Inter-set relationship calculation device and information processing device

Abstract

To provide an inter-set relation calculation device that can determine a relation between sets, and an information processing apparatus.SOLUTION: An inter-set relation calculation device determines a relation between sets in a set family SS, where d is a natural number, N is a natural number of 2 or more, the set family SS consists of N sets that are not empty, and sets Si (i=1, 2, ... N) respectively have 2 or more elements of d-dimensional vectors. The inter-set relation calculation device has: weight calculation means 221 that calculates a weight wi of the sets Si that are the elements of the set family SS; probability density function defining means 222 that defines a probability density function pi(x) generating the elements x; and relation index calculation means 225 that defines an index D (SS) of a distance according to a predetermined formula by using all the combinations of the sets Si of the set family SS and sets Sj (j=1, 2, ... N), determines an approximate value of the index D (SS) of the distance by the method of exhaustion, and calculates a relational index that is an index of the relation between the sets Si by using the approximate value.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] The present disclosure relates to an inter-set relationship calculation device and an information processing device. [Background technology]

[0002] In recent years, advances in computer network technology have led to the distribution of vast amounts of data. This data is related to certain items, and analyzing this data is expected to reveal some kind of relationship or meaning between the items.

[0003] As an example of such a technology, a technology has been developed that uses documents as items and presents important words in these documents (see Patent Document 1). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2018-195108 Summary of the Invention [Problem to be solved by the invention]

[0005] However, while conventional techniques can present the words that make up a document, they have the problem of difficulty in analyzing the relationships between documents using the words that make up the documents. Furthermore, it is difficult to analyze the relationships between multiple items, not just documents. It is also difficult to determine the relationships between sets of words that are needed to determine the relationships between items.

[0006] Therefore, an object of the present disclosure is to provide an inter-set relationship calculation device and an information processing device that are capable of finding the relationship between sets. [Means for solving the problem]

[0007] In order to solve the above problems, the present disclosure provides: Let d be a natural number and N be a natural number greater than or equal to 2. A set family SS = {S1, S2, S3, . . . , SN} is made up of N non-empty sets, and each set Si (i = 1, 2, . . . N) has two or more elements x that are d-dimensional vectors. An apparatus for determining relationships between sets in the set family SS, comprising: a weight calculation means for calculating a weight wi of each set Si, which is an element of the set family SS; a probability density function definition means for defining a probability density function pi(x) that generates the element x; Using all combinations of sets Si (i=1, 2, . . . N) and Sj (j=1, 2, . . . N), which are two elements of the set family SS, a distance index D(SS) is defined by the following formula (1):

number

[0008] The present disclosure also provides: Let d be a natural number and N be a natural number greater than or equal to 2. A set family SS = {S1, S2, S3, . . . , SN} is made up of N non-empty sets, and each set Si (i = 1, 2, . . . N) has two or more elements x that are d-dimensional vectors. An apparatus for calculating a relationship between sets in the set family SS, comprising: a weight calculation means for calculating a weight wi of each set Si, which is an element of the set family SS; Calculate the sample mean μi and sample covariance matrix Ci of the element x of each set Si, and calculate a distance index D(SS) using the following formula (2) using all combinations of the set Si (i=1, 2, . . . N) and the set Sj (j=1, 2, . . . N), which are two elements of the set family SS;

number

[0009] The present disclosure also provides: An information processing device that calculates coordinate values ​​for locating each item in a k-dimensional space using a set related to each item belonging to a category of interest, a relationship matrix generating means for generating a relationship matrix having the relationship indices calculated for the two sets by the relationship index calculating means as matrix elements; a coordinate value calculation means for calculating coordinate values ​​for arranging each item in a k-dimensional space by performing a predetermined transformation on the relationship matrix; The present invention provides an information processing device having the above.

[0010] The present disclosure also provides: An information processing device that generates a relationship graph with each item as a node using a set related to each item belonging to a category of interest, a relationship matrix generating means for generating a relationship matrix having the relationship indices calculated for the two sets by the relationship index calculating means as matrix elements; an adjacency matrix generating means for generating an adjacency matrix based on the calculated relationship matrix; a relationship graph generation means for generating a relationship graph corresponding to the generated adjacency matrix; The present invention provides an information processing device having the above.

[0011] In addition, the information processing device of the present disclosure includes: a morphological analysis means for extracting morphemes by performing a morphological analysis on a sentence written in a natural language when the sentence is associated with each item belonging to the category of interest; a word vector calculation means for calculating a d-dimensional word vector for each of the extracted morphemes; and The relationship matrix generating means may generate the relationship matrix using the set of calculated word vectors.

[0012] In addition, the information processing device of the present disclosure includes: an image analysis means for, when each item belonging to the category of interest is an image, performing image analysis on the image to identify words obtained as elements of a set related to the image that is the item; a word vector calculation means for calculating a d-dimensional word vector for each of the identified words; and The relationship matrix generating means may generate the relationship matrix using the set of calculated word vectors.

[0013] The present disclosure also provides: Let d be a natural number and N be a natural number greater than or equal to 2. A program for a computer to determine relationships between sets in a set family SS, where the set family SS = {S1, S2, S3, . . . , SN} consists of N non-empty sets, and each set Si (i = 1, 2, . . . N) has two or more elements x that are d-dimensional vectors, the program comprising: Computer, a weight calculation means for calculating a weight wi of each set Si, which is an element of the set family SS; a probability density function definition means for defining a probability density function pi(x) that generates the element x of the set Si; Using all combinations of sets Si (i=1, 2, . . . N) and Sj (j=1, 2, . . . N), which are two elements of the set family SS, a distance index D(SS) is defined by the following formula (3):

number

[0014] The present disclosure also provides: Let d be a natural number and N be a natural number greater than or equal to 2. A program for a computer to determine relationships between sets in a set family SS, where the set family SS = {S1, S2, S3, . . . , SN} consists of N non-empty sets, and each set Si (i = 1, 2, . . . N) has two or more elements x that are d-dimensional vectors, the program comprising: Computer, a weight calculation means for calculating a weight wi of each set Si, which is an element of the set family SS; Calculate the sample mean μi and sample covariance matrix Ci of the element x of each set Si, and calculate the distance index D(SS) calculated by the following formula (4) using all combinations of the set Si (i=1, 2, . . . N) and the set Sj (j=1, 2, . . . N), which are two elements of the set family SS;

