JP6152073B2 - Group association apparatus, method, and program - Google Patents

Description

  The present invention relates to a group association apparatus, method, and program, and more particularly, to a group association apparatus, method, and program for associating groups between data.

  Various methods such as associating images and sentences, associating English and Japanese words, and associating user IDs included in different databases are possible as methods for associating objects included in different data. In some applications, objects are grouped and associated. For example, when images and sentences are classified and matched according to their contents, or when words are associated together according to their meanings, users are grouped according to their communities and associated For example.

  In these associations, an association method has been proposed in the case where correspondence information about an object is given in advance or a distance between different data can be calculated (for example, Non-Patent Document 1). Also, some methods for associating objects even when there is no correspondence information or distance measure have been proposed (for example, Non-Patent Documents 2, 3, and 4).

Tomoharu Iwata, Shinji Watanabe, Hiroshi Sawada: “Fashion Coordinates Recommender System using Photographs from Fashion Magazines,” The twenty-second International Joint Conference on Artificial Intelligence (IJCAI), 2262-2267, 2011. Tomoharu Iwata, Tsutomu Hirao, Naonori Ueda: “Unsupervised Cluster Matching via Probabilistic Latent Variable Models,” The Twenty-Seventh AAAI Conference on Artificial Intelligence, 2013. Novi Quadrianto, Alex J. Smola, Le Song, Tinne Tuytelaars. Kernelized Sorting. IEEE Trans. On Pattern Analysis and Machine Intelligence PAMI, vol. 32 (10), pp. 1809-1821, 2010. Djuric, N., Grbovic, M., Vucetic, S., Convex Kernelized Sorting, AAAI Conference on Artificial Intelligence (AAAI), Toronto, Canada, 2012.

  However, the technique of Non-Patent Document 1 has a problem that it cannot be applied when correspondence information and a distance scale are not given in advance. In addition, the techniques of Non-Patent Documents 2, 3, and 4 have a problem that association with object groups cannot be performed because ungrouped data is targeted.

  The present invention has been made to solve the above problems, and an object of the present invention is to provide a group association apparatus, method, and program capable of accurately associating groups between different data.

  In order to achieve the above object, a group association apparatus according to the present invention receives a plurality of different data, each of which is an input of a plurality of data that is a set of objects grouped into N groups. A group association apparatus that associates groups among the plurality of data, and for each of the plurality of data, for each of two groups out of N groups of the data, A kernel calculation unit for calculating a kernel representing the relationship between two groups, and the plurality of the plurality of data calculated by the kernel calculation unit for each of the plurality of data based on each of the kernels. By reordering the N groups of the data so as to increase the dependency between the data, the group correspondence between the plurality of data is established. It is configured to include a, a rearrangement unit for performing.

  The kernel calculation unit may calculate the kernel using a similarity between distributions of objects included in the group for each of the two groups.

  In the group association device according to the present invention, the kernel may be any one of a linear kernel, a Gaussian kernel, and a polynomial kernel.

  The group association method according to the present invention is a plurality of different data, and each data is a set of objects grouped into N groups, and a plurality of data is input between the plurality of data. A group associating method for associating groups, wherein the kernel calculation unit is configured to perform, for each of the plurality of data, the two groups for each of two groups out of N groups of the data. A step of calculating a kernel representing a relationship between the plurality of data based on each kernel between the two groups calculated by the kernel calculation unit for each of the plurality of data. By reordering the N groups of the data so as to increase the dependency between the data, the group correspondence between the plurality of data is established. And executes comprise the steps of performing.

  Further, in the group association method according to the present invention, the step of calculating a kernel representing the relationship between the two groups in the kernel calculation unit includes, for each of the two groups, an object included in the group. The kernel may be calculated using the similarity between distributions.

  In the group association method according to the present invention, the kernel may be any one of a linear kernel, a Gaussian kernel, and a polynomial kernel.

  The program according to the present invention is a program for causing a computer to function as each unit constituting the group association apparatus.

  According to the group association apparatus, method, and program of the present invention, for each data of a plurality of different data, a kernel indicating each relationship between two groups out of N groups is calculated and calculated. Effect of rearranging groups of data so that the dependency between a plurality of data becomes high based on each kernel between two groups, so that groups between different data can be associated with high accuracy. Is obtained.

It is a block diagram which shows the main structures of the group matching apparatus which concerns on embodiment of this invention. It is a flowchart which shows the content of the group matching process routine in embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Principle of Embodiment of the Present Invention>

  First, the principle of the embodiment of the present invention will be described.

As input data, data X = {X ₁ ,..., X _N } and Y = {Y ₁ ,..., Y _N }, which are sets of two grouped objects, are given. To do. here,

Is a set of objects included in the nth group of the first data, _xni represents the ith object of the _nth group, and In represents the number of objects included in the nth group. As well

Represents a set of objects included in the nth group of the second data, y _{nj represents} the jth object of the _nth group, and Jn represents the number of objects included in the nth group. That is, each of the data X and Y is a set of objects grouped into N groups. In this description, it is assumed that two pieces of data are given. However, even when three or more pieces of data are given, it can be applied in the same manner by applying to every two pieces of data. is there.

