embodiment, all or a part of the processes described as being automatically performed can be manually performed, or the processes described as being performed manually can be performed. All or a part can be automatically performed by a known method. In addition, the processing procedures, control procedures, specific names, and information including various data and parameters shown in the above-described document and drawings can be arbitrarily changed unless otherwise specified.

  Further, each component of each illustrated apparatus is functionally conceptual, and does not necessarily need to be physically configured as illustrated. That is, the specific form of distribution / integration of each device is not limited to the one shown in the figure, and all or a part of the distribution / integration may be functionally or physically distributed in arbitrary units according to various loads or usage conditions. Can be integrated and configured.

[program]
FIG. 13 is a diagram illustrating that the information processing by the relevance calculation program according to the disclosed technique is specifically realized using a computer. As illustrated in FIG. 13, the computer 1000 includes, for example, a memory 1010, a CPU (Central Processing Unit) 1020, a hard disk drive interface 1030, a disk drive interface 1040, a serial port interface 1050, a video adapter 1060, A network interface 1070. Each part of the computer 1000 is connected by a bus 1080.

  The memory 1010 includes a ROM 1011 and a RAM 1012 as illustrated in FIG. The ROM 1011 stores a boot program such as BIOS (Basic Input Output System). The hard disk drive interface 1030 is connected to the hard disk drive 1031 as illustrated in FIG. The disk drive interface 1040 is connected to the disk drive 1041 as illustrated in FIG. For example, a removable storage medium such as a magnetic disk or an optical disk is inserted into the disk drive 1041. The serial port interface 1050 is connected to a mouse 1051 and a keyboard 1052, for example, as illustrated in FIG. The video adapter 1060 is connected to a display 1061, for example, as illustrated in FIG.

  Here, as illustrated in FIG. 13, the hard disk drive 1031 stores, for example, an OS 1091, an application program 1092, a program module 1093, and program data 1094. That is, the relevance calculation program according to the disclosed technique is stored in, for example, the hard disk drive 1031 as the program module 1093 in which an instruction to be executed by the computer is described. Specifically, a program module in which a procedure for executing the same information processing as each unit of the control unit 12 described in the above embodiment is described is stored in the hard disk drive 1031.

  Further, data used for information processing by the relevance calculation program is stored as program data 1094 in, for example, the hard disk drive 1031. The CPU 1020 reads out the program module 1093 and the program data 1094 stored in the hard disk drive 1031 to the RAM 1012 as necessary, and executes various procedures.

  Note that the program module 1093 and the program data 1094 related to the relevance calculation program are not limited to being stored in the hard disk drive 1031. For example, the program module 1093 and the program data 1094 may be stored in a removable storage medium. In this case, the CPU 1020 reads data via a removable storage medium such as a disk drive. Similarly, the program module 1093 and the program data 1094 related to the relevance calculation program are stored in another computer connected via a network (LAN (Local Area Network), WAN (Wide Area Network), etc.). Also good. In this case, the CPU 1020 reads various data by accessing another computer via the network interface.

[Others]
The relevance calculation program described in the present embodiment can be distributed via a network such as the Internet. The control program can also be executed by being recorded on a computer-readable recording medium such as a hard disk, a flexible disk (FD), a CD-ROM, an MO, and a DVD, and being read from the recording medium by the computer.

DESCRIPTION OF SYMBOLS 10, 10A Relevance degree calculation apparatus 11 Communication control part 12 Control part 12a Relevance degree calculation part 12b Deletion part 12c Rearrangement part 20 User terminal 1000 Computer 1010 Memory 1020 CPU
1030 Hard disk drive interface 1040 Disk drive interface 1050 Serial port interface 1051 Mouse 1052 Keyboard 1060 Video adapter 1061 Display 1070 Network interface 1080 Bus 1091 OS
1092 Application program 1093 Program module 1094 Program data

Claims (7)

In graph structure data, which is a data model that expresses the relationship between data by the relationship between the node and the edge, the propagation value from the node to the adjacent node is calculated for each edge using the relevance of the node and the edge weight. A relevance calculator that repeatedly calculates the relevance of each node to a set of nodes using a propagation value;
A deletion unit that excludes a predetermined node from a calculation target node based on the association degree of the node or the propagation value of the edge each time the association degree of the node is calculated by the association degree calculation unit. ,
The relevance calculating unit calculates the relevance of the calculation target node from which the predetermined node is excluded.   The deletion unit determines whether or not the relevance level of the node calculated by the relevance level calculation unit is less than a predetermined first threshold value, and determines a node whose relevance level of the node is less than the first threshold value. The relevance calculation apparatus according to claim 1, wherein the predetermined node is excluded from the calculation target nodes. A weighting value of an edge connected to the node is set for each node, and further includes a sorting unit that sorts the edges in descending order of the weighting value,
The relevance calculator calculates edge propagation values in the order rearranged by the rearranger,
The deletion unit determines whether or not the edge propagation value calculated by the relevance calculation unit is less than a predetermined second threshold, and when the edge propagation value is less than the second threshold The calculation of the propagation value of an edge having a weight value smaller than the weight value of the edge is stopped, and a node connected by the edge is excluded from the calculation target node as the predetermined node. The relevance calculation apparatus according to claim 1.   The degree-of-association calculation unit according to any one of claims 1 to 3, wherein the degree-of-association calculation unit repeatedly calculates the degree of association of the node according to a preset number of iterations. In graph structure data, which is a data model that expresses the relationship between data by the relationship between the node and the edge, the propagation value from the node to the adjacent node is calculated for each edge using the relevance of the node and the edge weight. A relevance calculator that repeatedly calculates the relevance of each node to a set of nodes using a propagation value;
A deletion unit that excludes a predetermined node from a calculation target node based on the association degree of the node or the propagation value of the edge each time the association degree of the node is calculated by the association degree calculation unit. ,
The degree-of-association calculation unit calculates the degree of association of the calculation target node from which the predetermined node is excluded. A relevance calculation method executed by a relevance calculation device,
In graph structure data, which is a data model that expresses the relationship between data by the relationship between the node and the edge, the propagation value from the node to the adjacent node is calculated for each edge using the relevance of the node and the edge weight. A relevance calculation step of repeatedly calculating the relevance of each node to a collection of nodes using the propagation value;
A step of removing a predetermined node from the calculation target node based on the degree of association of the node or the propagation value of the edge each time the degree of association of the node is calculated by the degree of association calculation step. ,
The degree-of-association calculating step calculates the degree of association of the calculation target node from which the predetermined node is excluded. In graph structure data, which is a data model that expresses the relationship between data by the relationship between the node and the edge, the propagation value from the node to the adjacent node is calculated for each edge using the relevance of the node and the edge weight. A relevance calculation step for repeatedly calculating the relevance of each node to a collection of nodes using the propagation value;
A step of removing a predetermined node from a calculation target node based on the degree of association of the node or the propagation value of the edge each time the degree of association of the node is calculated by the degree of association calculation step; To run
The relevance calculation step calculates the relevance of the calculation target node from which the predetermined node is excluded.

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