number

[0015] According to the present disclosure, it is possible to determine the relationships between sets. [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1 is a hardware configuration diagram of an information processing device according to an embodiment of the present disclosure. [Figure 2]1 is a functional block diagram showing a configuration of an information processing device according to a first embodiment of the present disclosure. [Figure 3] FIG. 2 is a diagram illustrating an example of information stored in a document database used in an embodiment of the present disclosure. [Figure 4] FIG. 10 is a diagram illustrating an example of information stored in a word database used in an embodiment of the present disclosure. [Figure 5] 4 is a flowchart showing a processing operation of the information processing device according to the first embodiment of the present disclosure. [Figure 6] FIG. 2 is a functional block diagram showing details of a relationship matrix generating means 22. [Figure 7] FIG. 1 is a conceptual diagram illustrating categories of interest. [Figure 8] FIG. 10 is a diagram showing an example of a vector set family SS when a vector set is obtained based on a word group. [Figure 9] FIG. 10 is a diagram showing an example of a vector set family SS when a vector set is obtained based on a word group. [Figure 10] FIG. 10 is a diagram showing an example of a vector set family SS when a vector set is obtained based on a word group. [Figure 11] FIG. 10 is a diagram for explaining dimensionality reduction of set elements. [Figure 12] FIG. 10 is a diagram for explaining dimensionality reduction of set elements. [Figure 13] FIG. 10 is a diagram for explaining dimensionality reduction of set elements. [Figure 14] FIG. 10 is a functional block diagram showing a configuration of an information processing device according to a second embodiment of the present disclosure. [Figure 15] FIG. 10 is a diagram illustrating an example of information stored in an image database used in an embodiment of the present disclosure. [Figure 16] FIG. 10 is a diagram illustrating an example of information stored in a word database used in an embodiment of the present disclosure. [Figure 17] 10 is a flowchart showing a processing operation of an information processing device according to a second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0017] Preferred embodiments of the present disclosure will be described in detail below with reference to the drawings. <1. First embodiment> <1.1.Device configuration> FIG. 1 is a hardware configuration diagram of an information processing device 100 according to an embodiment of the present disclosure. The information processing device 100 according to this embodiment can be realized by a general-purpose computer, and as shown in FIG. 1 , includes a CPU (Central Processing Unit) 1, a RAM (Random Access Memory) 2 serving as the computer's main memory, a large-capacity storage device 3 such as a hard disk, SSD (Solid State Drive), or flash memory for storing programs and data executed by the CPU 1, an instruction input I / F (interface) 4 such as a keyboard or mouse, a data input / output I / F (interface) 5 for communicating data with an external device such as a data storage medium, a display unit 6 such as a liquid crystal display, a GPU (Graphics Processing Unit) 7 serving as a processing unit specialized for graphics, and a frame memory 8 for storing images to be displayed on the display unit 6, all of which are connected to each other via a bus. Because the results of calculations by the GPU 7 are written to the frame memory 8, the GPU 7 and the frame memory 8 are often mounted on a video card having an interface to the display unit 6 and attached to the general-purpose computer via the bus.

[0018] In this embodiment, the CPU 1 may be a multi-core CPU. In this case, the CPU 1 has multiple CPU cores and is capable of parallel processing. Although only one RAM 2 is shown in the example of FIG. 1, each CPU core of the CPU 1 is configured to access one RAM 2. Note that there may be multiple CPUs 1. Furthermore, the multi-core CPU may be a CPU that logically has multiple CPU cores.

[0019] Fig. 2 is a functional block diagram showing the configuration of an information processing device according to the first embodiment. In Fig. 2, 10 denotes a word database, 11 denotes a document database, 20 denotes a processing unit, 21 denotes a word vector calculation means, 22 denotes a relationship matrix generation means, 23 denotes a coordinate value calculation means, 24 denotes an item placement means, 25 denotes a morphological analysis means, and 30 denotes an output means. The information processing device shown in Fig. 2 uses a set related to each item belonging to a category of interest to calculate coordinate values ​​for placing each item in a k-dimensional space.

[0020] The information processing device shown in Figure 2 calculates the relationship between items based on the following concept. Assume that a certain category of interest is composed of multiple items. For example, if the category of interest is a literary genre, the items in that category are individual literary works, such as Natsume Soseki's "Botchan." In this case, there is a desire to understand the relationship between each item in the category of interest. A typical example of the relationship between items is similarity. If we can determine the degree of similarity between two items in the category of interest for all combinations, we can consider the relationship to be understood. This overall relationship can be expressed as a real symmetric matrix. That is, it is a matrix whose j-th row and i-th column components are real-valued index values ​​representing the degree of pairwise relationship between the j-th item and the i-th item. A symmetric matrix is ​​obtained when the relationship is symmetric, i.e., when the index value remains the same even when i and j are swapped. We refer to this real symmetric matrix as a pairwise relationship matrix. When each item in a category of interest is associated with a set, it is possible to calculate the similarity of the items using information about each element of the set, since there is likely to be a relationship between the item and the elements of the associated set.

[0021] The word vector calculation means 21 calculates a word vector, which is a position in a d-dimensional coordinate space (d is a natural number), based on the meaning of each word. A word vector is an element included in a set related to an item called a document, and is a d-dimensional vector. The word vector calculation means 21 is a word-to-vector conversion means that, when a single word is input, outputs a d-dimensional vector using a predetermined method. For example, word analysis software technology such as "Word2Vec" from Google Inc. can be used as the word vector calculation means 21. The relationship matrix generation means 22 calculates a relationship matrix R relating to the relationship between sets from the vector values ​​of the elements of the set. The coordinate value calculation means 23 calculates the coordinate values ​​of each item based on the relationship matrix R. The item placement means 24 places items based on the calculated coordinate values ​​of each item. The morphological analysis means 25 reads each document from the document database 11 and performs morphological analysis on the sentences included in each document to extract words that are morphemes. The word vector calculation means 21, relationship matrix generation means 22, coordinate value calculation means 23, item placement means 24, and morphological analysis means 25 are included in the calculation processing unit 20, and are realized by the CPU 1 executing a program. The output means 30 is a means for graphically outputting items placed at coordinate values ​​in space by the item placement means 24, and is realized by the display unit 6, such as a printer or display device, via the data input / output I / F 5.

[0022] The word database 10 is a database that stores word IDs that identify words in association with the words themselves, and is realized by the storage device 3. The document database 11 is a database that stores documents made up of text information in association with document IDs that identify the documents, and is realized by the storage device 3.

[0023] FIG. 3 is a diagram illustrating an example of information stored in the document database 11. In this embodiment, a set (a set of words) related to each item (document) belonging to a category of interest (a predetermined group of documents managed by the word database 10, the document database 11, etc.) is used as input data to display a relationship graph in which each item is a node. Here, the information stored in the document database 11, i.e., a set of documents, becomes a category of interest, and each document becomes an item. A set of words contained in each document becomes a set related to each document. A set related to each item means a set associated (corresponding or linked) with each item, and includes a set included in each item and a set attached to each item. For example, if each item is a document, a set included in each item is a set of words contained in the document. Typically, a document is composed of sentences written in a natural language. Therefore, if each item is a document, a sentence written in a natural language is associated with each item. Furthermore, a set attached to each item is, for example, if each item is a group, a set of elements (usually expressible as some kind of word) included in the group.

[0024] For example, if the interest category is movies and each item in the interest category is an individual movie, then the set associated with each item can be the set of actors who appeared in those movies. Alternatively, if the interest category is actors and each item in the interest category is an individual actor, then the set associated with each item can be the set of movies that the actor has appeared in. In these two examples, the relationship between movies and actors can be transformed from a data structure in which one is the interest and the other is the associated set to the reverse data structure. Furthermore, by applying the same transformation again, the original relationship can be restored. This type of relationship is generally called a dual. The relationship between documents and words can also be transformed into a dual relationship. That is, words are considered as interests, and the set of documents containing each word is considered the associated set.

