Information processing device, information processing method, and program

Abstract

To provide an information processing apparatus which can present relationships between items belonging to a category of interest, an information processing method, and a program.SOLUTION: An information processing apparatus 100 which calculates coordinate values for arranging items in a k-dimensional space using a set related to the items belonging to a category of interest includes: relational matrix generation means 22 which generates a relational matrix by calculating an index value of relationship between sets related to two items, between the two items, for each of the items belonging to the category of interest; adjusted matrix generation means 23 which generates an adjustment function which monotonously changes using an average μ of components of a triangular matrix in the relational matrix, and generates an adjusted matrix by causing the adjustment function to act on each of the components of the relational matrix; and coordinate value calculation means 24 which calculates coordinate values for arranging the items in the k-dimensional space by applying a predetermined conversion to the adjusted matrix.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present disclosure relates to a technology for extracting relationships between items that belong to a category of interest based on data related to each item, and visualizing the structure of the entire category. [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 that it is difficult to analyze the relationships between documents using the words that make up the documents.Furthermore, it is also difficult to analyze the relationships between multiple items, not just documents.

[0006] Therefore, an object of the present disclosure is to provide an information processing device, an information processing method, and a program that are capable of presenting the relationships between items that belong to a category of interest. [Means for solving the problem]

[0007] In order to solve the above problems, the present disclosure 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 between two items by calculating an index value of a relationship between sets related to the two items for each item belonging to the category of interest; an adjusted matrix generating means for generating an adjustment function that changes monotonically using a mean μ of elements of a triangular matrix in the relationship matrix, and for generating an adjusted matrix by applying the adjustment function to each element of the relationship matrix; a coordinate value calculation means for performing a predetermined transformation on the adjusted matrix to calculate coordinate values ​​for arranging each item in a k-dimensional space; The present invention provides an information processing device having the above.

[0008] In addition, the information processing device according to the present disclosure includes: The adjustment function may be a monotonically increasing function, and may be a sigmoid function shown in equation (1) constructed using the average μ of the elements of the triangular matrix in the relationship matrix S.

number

[0009] In addition, the information processing device according to the present disclosure includes: The adjustment function may be a monotonically decreasing function, which is a sigmoid function shown in equation (2) configured using the average μ of the elements of the triangular matrix in the relationship matrix S.

number

[0010] In addition, the information processing device according to the present disclosure includes: The adjustment function is a monotonically increasing function and is configured using the mean μ and standard deviation σ of the elements of the triangular matrix in the relationship matrix S, and is expressed by the normal distribution N(μ, σ) shown in Equation (3). 2) may be a cumulative probability density function of

number

[0011] In addition, the information processing device according to the present disclosure includes: The adjustment function is a monotonically decreasing function and is configured using the mean μ and standard deviation σ of the elements of the triangular matrix in the relationship matrix S, and is expressed by the normal distribution N(μ, σ) shown in Equation (4). 2 ) may be a cumulative probability density function of

number

[0012] In addition, the information processing device according to the present disclosure includes: The adjustment function may use a coefficient r that satisfies r≧1 and a reduction coefficient s that satisfies 0≦s≦1, and may use coefficients a′ and μ′ obtained by the following equation (5) instead of the coefficient a and the coefficient μ.

number

[0013] In addition, the information processing device according to the present disclosure includes: The adjustment function may use a coefficient r that satisfies r≧1 and a reduction coefficient s that satisfies 0≦s≦1, and may use coefficients σ′ and μ′ obtained by the following equation (6) instead of the coefficients σ and μ.

number

[0014] In addition, the information processing device according to the present disclosure includes: The relationship matrix generation means may calculate, as an index value of the relationship, normalized self-information of a two-variable joint probability distribution generated based on the number of elements of a universal set that includes the sets related to the two items, the number of elements of a set related to one item, the number of elements of a set related to the other item, and the number of elements of an intersection of the set related to one item and the set related to the other item.

[0015] In addition, the information processing device according to the present disclosure includes: The relationship matrix generation means may calculate, as an index value of the relationship, a normalized mutual information of a joint probability distribution of two variables that is generated based on the number of elements of a universal set that includes the sets related to the two items, the number of elements of a set related to one item, the number of elements of a set related to the other item, and the number of elements of an intersection of a set related to one item and a set related to the other item.

[0016] In addition, the information processing device according to the present disclosure includes: The method further comprises 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, The relationship matrix generating means may generate the relationship matrix using the set of extracted morphemes.

[0017] In addition, the information processing device according to the present disclosure includes: further comprising image analysis means for performing image analysis on the images to identify words when each item belonging to the category of interest is an image; The relationship matrix generating means may generate the relationship matrix using the set of identified words.