  As processing, first, the two given data are read. Next, for each of the two data, a kernel representing the relationship between the groups is calculated for each of the two groups out of the N groups. In the calculation, if the statistical properties of the two groups approximate, the value of the kernel will be high.

  Next, using the calculated kernel value, the groups between the two data are associated by rearranging the N groups so that the dependency between the two data becomes the highest.

Mapping by the following formula (3) is expressed by rearrangement matrix π∈Π _N.

Here, 1 _N is an N-dimensional vector whose elements are all 1. Then, by the following equation (4), dependence of the data X _N and Y _N is the object set that are grouped seeks rearrangement matrix that maximizes.

  Here, D (•) is a measure of dependence. As a measure of dependence, the Hilbert-Schmidt Independence Criterion (HSIC) described later is used. It should be noted that other dependency scales such as mutual information can be used as the dependency scale.

  As described above, in the embodiment of the present invention, for each of a plurality of different data, a kernel is calculated for each of two groups out of N groups for each data, and the dependency between the plurality of data is determined. The groups are associated with each other by rearranging the N groups so as to increase the performance.

<Configuration of Group Correlation Device According to Embodiment of the Present Invention>

  Next, the configuration of the group association apparatus according to the embodiment of the present invention will be described. As shown in FIG. 1, a group association apparatus 100 according to an embodiment of the present invention includes a CPU, a RAM, a ROM for storing a program and various data for executing a group association processing routine described later, Can be configured with a computer including Functionally, the group association apparatus 100 includes an input unit 10, a calculation unit 20, and an output unit 50 as shown in FIG.

  The input unit 10 receives a plurality of different data, each data being a set of objects grouped into N groups. In the present embodiment, the plurality of data are two pieces of data X and Y.

  The calculation unit 20 includes a data storage unit 30, a kernel calculation unit 32, and a rearrangement unit 34.

  The data storage unit 30 stores two data received by the input unit 10.

  The kernel calculation unit 32 first reads two data stored in the data storage unit 30. Next, based on the read two data, for each of the two data, a kernel representing the relationship between the two groups is calculated for each of the two groups out of the N groups of the data. .

  The calculation in the kernel calculation unit 32 regards each of the N groups of the data as a distribution, and calculates a kernel using each statistical property between the distributions of the groups as a similarity. First, a kernel that is the degree of similarity between two objects included in two groups of the data is calculated. Then, based on the calculated kernels between the two objects, the kernels between the distributions of the two groups of the N groups are calculated for the data. Here, with the kernel embedding method, the distribution can be expressed by one point on the reproduction kernel Hilbert space using a kernel between objects. Then, it is considered that the kernel between distributions on the reproduction kernel Hilbert space is a kernel between two groups.

  As a kernel between objects and a kernel between distributions, any kernel among a linear kernel, a Gaussian kernel, and a polynomial kernel can be used.

A linear kernel between the objects x _ni and x _mj can be calculated by the following equation (5).

Further, a Gaussian kernel between the objects x _ni and x _mj can be calculated by the following equation (6).

A polynomial kernel between the objects x _ni and x _mj can be calculated by the following equation (7).

Linear kernel between groups X _n and X _m on the reproducing kernel Hilbert space can be calculated by the following equation (8).

Also, the Gaussian kernel between groups _{X n} and _{X m} can be calculated by the following equation (9).

Further, the polynomial kernel between groups _{X n} and _{X m} can be calculated by the following equation (10).

Then, the kernel calculation unit 32 performs, for each data, for each of the two data based on each kernel between the two groups calculated according to the above formula (8), (9), or (10). Get a matrix summarizing kernels between all groups. In the present embodiment, K is the sum of kernels between all groups of the first data X. Here, K is an N × N matrix, and the (n, m) element of K represents the kernel K (X _n , X _m ) of the n th group and the m th group. Similarly, let L be the sum of kernels between all groups of the second data Y.

  The rearrangement unit 34 determines the N pieces of data so that the dependency between the two data becomes high based on each kernel between the two groups calculated by the kernel calculation unit 32 for each of the two data. Are rearranged to associate groups between two pieces of data.

  For example, the rearrangement unit 34 first reads K for data X and L for data Y obtained by the kernel calculation unit 32. Then, the N groups are rearranged so that the dependency between the data of X and Y becomes high. Here, the Hilbert-Schmidt Independence Criterion (HSIC) is used as a measure of dependence. The HSIC between the two data is expressed by the following equation (11).

Here, tr represents a trace, and H = I−1 _N 1 _N ^T / N represents a centering matrix. Further, ￣K = HKH and ￣L = HLH. The permutation matrix is obtained so as to maximize the HSIC by the following equation (12).