[0025] Also, if the category of interest is a group of images and each item belonging to the category of interest is an individual image, a set of words indicating the content expressed in the image can be used as a set associated with each item.

[0026] As shown in Fig. 3, the document database 11 stores document names, author names, and document data in association with document IDs, which are document identification information for identifying documents. For document data, the storage address of the document data only needs to be recorded so that the document data can be acquired by identifying the document ID. The example in Fig. 3 shows that a document (work) titled "XXXXXX" by author "Mr. A" is registered with document ID "B001."

[0027] FIG. 4 is a diagram showing an example of information stored in the word database 10. As shown in FIG. 4, the word database 10 stores words and document IDs of documents in which the words appear, in association with word IDs, which are word identification information for identifying the words. In the example of FIG. 4, the word registered as word ID "T0001" in the first line appears five times in the document identified by document ID "B001" and appears three times in the document identified by document ID "B002." In addition, the word registered as word ID "T0002" in the second line appears three times in the document identified by document ID "B001" and appears eight times in the document identified by document ID "B002."

[0028] Each word registered in the word database 10 is associated with a document ID, and therefore stores a set (a set of words) associated with each document belonging to a group of documents (registered in the document database 11) that is a category of interest. In this embodiment, information about the words recorded in the word database 10 is used as input to create a scatter plot with each document as a node. Since the word database 10 has the configuration shown in FIG. 4, it is also possible to identify the word IDs of all words that appear in a document by referencing the document ID. In the example of FIG. 4, both the word registered as word ID "T0001" and the word registered as word ID "T0002" are included in both the set associated with document ID "B001" and the set associated with document ID "B002."

[0029] In reality, each of the components shown in FIG. 2 is realized by installing a dedicated program in hardware such as a computer and its peripheral devices, as shown in FIG. 1. That is, the computer executes the contents of each component in accordance with the dedicated program. In this embodiment, the CPU is preferably a multi-core CPU. Note that in this specification, the term "computer" refers to a device that has a processing unit such as a CPU or GPU and is capable of data processing, and includes not only general-purpose computers such as personal computers, but also mobile terminals such as tablets equipped with a CPU, and computers incorporated in various devices.

[0030] <1.2. Processing Operation> The information processing device of this embodiment generates a scatter diagram in which each item is arranged by executing a predetermined information processing. Next, the processing operation of the information processing device shown in FIGS. 1 and 2 will be described along with the information processing method of this embodiment. FIG. 5 is a flowchart showing the processing operation of the information processing device of the first embodiment. First, the morphological analysis means 25 reads each document from the document database 11 and extracts words contained in each document (step S11). Specifically, the morphological analysis means 25 performs morphological analysis on the extracted document and extracts words of specific parts of speech. The specific parts of speech are specified in advance. For example, if the part of speech is specified as "noun," only noun words are extracted. The extracted words are registered in the word database 10, as shown in FIG. 4, together with the number of times they appear in the document.

[0031] Next, for each word registered in the word database 10 as a category of interest, a word vector, which is the coordinates of the word, is calculated (step S12). Specifically, the word vector calculation means 21 calculates a word vector, which is a position in a d-dimensional (d is a natural number) coordinate space, based on the meaning of each word.

[0032] Here, the set of documents registered in the document database 11 is V, and each document is v j Let the number of elements in a set of documents V be n. The set of documents is a category of interest, and document v j Then, each document v j ∈V, i.e., each document v j are elements of the set V. Each document v j A set of words of a specific part of speech extracted by morphological analysis is called T j Let's say.

[0033] T j ={t j1 , t j2 , t j3 ,···} , j=1,2,3,···,n

[0034] each word t ji(In the word database 10, it is managed by word ID) and each word is associated with the document v j (In the word database 10, it is managed by document ID) The value of the number of times it appears in the document can be obtained (see Figure 4).

[0035] Next, a relationship matrix R relating to the relationship between the sets is calculated from the vector values ​​of the elements of the sets (step S13). Specifically, the relationship matrix generation means 22 calculates an index value of the relationship and generates a relationship matrix R in which the index value of the relationship is the matrix element. Here, the relationship is information indicating the relationship between the two, and can be expressed by various indices. For example, similarity, which is the degree to which the two are similar, or distance, which is the degree to which the two are separated, can be used. The closer the two are, the greater the similarity, and the farther the two are, the greater the distance. Therefore, similarity and distance can be converted into each other using a predetermined conversion formula. Specifically, in the process of calculating the relationship matrix R, first, for each j,i, the document v j Set T is the set of words that appear in j , document v i Set T is the set of words that appear in i The index value r that represents the relationship between ji Calculate.

[0036] The relationship matrix R is the relationship index value r as shown in the following formula (11). ji Let be the matrix whose component is the jth row and the ith column.

[0037] R=[r ji ](j=1,2,3,···,n;i=1,2,3,···,n)···(11)

[0038] The relationship matrix R is an n-th order square matrix corresponding to the number of documents n. The relationship matrix R is a real symmetric matrix. In this embodiment, the relationship matrix R is adjusted so that the distance between documents becomes 0. That is, r ii , r jj All of the diagonal elements of the relationship matrix R such as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

[0039] Once the relationship matrix R is obtained by the process in step S13, coordinate values ​​are calculated based on the relationship matrix R (step S14). Specifically, the coordinate value calculation means 23 calculates coordinate values ​​for arranging each item in the k-dimensional space based on the relationship matrix R. A specific processing method is as follows: ji It depends on whether it is distance or similarity.

[0040] First, each element r of the relationship matrix R ji The case where each element r of the relationship matrix R is the distance is explained below. ji is the distance, the coordinate value calculation means 23 performs Young-Householder transformation on the relationship matrix R to obtain a matrix Y, and then converts the matrix Y into Y=X T A calculation is performed using multidimensional scaling, which decomposes the data into the form of X. This calculates the coordinate values ​​for placing each item in k-dimensional space.

[0041] In this case, first, the coordinate value calculation means 23 performs Young-Householder transformation on the relationship matrix R. The Young-Householder transformation is a transformation that uses a centering matrix Cn on an n-row, n-column square matrix to obtain a matrix Y according to the following equation (12).

[0042] Y=-1 / 2 CnRCn (12)

[0043] When n=3, Cn is expressed by the following equation (13).

[0044]

number

[0045] Next, we convert the matrix Y to Y=X T By decomposing it into the form of X, we obtain matrix X. This matrix X is a coordinate sequence with k rows and n columns, and we can obtain the k-dimensional coordinates of n items.

[0046] Next, each element r of the relationship matrix R ji is the similarity.

[0047] Each element r of the relationship matrix R ji is the similarity, in step S14, the coordinate value calculation means 23 generates a graph Laplacian matrix P from the relationship matrix R, and then calculates coordinate values ​​for locating each item in k-dimensional space based on the graph Laplacian matrix P. A k-row, n-column graph Laplacian matrix P is generated from an n-row, n-column square matrix, and the k-dimensional coordinates of the n items are obtained.