[0018] The present disclosure also provides: 1. An information processing method in which a computer calculates coordinate values ​​for locating each item in a k-dimensional space using a set associated with each item belonging to a category of interest, the method comprising: The computer generating a relationship matrix by calculating, for each item belonging to the category of interest, an index value of the relationship between two items and sets related to the two items; generating a monotonically varying adjustment function using the average μ of the elements of the triangular matrix in the relationship matrix, and generating an adjusted matrix by applying the adjustment function to each element of the relationship matrix; An information processing method is provided that performs a predetermined transformation on an adjusted matrix to calculate coordinate values ​​for locating each item in a k-dimensional space.

[0019] The present disclosure also provides: A program that causes a computer to calculate coordinate values ​​for locating each item in a k-dimensional space using a set associated with each item belonging to a category of interest, the program comprising: Computer, a relationship matrix generating means for generating a relationship matrix between two items by calculating an index value of a relationship between sets related to the two items for each item belonging to the category of interest; an adjusted matrix generating means for generating a monotonically varying adjustment function using the average μ of the elements of the triangular matrix in the relationship matrix, and for generating an adjusted matrix by applying the adjustment function to each element of the relationship matrix; coordinate value calculation means for performing a predetermined transformation on the adjusted matrix to calculate coordinate values ​​for arranging each item in a k-dimensional space; We provide a program that functions as a [Effects of the Invention]

[0020] According to the present disclosure, it is possible to visualize the relationships between items belonging to a category of interest. [Brief explanation of the drawings]

[0021] [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 illustrating a configuration of an information processing device according to an 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] 10 is a flowchart illustrating a processing operation of an information processing device according to an embodiment of the present disclosure. [Figure 6] FIG. 10 is a diagram showing the relationship between a histogram of elements of a triangular matrix in a relationship matrix S and an adjustment function f(x). [Figure 7] FIG. 10 is a diagram illustrating the relationship between a reduction coefficient s and an adjustment function f(x). [Figure 8] FIG. 10 is a diagram for explaining a scatter diagram. DETAILED DESCRIPTION OF THE INVENTION

[0022] Preferred embodiments of the present disclosure will be described in detail below with reference to the drawings. <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 central processing unit (CPU) 1, a random access memory (RAM) 2 serving as the computer's main memory, a large-capacity storage device 3 such as a hard disk, solid-state drive (SSD), or flash memory for storing programs and data executed by the CPU 1, an instruction input interface (I / F) 4 such as a keyboard or mouse, a data input / output interface (I / F) 5 for communicating data with external devices such as data storage media, a display unit 6 such as a liquid crystal display, a graphics processing unit (GPU) 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 one another via a bus. Because the results of calculations performed 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 equipped with an interface to the display unit 6 and attached to the general-purpose computer via the bus.

[0023] 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.

[0024] Fig. 2 is a functional block diagram showing the configuration of an information processing device according to this embodiment. In Fig. 2, 10 denotes a word database, 11 denotes a document database, 20 denotes a calculation processing unit, 21 denotes a common element number matrix generation means, 22 denotes a relationship matrix generation means, 23 denotes an adjusted distance matrix generation means, 24 denotes a coordinate value calculation means, 27 denotes an item placement means, 25 denotes a morphological analysis means, and 30 denotes an output means.

[0025] The common element number matrix generation means 21 is a means for calculating a common element number matrix M for any combination of two documents, where the documents are items, based on two sets whose elements are words contained in each document. Each element of the common element number matrix M is the number of common elements between the two sets. The relationship matrix generation means 22 is a means for calculating a relationship matrix S from the common element number matrix M. The adjusted matrix generation means 23 is a means for applying an adjustment function to the relationship matrix S to calculate an adjusted matrix W. The coordinate value calculation means 24 is a means for calculating the coordinate values ​​of each item based on the adjusted matrix W. The item placement means 27 is a means for placing items based on the calculated coordinate values ​​of each item. The morphological analysis means 25 is a means for reading each document from the document database 11 and extracting words contained in each document. The common element number matrix generation means 21, relationship matrix generation means 22, adjusted matrix generation means 23, coordinate value calculation means 24, item placement means 27, and morphological analysis means 25 are included in the calculation processing unit 20 and are realized by the CPU 1 executing a program.

[0026] The output means 30 is a means for graphically outputting items placed at coordinate values ​​in space by the item placement means 27, and is realized by a display unit 6 such as a printer or a display device via the data input / output I / F 5.

[0027] 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.

[0028] 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) associated with 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 directed graph in which each item is a node. Here, the information stored in the document database 11, i.e., a set of documents, is the category of interest, and each document is an item. A set of words contained in each document is a set associated with each document. A set associated with each item refers to a set associated (corresponding or linked) with each item, including 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 included 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, a set of elements (usually expressible as some kind of word) included in the group if each item is a group.