  Equation (12) is maximized by using a method using DC Programming, a method solving as a restricted eigenvalue problem (Non-Patent Document 3), a method solving as a convex problem (Non-Patent Document 4), or the like.

<Operation of Group Correlation Device According to Embodiment of the Present Invention>

  Next, the operation of the group association apparatus 100 according to the embodiment of the present invention will be described. When the input unit 10 receives two pieces of data, each of which is a set of objects grouped into N groups, the data is stored in the data storage unit 30. Then, the group association apparatus 100 executes a group association processing routine shown in FIG.

  First, in step S <b> 100, two data are acquired from the data storage unit 30.

  Next, in step S102, based on the two data acquired in step S100, for each of the two data, according to the above formula (8), (9), or (10), N pieces of the data Compute each kernel between two of the groups. Then, for each of the two data, a matrix in which the kernels between all the groups are collected is obtained for each data.

  Next, in step S106, based on each kernel between the groups calculated for each of the two data in step S102, the dependency between the two data is maximized according to the above equation (12). , Find a permutation matrix that rearranges the N groups of data. Then, based on the obtained rearrangement matrix, N groups of data are rearranged, and groups are associated between the two data. In step S108, two data in which groups between the data are associated in step S106 are output, and the process ends.

<Experimental result>

  Next, experimental results performed based on the method according to the present embodiment will be described.

  In order to evaluate the method according to the embodiment of the present invention, an experiment was performed for each data set using four labeled data sets as a first experimental example. For the experiment, feature values of each data set were randomly divided, and two data were created for each data set.

  In the first experimental example, KS-mean and KS-object were used as a method for comparison with the present embodiment. KS-mean is a method of representing a feature amount for each group as an average, and associating groups using convex kernelized sorting (Non-Patent Document 4), which is an object association method. KS-object is a method of first associating objects by using convex kernelized sorting, and then calculating the corresponding probability between groups based on the number of associated objects, and associating the groups.

  In the method according to the present embodiment in the first experimental example, Equation (5) is applied to the calculation of each kernel between objects, and Equation (8) is applied to the calculation of each kernel between groups.

  Table 1 shows the average correct answer rate and standard error of each experimental result in the first experimental example. The method according to the embodiment of the present invention shows the highest correct answer rate in all the data sets, and the group association can be found effectively. Since KS-object requires a large amount of calculation, it is not applied to the data sets of Satimage and Letter having a large number of objects.

  Further, as a second experimental example, an experiment was performed in which categories of documents in six languages (English, German, Finnish, French, Japanese) included in Wikipedia (registered trademark) are associated.

  In the second experimental example, KS-mean was used as a method for comparison with the present embodiment. In the method according to the present embodiment in the second experimental example, equation (6) is applied to the calculation of each kernel between objects, and equation (9) is applied to the calculation of each kernel between groups.

  Table 2 shows the average correct answer rate and standard error of each experimental result in the second experimental example. With the exception of one language pair, the method according to the embodiment of the present invention shows a higher correct answer rate than KS-mean, indicating the effectiveness of the method according to the embodiment of the present invention.

  As described above, according to the group association device according to the present embodiment, for each data of two different data, each kernel between two groups out of N groups is calculated and calculated. By rearranging the data groups so that the dependency between the two data becomes high based on the respective kernels between the two groups, the groups between the different data can be associated with each other with high accuracy.

  Note that the present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the gist of the present invention.

DESCRIPTION OF SYMBOLS 10 Input part 20 Operation part 30 Data storage part 32 Kernel calculation part 34 Rearrangement part 100 Group matching apparatus

Claims (5)

Group associating device for associating a plurality of pieces of data with a plurality of different data, each of which is a set of objects grouped into N groups, and associating the groups among the plurality of data Because
For each of the plurality of data, a kernel calculation unit that calculates a kernel representing a relationship between the two groups for each of two groups out of N groups of the data;
Based on each kernel between the two groups calculated for each of the plurality of data by the kernel calculation unit, the N groups of the data are increased so that the dependency between the plurality of data is increased. By reordering, a reordering unit that associates groups among the plurality of data,
A group association apparatus including   The group association device according to claim 1, wherein the kernel calculation unit calculates the kernel using a similarity between distributions of objects included in the group for each of the two groups. A group association method for associating a group between a plurality of pieces of data, each of which is a plurality of different data, each of which is a set of objects grouped into N groups. Because
A kernel calculator for each of the plurality of data, for each of two groups out of N groups of the data, calculating a kernel representing the relationship between the two groups;
Based on each kernel between the two groups calculated by the kernel calculation unit for each of the plurality of data, the sorting unit increases the dependency between the plurality of data. Rearranging the N groups of the group to associate groups among the plurality of data; and
Group matching method including   The step of calculating a kernel representing the relationship between the two groups in the kernel calculation unit calculates the kernel using the similarity between distributions of objects included in the group for each of the two groups. The group association method according to claim 3.   The program for functioning a computer as each part which comprises the group matching apparatus of Claim 1 or 2.