[0048] As explained above, in step S14, each element r of the relationship matrix R ji If the distance is, we apply Young-Householder transformation to the relationship matrix R to obtain matrix Y, and then we convert matrix Y to Y=X T The coordinate values ​​for arranging each item in k-dimensional space are calculated by applying the multidimensional scaling method that decomposes it into the form of X. Meanwhile, each component r of the relationship matrix R ji is the similarity, a graph Laplacian matrix P is generated from the relationship matrix R, and then the coordinate values ​​for arranging each item in the k-dimensional space are calculated based on the graph Laplacian matrix P.

[0049] Whether the components of the relationship matrix calculated in step S13 are distance or similarity can be set appropriately depending on the type of data to be handled, the purpose of visualization, and the like.

[0050] Once the coordinate values ​​are calculated in step S14, the item is placed (step S15). Specifically, the item placement means 24 places the item corresponding to the calculated coordinate values. In practice, a node including the name of the item or the like is assigned to a predetermined coordinate value, and data for an output means such as a display device is generated and output from the output means 30 such as the display unit 6.

[0051] <1.3. Details of the process in step S13 by the relationship matrix generation means 22> As described above, in this embodiment, in step S13, the relationship matrix generation means 22 calculates the index value r of the symmetric relationship using the word vector. jiThis index value r ji Details of the calculation of will be explained below. Fig. 6 is a functional block diagram showing details of the relationship matrix generation means 22. As shown in Fig. 6, the relationship matrix generation means 22 has weight calculation means 221, probability density function definition means 222, and relationship index calculation means 225.

[0052] In this embodiment, the category of interest consists of n items, where n is a natural number equal to or greater than 2, and each item is a document. The set associated with each item consists of words, and each word is associated with a d-dimensional vector. Under this setting, we now want to find a relationship matrix R consisting of n rows and n columns. The j-th row and ith column component r of the relationship matrix R is ji is an index value that represents the relationship between the jth item and the ith item. A d-dimensional vector set is obtained through the set of words related to the jth item, and similarly for the ith item. The two d-dimensional vector sets obtained in this way can be viewed as a vector set family.

[0053] The following describes a method for determining an index value representing the relationship between vector sets belonging to a vector set family, regardless of its origin, without being limited to the settings of this embodiment. The term "vector set family" is defined again as follows: Generally, a "set family" is a set whose elements are sets. A vector set family SS is a set family whose elements are N vector sets, where N is a natural number greater than or equal to 2. Each vector set Si (i = 1, 2, 3, . . . , N), which is an element of the vector set family SS, has ni d-dimensional vectors as elements. Here, d and ni are both natural numbers. When d = 1, it becomes a scalar, but in this case, it is treated as a one-dimensional vector in the same way as when d is 2 or greater. Also, ni is a natural number greater than or equal to 2. That is, each set Si (i = 1, 2, . . . N) has two or more elements x, which are d-dimensional vectors.

[0054] Figure 7 shows an example of a vector set family. In this example, N = 5 and d = 2 (dimensions). The range enclosed by a circle represents each set Si (i = 1 to 5). Given a vector set family SS, the objective is to calculate the relationship index E(SS), which is a single index value that represents the relationship between each vector set belonging to the vector set family. As mentioned above, relationships can be expressed as similarity or distance, and similarity and distance can be converted into each other using a predetermined conversion formula. Therefore, once either similarity or distance is determined, the relationship can be determined. Here, the distance index D(SS) is calculated first. Figures 8 to 10 show an example of a vector set family SS obtained by using the word analysis software Word2Vec based on a group of words. The distribution of d-dimensional vectors associated with each word is shown. The value of d could be, for example, 300 dimensions, but in Figures 8 to 10 it is reduced to two dimensions. The range enclosed by a circle represents each vector set Si.

[0055] When calculating the distance index D(SS) (the overall dissimilarity of N sets), the distributions approach each other as we move from FIG. 8 to FIG. 10, so the value of the obtained distance index D(SS) should gradually decrease. Returning to the original setting of this embodiment, what we want to calculate is the index value r of the relationship between two items consisting of the jth item and the ith item. ji Therefore, we need only consider the case where N = 2. However, the method described below can be extended to cases where N is 3 or more.

[0056] In the following, element x is assumed to be a d-dimensional vector. However, for convenience, we will explain the case where d=1. For a set Si, which is each element of a set family SS of vectors, we assume that there exists a probability distribution that generates a vector that is element x of that set. The probability density function of this probability distribution is defined as pi(x), where pi(x)≧0.

[0057] Here, the sample mean (vector) of element x in set Si is written as μi, and the sample covariance matrix is ​​Ci. The probability density function pi(x) is assumed to follow a d-dimensional normal distribution Nd(μi, Ci), and a method using this probability density function can be considered. However, using a d-dimensional distribution directly to find a d-dimensional normal distribution is undesirable for the following two reasons.

[0058] First, the size of the covariance matrix becomes too large. The covariance matrix has d rows and d columns, and 2 It has components. Therefore, when d=300, it has 90,000 components, which is too large to handle. Secondly, it is easy for the covariance matrix to degenerate, resulting in an inverse matrix that no longer exists. When this happens, it becomes impossible to calculate the value by substituting it into the formula for the probability density function of the normal distribution. Degeneration occurs when the value of nA, the number of elements in the set SA, is smaller than d.

[0059] Therefore, it is preferable to reduce the dimension of the original data from d dimensions to d' dimensions. This can be done using principal component analysis. Figures 11 to 13 are diagrams for explaining the dimensionality reduction of set elements. Figures 11 to 13 explain the case where two dimensions are reduced to one dimension (d=2 → d=1). Figure 11 shows a case where two sets SA and SB in two dimensions each have 10 set elements. Each element is expressed by a two-dimensional vector. In the example shown in Figure 11, the elements of the two sets do not intersect in two-dimensional space. Therefore, their relationship should be determined to be distant (large distance, small similarity).

[0060] FIG. 12 is a diagram showing the state after principal component analysis is performed on the elements of the two sets SA and SB shown in FIG. 11. As described above, dimension reduction can be performed using principal component analysis. However, as shown in FIG. 12, when principal component analysis is performed and the elements of the two sets are projected onto the first principal component axis and viewed as a one-dimensional distribution, the elements of the two sets become mixed. This results in elements that should actually be determined to be distantly related being merged together. Therefore, in this embodiment, dimension reduction is performed by projecting onto a line connecting the means.

[0061] Fig. 13 is a diagram showing an example of dimension reduction performed by projecting onto a line connecting the means. As shown in Fig. 13, the average value is calculated for each of the elements of each set SA and SB. By projecting onto the line connecting the average values ​​of the two sets (the dashed line in Fig. 13), it is possible to reduce the dimension from two dimensions to one dimension. Although Figs. 11 to 13 show two sets, this can also be applied to three or more sets. Under these conditions, the probability density function definition means 222 defines the probability density function pi(x) by the following equation (14).

[0062]

number

[0063] In equation (14), the mean vector μi is a d-dimensional vector whose components are real values. The covariance matrix Ci is a real symmetric matrix with d rows and d columns, and is also a positive definite matrix. Equation (14) represents a normal distribution in the case of multivariate data. The distribution specified by equation (14) is denoted as Nd(μi, Ci).

[0064] The weight calculation means 221 calculates a weight wi for a set S. Specifically, when the set S has ni elements, the weight calculation means calculates the weight wi by performing a process according to the following equation (15).