[0029] 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.

[0030] 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 depicted in the image can be adopted as a set associated with each item.

[0031] 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."

[0032] 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."

[0033] 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 document group (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 directed graph in which each document is 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."

[0034] 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.

[0035] <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 this embodiment. First, the morphological analysis means 25 reads each document from the document database 11 and extracts words contained in each document (step S10). 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.

[0036] 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.

[0037] T j ={t j1 , t j2 , t j3 ,···} , j=1,2,3,···,n

[0038] 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).

[0039] Next, for any two combinations of documents from the set of documents registered in the document database 11 as categories of interest, a common element number matrix M is calculated using two sets of words contained in each document (step S20). Each element of the common element number matrix M is the number of common elements between the two sets. This common element number matrix M is a square matrix consisting of n rows and n columns. Furthermore, this common element number matrix M is a symmetric matrix, that is, a matrix that matches its own transposed matrix. The common element number is the number of elements (here, words) that appear in common in the sets related to the two documents. The number of common elements that appear in common in the sets related to the two documents, document vj and document vi, is m ji As a specific process in step S20, first, for all combinations of each document vj where j=1, 2, 3, . . . , n and each document vi where i=1, 2, 3, . . . , n among n documents, the number of common elements m ji Find the value of the number of common elements m ji is expressed by the following (Equation 11).

[0040] m ji =n(T j ∩T i )(j=1,2,3,···,n;i=1,2,3,···,n)…… (Equation 11) Here, n() represents the number of elements in the set.

[0041] When the word database 10 is used, the process shown in (Equation 11) is acquired by identifying two document IDs and counting the number of word IDs recorded in association with the two.

[0042] The common element number matrix M is the number of common elements m ji Let be the matrix whose component is the jth row and the ith column.

[0043] M=[m ji ](j=1,2,3,···,n;i=1,2,3,···,n)…… (Equation 12)

[0044] Under these conditions, the number of common elements m ji and the number of common elements m ij are equal, the common element number matrix M is a symmetric matrix.

[0045] Next, a relationship matrix S is calculated from the common element number matrix M (step S30). Here, the relationship is information indicating the relationship between two entities, and can be expressed by various indices. For example, similarity, which indicates the degree to which two entities are similar, or distance, which indicates the degree to which two entities are distant from each other, can be used. The closer the entities are to each other, the greater the similarity, and the farther the entities are from each other, 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 S, first, for each j and 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 s that represents the relationship between ji Calculate the index value s ji is a function f(m jj, m ii, m ji ) and m jj, m ii, m ji It is calculated from the number of common elements of the three.

[0046] s ji =f(m jj, m ii, m ji )…… (Equation 13)

[0047] s shown in (Equation 13) ji does not necessarily have symmetry s ji = s ij In other words, the common element number matrix M is guaranteed to be a symmetric matrix, but the relationship matrix S is still a function f(m jj ,m ii ,m ji ) can be symmetric or asymmetric depending on the specific definition of s.ji The function f(m jj ,m ii ,m ji ) There are a great many options for the specific form of the variance. In this embodiment, as will be described later, the asymmetric normalized autoinformation of the joint probability distribution of two variables, the asymmetric normalized mutual information of the joint probability distribution of two variables, the regression coefficient of the joint probability distribution of two variables, etc. are mainly used.

[0048] Index value s ji Among the common elements to calculate the number of common elements m jj is the document v j The number of words of a particular part of speech in ii is document v i The number of common elements m ji , number of common elements m ij are both documents v i and document v j Since it is a number that appears in common in m ji =m ij is.

[0049] The relationship matrix S is the relationship index value s as shown in the following (Equation 14). ji Let be the matrix whose component is the jth row and the ith column.

[0050] S=[s ji ](j=1,2,3,···,n;i=1,2,3,···,n)…… (Equation 14)

[0051] The number of row and column components of the relationship matrix S is the same as the common element number matrix M, and corresponds to the number of documents n. Ta n In this embodiment, the distance between the nodes is adjusted to 0. That is, s ii , s jj All of the diagonal elements of the relationship matrix S 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

[0052] After the relationship matrix S is obtained by the process in step S30, a monotonically changing adjustment function is generated based on the relationship matrix S, and the adjustment function is applied to obtain the adjusted matrix W (step S40). Specifically, the adjusted matrix generation means 23 calculates the index values ​​s of the relationships that constitute the relationship matrix S. ji Using the corresponding component w ji The adjusted matrix W is generated by calculating each component w of the adjusted matrix W. ji can be obtained using either a monotonically increasing adjustment function or a monotonically decreasing adjustment function as the monotonically changing adjustment function. The monotonically changing adjustment function is generated based on the relationship matrix obtained by the relationship matrix generation means 22.