[0065]

number

[0066] As shown in equation (15), the weight wi of a set Si is obtained by dividing the number of elements ni of the set Si by the sum of the number of elements of all N sets.

[0067] Next, the relationship index calculation means 225 calculates an index of the relationship using the calculated weights. First, the amount of information used by the relationship index calculation means 225 will be explained. Known information amounts between multiple distributions include the Kullback-Leibler divergence, which can be defined between two distributions, and the Jensen-Shannon divergence, which can be defined between multiple distributions. Therefore, when attempting to find a general-purpose index of the relationship that can be applied between multiple distributions, it is effective to use the Jensen-Shannon divergence.

[0068] Here, suppose there are N probability distributions P1, P2, P3, . . . , PN, each of which is given weights w1, w2, w3, . . . , wN. Then, let wi > 0 (i = 1, 2, 3, . . . , N). Also, let the sum of the N weights wi be 1. In this case, the probability distribution P is defined by the following equation (16).

[0069]

number

[0070] When the probability distribution P is defined as in equation (16), the Jensen-Shannon information D between P1, P2, P3, . . . , PN is JS (P1, P2, P3, . . . , PN) are defined by the following equation (17).

[0071]

number

[0072] In the first equation of equation (17), D KL (Pi||P) is the Kullback-Leibler divergence. As shown in the second equation of (17), D JS(P1,P2,P3,...,PN) takes values ​​greater than or equal to 0 and less than or equal to log2(N). Jensen-Shannon divergence is not only applicable to multiple distributions, but also has the advantage of being symmetric. Therefore, even if you treat the distributions and weights as a set and swap any two terms, you will return to the original formula. Also, if you leave the weights as they are and swap only the distributions, symmetry holds when all the weights are equal and wi=1 / N.

[0073] Here, the Kullback-Leibler divergence D used in the first equation of equation (17) is KL We will explain (Pi||P). Kullback-Leibler divergence is an index that shows the difference between two probability distributions.

[0074] Given two discrete probability distributions P and Q, where the probability of taking value i is P(i) and Q(i), respectively, the Kullback-Leibler divergence D of P with respect to Q is KL (P||Q) is defined by the following equation (18).

[0075]

number

[0076] Given two continuous probability distributions P and Q, where the probability of taking value i is P(x) and Q(x), respectively, the Kullback-Leibler divergence D of P with respect to Q is KL (P||Q) is defined by the following equation (19).

[0077]

number

[0078] The Kullback-Leibler divergence has the following properties: - Takes a non-negative value. D KL (P||Q)≧0 The equality holds if and only if P=Q -There is no symmetry, and if you swap the front and back, they will generally not be equal. DKL (P||Q)≠D KL (Q||P) ·Not defined between three or more probability distributions.

[0079] When two probability distributions P and Q are normal distributions Nd(μP,CP) and Nd(μQ,CQ), respectively, the Kullback-Leibler divergence D of P with respect to Q is KL (P||Q) is expressed as the following equation (20).

[0080]

number

[0081] Based on the above content of the Kullback-Leibler divergence, in this embodiment, the two-sided Jensen-Shannon divergence that can be defined between multiple distributions is defined by the following equation (21).

[0082]

number

[0083] In equation (21), the Kullback-Leibler divergence is defined as the sum of the head and tail. DrJS(S) is JS In (S), the relationship between p and pi is reversed. Transforming equation (21) using equation (17) results in the following equation (22).

[0084]

number

[0085] Here, we reflect the relationship between two different sets in N sets Si. For convenience, we will refer to one as set Si and the other as set Sj. Since it is essentially the same as i, j = 1, 2, 3, . . . , N. Set Sj has nj d-dimensional vectors as elements. Here, d and nj are both natural numbers. Furthermore, let μj be the sample mean (vector) of element x of set Sj, and Cj be the sample covariance matrix. The probability density function pj(x) follows the d-dimensional normal distribution Nd(μj, Cj). By modifying equation (22) to reflect the relationship between sets Si and Sj, we can express it as in equation (23) below.

[0086]

number

[0087] <1.3.1. First Method> The relationship index calculation means 225 can calculate the relationship index using two methods. First, the first method will be described. In the first method, the two-sided Jensen-Shannon divergence shown in equation (23) is applied to the set SS. Specifically, when the probability density function pi(x) is used for the two-sided Jensen-Shannon divergence shown in equation (23), the distance index D(SS) can be expressed as shown in the following equation (24).

[0088]

number

[0089] That is, the distance index D(SS) can be defined by equation (24) using all combinations of the two elements of the set family SS, set Si (i = 1, 2,...N) and set Sj (j = 1, 2,...N). The relationship index calculation means 225 calculates the distance index D(SS) by executing processing according to equation (24). However, in practice, an approximation value D'(SS) of the distance index D(SS) is calculated by the quadrature method by division. The approximation value D'(SS) can also be treated as an index of distance between N sets Si(Sj) belonging to the set family SS. The distance index is an index of relationship in which the larger the value, the more distant the relationship. The relationship index calculation means 225 may calculate a value obtained by subtracting the approximation value D'(SS), which can be considered as an index of distance, from 1 as an index of similarity between two or more sets. The similarity index is an index of relationship in which the larger the value, the closer the relationship.

[0090] The approximation D'(SS) of the Jensen-Shannon divergence D(SS) using the probability density function pi(x) can be used as an index of distance between sets Si. Once the index of distance is obtained, it is also possible to easily obtain an index of similarity. In this way, it is possible to calculate the relationship index E(SS), which is an accurate index of relationship.

[0091] <1.3.2. Second Method> The second method is now explained. The second method is suitable when the probability distribution is a normal distribution Nd(μi, Ci). In this case, the probability density function pi(x) can be expressed as in the following equation (25).

[0092]

number

[0093] The probability density function pj(x) can be expressed by replacing i with j in equation (25). On the other hand, the Kullback-Leibler divergence between normal distributions can be expressed as in equation (26) below.

[0094]

number

[0095] Using equation (26), the Jensen-Shannon divergence shown in equation (21) can be expressed as the following equation (27).

[0096]

number

[0097] When this is applied to the set family SS, the distance index D(SS) can be expressed as the following equation (28).

[0098]

number

[0099] That is, the distance index D(SS) can be calculated by equation (28) using all combinations of sets Si (i = 1, 2, . . . N) and sets Sj (j = 1, 2, . . . N), which are two elements of the set family SS. The relationship index calculation means 225 calculates the distance index D(SS) by executing processing in accordance with equation (28). The distance index is an index of relationship in which the larger the value, the more distant the relationship. The relationship index calculation means 225 may calculate a value obtained by subtracting the distance index D(SS) from 1 as an index of similarity between two or more sets. The similarity index is an index of relationship in which the larger the value, the closer the relationship. The approximation value D'(SS) of the Jensen-Shannon divergence D(SS) using the probability density functions pi(x) and pj(x) is used as the distance index between sets Si and Sj. Once the distance index is obtained, the similarity index can also be easily obtained. In this manner, the relationship index E(SS), which is an index value of the accurate relationship, can be calculated.

[0100] In the functional block diagram shown in Figure 2, it is also possible to realize an inter-set relationship calculation device that does not include the word vector calculation means 21, coordinate value calculation means 23, item placement means 24, and morphological analysis means 25, but only includes the weight calculation means 221, probability density function definition means 222, and relationship index calculation means 225, which are part of the relationship matrix generation means 22. In this case, in the hardware configuration shown in Figure 1, the weight calculation means 221, probability density function definition means 222, and relationship index calculation means 225 are realized by the CPU 1 executing a program stored in the storage device 3. In the case of the second method, the probability density function definition means 222 may not be provided. The inter-set relationship calculation device is a device that finds the relationship between two sets Si and Sj, which have elements of a d-dimensional vector.

[0101] <1.3.3. Comparison with other technologies> The advantages of this embodiment over other techniques will be described. When the only information associated with each item belonging to a category of interest is the number of elements in the set, a method using normalized mutual information is known as a method for calculating the relationship between sets using that information. When the number of elements in a set is small, there is a problem in that the accuracy of calculating the numerical value of the relationship index decreases. In this embodiment, when the elements of the set are vectors, the index of the relationship between the sets is determined using information on the distribution of the vectors, thereby alleviating the problem of decreased accuracy.

[0102] Furthermore, similar to this embodiment, when the input data is a vector set, a different index value from that of this embodiment can be considered. For example, by utilizing the fact that (total variance) = (intra-cluster variance) + (inter-cluster variance), it is possible to calculate an index of relationship as the ratio of the inter-cluster variance to the total variance. In this case, even if the distribution shapes are different, there is a problem in that if the mean values ​​are the same, the value of the inter-set distance will be 0. In this embodiment, the value of the inter-set distance will be 0 only when the distribution shapes are the same. Therefore, even if only the mean values ​​are the same, if the variances are different, a value other than 0 will be obtained as the inter-set distance. In this embodiment, the index even reflects the difference in variance.

[0103] It is also possible to use the Jensen-Shannon divergence on the front side as an index of inter-set distance. However, the parent distribution is used in the definition formula. The same is true for the Jensen-Shannon divergence on the back side. In this case, the logarithmic function is in the form of a sum, and further transformation of the formula is not possible. Therefore, even for normal distributions, the index value cannot be accurately calculated from the parameter values. In this embodiment, the double-sided Jensen-Shannon index is defined by simply adding the front and back sides. This eliminates the parent distribution. In the case of normal distributions, the index value can be expressed as a parameter formula, so it can be accurately calculated by substitution calculation.

[0104] In addition, in the case of the Jensen-Shannon divergence, if the front and back of the Kullback-Leibler divergence are swapped, a reverse version different from the front version appears. However, in the definition formula of this embodiment, even if the same thing is done, the formula returns to the same formula, so either the front or back version can be used.

[0105] 2. Second embodiment <2.1.Device configuration> Next, a second embodiment will be described. FIG. 14 is a functional block diagram showing the configuration of an information processing device according to a second embodiment of the present disclosure. In FIG. 14, 13 denotes a word database, 14 denotes an image database, 20a denotes a processing unit, 21 denotes a word vector calculation means, 22 denotes a relationship matrix generation means, 27 denotes an adjacency matrix generation means, 28 denotes a relationship graph generation means, 29 denotes an image analysis means, and 30 denotes an output means. The information processing device shown in FIG. 14 generates a relationship graph showing the relationships between each item using a set related to each item belonging to a category of interest. The hardware configuration of the information processing device according to the second embodiment is the same as that of the first embodiment, as shown in FIG. 1.

[0106] As in the first embodiment, the word vector calculation means 21 is a means for calculating word vectors, which are positions in a d-dimensional coordinate space (d is a natural number), based on the meaning of each word. As in the first embodiment, the relationship matrix generation means 22 is a means for calculating a relationship matrix R regarding the relationship between sets, using word vectors, which are elements of the sets. As in the first embodiment, the adjacency matrix generation means 27 is a means for pruning the relationship matrix R to calculate the adjacency matrix W. The relationship graph generation means 28 is a means for generating a relationship graph based on the adjacency matrix W. The image analysis means 29 is a means for reading each image from the image database 14 and identifying words appropriate for each image. The word vector calculation means 21, the relationship matrix generation means 22, the adjacency matrix generation means 27, the relationship graph generation means 28, and the image analysis means 29 are included in the calculation processing unit 20, and are realized by the CPU 1 executing a program.

[0107] The output means 30 is a means for graphically outputting the relationship graph generated by the relationship graph generation means 28, and similarly to the first embodiment, is realized by the display unit 6, such as a printer or a display device, via the data input / output I / F 5. The word database 13 is a database that stores word IDs that identify words in association with the words, and is realized by the storage device 3 shown in Fig. 1. The image database 14 is a database that stores images (image data) made up of multiple pixels in association with image IDs that identify the images, and is realized by the storage device 3.

[0108] 15 is a diagram showing an example of information stored in the image database 14. In this embodiment, a set (a set of words) related to each item (image) belonging to a category of interest (a predetermined group of images managed by the image database 14, etc.) is used as input data, and a process is performed to display a relationship graph in which each item is a node. Here, the set of images stored in the image database 14 becomes the category of interest, and each image becomes an item. Then, the set of words corresponding to each image becomes the set related to each image.

[0109] The set associated with each item refers to a set associated (corresponding, linked) with each item, and includes a set contained in each item and a set attached to each item. For example, if each item is a document, the set contained in each item is the set of words contained in the document. Typically, documents are composed of sentences written in natural language. Therefore, if each item is a document, each item is associated with a sentence written in natural language.

[0110] Morphological analysis of a sentence can be used to break it down into a group of words. It is also possible to extract only words of a user-specified part of speech from those words. In addition, if a user specifies a conjugated part of speech, such as a verb or adjective, the original form can be obtained. The collection of original words of a specific part of speech (or multiple parts) extracted from a sentence by morphological analysis can be used as an associated set for that item. For example, MeCab is an example of freeware that performs morphological analysis.

[0111] Furthermore, the set associated with each item is, for example, a set of elements associated with each item under some condition, or, if each item is a group, a set of elements included in that group. The sets included in each item and the sets associated with each item can usually be expressed as some kind of word.

[0112] For example, if a category of interest is a group of images and each item in the category of interest is an individual image, the set associated with each item can be a set of words that describe what the image represents.

[0113] As shown in Fig. 15, the image database 14 stores image names, artist names, and image data in association with image IDs, which are image identification information for identifying images. The image data only needs to have a storage address recorded so that the image data can be acquired by identifying the image ID. The example in Fig. 15 indicates that an image (work) titled "XXXXXX" by artist "Mr. A" is registered with image ID "B001." For example, an image of a painting by a certain artist (painter) can be used as the image.

[0114] Fig. 16 is a diagram showing an example of information stored in word database 13. As shown in Fig. 16, word database 13 stores words and image IDs of images to which the words are assigned as tags that express the content, in association with word IDs that are word identification information that identify the words. In the example of Fig. 16, the word registered as word ID "T0001" in the first line expresses the content of the image identified by image ID "B001."

[0115] Each word registered in the word database 13 is associated with an image ID, and therefore stores a set (a set of words) related to each image belonging to a group of images (registered in the image database 14) that is a category of interest. In this embodiment, information on the words recorded in this word database 13 is used as input to create a relationship graph in which each image is a node. Since the word database 13 has the configuration shown in Fig. 16, it is also possible to identify the word IDs of all words tagged to an image by referencing the image ID.

[0116] In reality, each of the components shown in FIG. 14 is realized by installing a dedicated program in hardware such as a computer and its peripheral devices, as shown in FIG. 1. That is, the computer executes the contents of each of the components in accordance with the dedicated program. In this embodiment, the CPU is preferably a multi-core CPU. Note that in this specification, the term "computer" refers to a device that has a processing unit such as a CPU or GPU and is capable of data processing, and includes not only general-purpose computers such as personal computers, but also mobile terminals such as tablets equipped with a CPU, and computers incorporated in various devices.

[0117] <2.2. Processing Operation> The information processing device 100a according to this embodiment generates a relationship graph by executing predetermined information processing. Next, the processing operation of the information processing device 100a shown in FIGS. 1 and 14 will be described along with a method for generating a relationship graph according to this embodiment. FIG. 17 is a flowchart showing the processing operation of the information processing device according to the second embodiment. First, the image analysis means 29 reads and analyzes each image from the image database 14 and determines words corresponding to the content expressed by each image (step S21). Specifically, the image analysis means 29 performs image analysis on each image to identify words to be tagged. Various known image analysis methods can be used as the image analysis method performed by the image analysis means 29. For example, image tagging software called "Clarifai" by Clarifai, Inc., USA, can be used as image analysis software. The identified words are associated with the image ID of the image and registered in the word database 13 as shown in FIG. 16.

[0118] Next, for each word registered in the word database 13 as a category of interest, a word vector, which is a word coordinate, is calculated (step S22). Specifically, similar to the first embodiment, the word vector calculation means 21 calculates a word vector, which is a position in a d-dimensional (d is a natural number) coordinate space, based on the meaning of each word. A word vector is an element included in a set related to an item called a document, and is a d-dimensional vector. The relationship between two words is identified using a predetermined method. For example, the word vector calculation means 21 can use technology from word analysis software such as "Word2Vec" by Google Inc.

[0119] The processes up to step S22 may be performed by another computer, etc. Then, the information processing device 100 according to this embodiment may read the word vector data processed by the other computer, etc., and execute the processes from step S23 onwards.

[0120] Next, a relationship matrix R relating to the relationship between the sets is calculated from the vector values ​​of the elements of the sets (step S23). Specifically, the relationship matrix generation means 22 calculates an index value of the relationship and generates a relationship matrix R in which the index value of the relationship is the matrix element. Here, the relationship is information indicating the relationship between the two, and can be expressed by various indices. For example, similarity, which is the degree to which the two are similar, or distance, which is the degree to which the two are separated, can be used. The closer the two are, the greater the similarity, and the farther the two are, the greater the distance. Therefore, similarity and distance can be converted into each other using a predetermined conversion formula. Let V be the set of images registered in the image database 14, and each image be v. j Let the number of elements in the image set V be n. The image set is a category of interest, and the image v j is the item. And each image v j ∈V, i.e., each image v j are elements of the set V. Each image v j From the image analysis, we define a set of words as T jIn this case, in step S23, for j, i indicating an arbitrary order among n images, image v j Set T, the set of words corresponding to j , image v i Set T, the set of words corresponding to i The index value r that represents the relationship between ji The relationship matrix R is calculated by dividing the relationship index value r ji is a matrix having the j-th row and ith column component. Details of the process in step S23 are the same as those in step S13 in the first embodiment, and are as described in the first embodiment.

[0121] After the relationship matrix R is obtained by the process in step S23, edge weeding is then performed on the relationship matrix R to obtain an adjacency matrix W (step S24). Step S24 is an adjacency matrix generation step. Specifically, the adjacency matrix generation means 27 calculates the index values ​​r of the relationships that make up the relationship matrix R. ji Using the corresponding component w ji The adjacency matrix W is generated by calculating each element w of the adjacency matrix W. ji is calculated by executing the process according to the following equation (33).

[0122] w ji =r ji (r ji (if the value of is greater than or equal to a given value) w ji =0 (r ji (if the value of is less than some given value) ···(33)

[0123] In step S24, a process is performed to forcibly cut off edges with weak weights. ji When the value of is small, w ji As the value of r ji Instead of using r, we replace it with 0. This operation is sometimes called "cutting the edge." ji Determine whether the value of is greater than or equal to a predetermined value.ji The value (threshold value) can be set appropriately.

[0124] In the above formula (33), the predetermined value can be specified in advance by the operator. Instead of specifying the value itself, the operator can specify what percentage of the number of edges n(n-1) / 2 in the fully connected symmetric relation graph is to be weeded, i.e., r ji Regardless of the value of w ji The predetermined value may be calculated by a percentile method by specifying the percentage at which the value of is set to 0. Alternatively, the predetermined value may be calculated automatically based on a criterion such as maximizing the small-world property.

[0125] The adjacency matrix W is the index value r of the symmetric relationship as shown in the following equation (34). ji The component w corresponding to ji Let be the matrix whose component is the j-th row and the ith column. Therefore, the adjacency matrix W is a symmetric square matrix of order n, corresponding to the number of images n.

[0126] W=[w ji ](j=1,2,3,···,n;i=1,2,3,···,n)··· (34)

[0127] It is possible to use the relationship matrix R as the adjacency matrix W. However, in that case, the graph will be fully connected. When using the relationship matrix R as the adjacency matrix W, the corresponding component w ji The value of will never be 0. When the adjacency matrix W is viewed as a graph, it is fully connected, although the weights of each edge may vary. When a graph is fully connected, there is a problem in that it is difficult to intuitively grasp the structure when viewing an image of the graph.

[0128] Next, a relationship graph is created based on the adjacency matrix W (step S25). Step S25 is a relationship graph generation step. Specifically, the relationship graph generation means 28 generates a relationship graph by dividing each element w jiA graph for graphical output is created using the above. The relationship graph generation means 28 can be, for example, a means that realizes a method based on a known mechanical model. This mechanical model method works roughly as follows: A model is introduced in which each node in the graph can move freely and each node carries an electric charge of the same value. Because charges of the same sign repel each other, a repulsive force is exerted depending on the distance between nodes. If there are no edges at all, the nodes will scatter. On the other hand, a spring model is introduced in which a contraction force is exerted on edges in proportion to their extension. As the initial state, nodes are randomly scattered, a physical simulation is performed, and the iterations are terminated when the result stabilizes. GraphViz, for example, is a well-known freeware that implements this method. The created graph is then output to output means 30, such as a display device.

[0129] Although the preferred embodiments of the present disclosure have been described above, the present disclosure is not limited to the above embodiments and various modifications are possible. For example, in the first embodiment, the word database 10, the document database 11, the coordinate value calculation means 23, the item placement means 24, and the morphological analysis means 25 were provided, and each item belonging to a category of interest was treated as a document, and coordinate values ​​for arranging each document, which is an item, in k-dimensional space were calculated. However, instead of the word database 10, the document database 11, and the morphological analysis means 25 shown in the first embodiment, the word database 13, the image database 14, and the image analysis means 29 shown in the second embodiment may be provided, and each item belonging to a category of interest may be treated as an image, and coordinate values ​​for arranging each image, which is an item, in k-dimensional space may be calculated.

[0130] In the second embodiment, the word database 13, the image database 14, and the image analysis means 29 are provided, and a relationship graph showing the relationships between each item is generated using a set related to each item belonging to the category of interest. However, instead of the word database 13, the image database 14, and the image analysis means 29 shown in the second embodiment, the word database 10, the document database 11, and the morphological analysis means 25 shown in the first embodiment may be provided, and each item belonging to the category of interest may be treated as a document, and a relationship graph showing the relationships between each item, that is, a document, may be generated. [Explanation of symbols]

[0131] 1...CPU(Central Processing Unit) 2...RAM(Random Access Memory) 3...Storage device 4. Instruction input I / F 5. Data input / output interface 6...Display section 7. GPU 8. Frame memory 10. Word Database 11. Document database 13. Word Database 14. Image database 20, 20a... Processing unit 21. Word vector calculation method 22. Relationship matrix generation method 221...Weight calculation means 222···Probability density function definition means 225···Means for calculating relationship indices 23. Coordinate value calculation means 24. Item placement method 27. Adjacency matrix generation means 28. Relationship graph generation method 29. Image analysis methods 30. Output means 100, 100a... Information processing device

Claims

1. Let d be a natural number and N be a natural number greater than or equal to 2. A set family SS = {S1, S2, S3, ..., SN} consists of N non-empty sets, and each set Si (i = 1, 2, ..., N) has two or more elements x that are d-dimensional vectors. An apparatus for determining relationships between sets in the set family SS, comprising: a weight calculation means for calculating a weight wi of each set Si, which is an element of the set family SS, by executing a process according to the following equation (35) when the set Si has ni elements; [Equation 25] ・・・（３５） a probability density function definition means for defining a probability density function pi(x) that generates the element x; and a distance index D(SS) defined by the following formula (1) using all combinations of sets Si (i=1, 2, . . . N) and sets Sj (j=1, 2, . . . N), which are two elements of the set family SS; [Equation 1] ・・・（１） a relationship index calculation means for calculating an approximation of the distance index D(SS) by a division quadrature method and calculating a relationship index, which is an index of a relationship between each set Si belonging to the set family SS, using the approximation; An inter-set relationship calculation device having the above.

2. Let d be a natural number and N be a natural number greater than or equal to 2. A set family SS = {S1, S2, S3, ..., SN} is made up of N non-empty sets, and each set Si (i = 1, 2, ..., N) has two or more elements x that are d-dimensional vectors. The apparatus for determining the relationship between sets in the set family SS comprises: a weight calculation means for calculating a weight wi of each set Si that is an element of the set family SS when the set Si has ni elements, by executing a process according to the following equation (36): [Equation 26] ・・・（３６） The sample mean μ and the sample covariance matrix C of the element x of each set S are calculated, and a distance index D(SS) is calculated by the following formula (2) using all combinations of the set S (i = 1, 2, ... N) and the set S (j = 1, 2, ... N), which are two elements of the set family S; [Equation 2] ・・・（２） a relationship index calculation means for calculating a relationship index, which is an index of a relationship between each set Si belonging to the set family SS, using the index D(SS); An inter-set relationship calculation device having the above.

3. An information processing device that calculates coordinate values ​​for locating each item in a k-dimensional space using a set related to each item belonging to a category of interest, a relationship matrix generating means for generating a relationship matrix having the relationship indices calculated for two sets related to each item by the relationship index calculating means according to claim 1 or 2 as matrix elements; a coordinate value calculation means for calculating coordinate values ​​for arranging each item in a k-dimensional space by performing a predetermined transformation on the relationship matrix; An information processing device having the above.

4. An information processing device that generates a relationship graph with each item as a node using a set related to each item belonging to a category of interest, a relationship matrix generating means for generating a relationship matrix having the relationship indices calculated for two sets related to each item by the relationship index calculating means according to claim 1 or 2 as matrix elements; an adjacency matrix generating means for generating an adjacency matrix based on the calculated relationship matrix; a relationship graph generation means for generating a relationship graph corresponding to the generated adjacency matrix; An information processing device having the above.

5. a morphological analysis means for extracting morphemes by performing a morphological analysis on a sentence written in a natural language when each item belonging to the category of interest is associated with the sentence, the set associated with each item being made up of words, and each word being associated with a d-dimensional vector; a word vector calculation means for calculating a d-dimensional word vector for each of the extracted morphemes; and The information processing device according to claim 3 , wherein the relationship matrix generating means generates the relationship matrix using the set of calculated word vectors.

6. an image analysis means for performing image analysis on the images to identify words obtained as elements of a set related to the images, when each item belonging to the category of interest is an image, a set of words corresponding to each image is a set related to each image, and a d-dimensional vector is associated with each word; a word vector calculation means for calculating a d-dimensional word vector for each of the identified words; and The information processing device according to claim 3 , wherein the relationship matrix generating means generates the relationship matrix using the set of calculated word vectors.

7. Let d be a natural number and N be a natural number greater than or equal to 2. A program for a computer to determine relationships between sets in a set family SS, where the set family SS = {S1, S2, S3, ..., SN} consists of N non-empty sets, and each set Si (i = 1, 2, ..., N) has two or more elements x that are d-dimensional vectors, comprising: Computer, a weight calculation means for calculating a weight wi of each set Si, which is an element of the set family SS, by executing a process according to the following equation (37) when the set Si has ni elements; [Equation 27] ・・・（３７） a probability density function definition means for defining a probability density function pi(x) that generates the element x of the set Si; Using all combinations of sets Si (i=1, 2, . . . N) and sets Sj (j=1, 2, . . . N), which are two elements of the set family SS, a distance index D(SS) is defined by the following formula (3): [Equation 3] ・・・（３） A program for functioning as a relationship index calculation means that calculates an approximation of the distance index D(SS) by the divisional quadrature method and calculates a relationship index, which is an index of the relationship between each set Si belonging to the set family SS, using the approximation.

8. Let d be a natural number and N be a natural number greater than or equal to 2. A program for a computer to determine relationships between sets in a set family SS, where the set family SS = {S1, S2, S3, ..., SN} consists of N non-empty sets, and each set Si (i = 1, 2, ..., N) has two or more elements x that are d-dimensional vectors, comprising: Computer, a weight calculation means for calculating a weight wi of each set Si, which is an element of the set family SS, by executing a process according to the following equation (38) when the set Si has ni elements; [0000] ・・・（３８） Calculate the sample mean μi and sample covariance matrix Ci of the element x of each set S, and calculate the distance index D(SS) calculated by the following formula (4) using all combinations of the set S (i = 1, 2, ... N) and the set S (j = 1, 2, ... N), which are two elements of the set family S, [Equation 4] ・・・（４） a relationship index calculation means for calculating a relationship index, which is an index of a relationship between each set Si belonging to the set family SS, using the index D(SS); A program to function as a

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