[0053] When the characteristics of the components of the relationship matrix obtained in step S30 are utilized as they are, a monotonically increasing adjustment function f(x) is used in step S40. On the other hand, when the characteristics of the components of the relationship matrix obtained in step S30 are reversed, a monotonically decreasing adjustment function g(x) is used in step S40. As the monotonically increasing adjustment function f(x), for example, those shown in (Formula 15) and (Formula 16) below can be used. Furthermore, as the monotonically decreasing adjustment function g(x), for example, those shown in (Formula 17) and (Formula 18) below can be used. The following (Formula 15) is an example of a monotonically increasing adjustment function f(x).

[0054] (Equation 15)

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[0055] In (Equation 15), x is the relationship index value s ji Substituting f(x), we get the component w ji In (Equation 15), σ is the standard deviation of the elements of the triangular matrix in the relationship matrix S, and σ 2is the variance of the elements of the triangular matrix in the relationship matrix S, and μ is the average of the elements of the triangular matrix in the relationship matrix S. Here, the triangular matrix refers to an upper triangular matrix or a lower triangular matrix of the relationship matrix S excluding the diagonal elements. In this embodiment, the variances σ of the upper triangular matrix and the lower triangular matrix in the relationship matrix S are 2 Since the mean μ is the same for both, either an upper triangular matrix or a lower triangular matrix can be used. In this way, the monotonically increasing adjustment function f(x) shown in (Equation 15) is a function generated based on the relationship matrix S. exp() is an exponential function with Napier's number as the base, and the value in () following exp is the exponent. (Equation 15) is a function generated based on the normal distribution N(μ, σ 2 ) from minus infinity to x, that is, the cumulative probability density function. In reality, it is not possible to set minus infinity, so the adjusted matrix generation means 23 sets a sufficiently small negative value to the component w ji Calculate.

[0056] FIG. 6 is a diagram showing the relationship between the histogram of the elements of the triangular matrix in the relationship matrix S and the adjustment function f(x). In the example of FIG. 6, the elements of the triangular matrix are concentrated around 0. In such a case, each element s in the relationship matrix S ji By applying the adjustment function f(x) to each component w of the adjusted matrix W, ji The value of approaches a normal distribution. By applying the adjustment function f(x) in this way to obtain the adjusted matrix W, it becomes possible to emphasize the cluster separability.

[0057] Moreover, the adjusted matrix generating means 23 executes processing according to the following (Equation 16) instead of the adjustment function f(x) shown in the above (Equation 15) to generate each component w of the adjusted matrix W. ji may be calculated.

[0058] (Equation 16)

number

[0059] In (Equation 16), x is the relationship index value s ji Substituting f(x), we get the component w ji In (Equation 16), μ is the mean of the elements of the triangular matrix in the relationship matrix S. The variance σ of the elements of the triangular matrix in the relationship matrix S is 2 is not used. In this way, the monotonically increasing adjustment function f(x) shown in (Equation 16) is a function generated based on the relationship matrix S. a is a coefficient obtained by dividing 2 by the standard deviation σ, and a=2 / σ. (Equation 16) is a sigmoid function.

[0060] Comparing the case where the cumulative probability density function shown in (Formula 15) is used with the case where the sigmoid function shown in (Formula 16) is used, the cumulative probability density function shown in (Formula 15) requires an increased amount of calculation due to integration operations, whereas the sigmoid function shown in (Formula 16) requires a smaller amount of calculation. Therefore, the adjusted matrix W can be obtained faster when using the sigmoid function shown in (Formula 16).

[0061] Moreover, the following (Equation 17) is an example of a monotonically decreasing adjustment function g(x).

[0062] (Equation 17)

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[0063] In (Equation 17), x is the relationship index value s ji Substituting g(x), we get the component w ji As is clear from comparing (Equation 15) and (Equation 17), the adjustment function g(x) is 1 minus the monotonically increasing adjustment function f(x) shown in (Equation 15). As in (Equation 15), in (Equation 17), σ is the standard deviation of the elements of the triangular matrix in the relationship matrix S, and σ 2is the variance of the elements of the triangular matrix in the relationship matrix S, and μ is the average of the elements of the triangular matrix in the relationship matrix S. Here, the triangular matrix refers to an upper triangular matrix or a lower triangular matrix of the relationship matrix S excluding the diagonal elements. In this embodiment, the variances σ of the upper triangular matrix and the lower triangular matrix in the relationship matrix S are 2 Since the mean μ is the same for both, either an upper triangular matrix or a lower triangular matrix may be used. In this way, the monotonically decreasing adjustment function g(x) shown in (Equation 17) is a function generated based on the relationship matrix S.

[0064] Although not shown in the figure, when a monotonically decreasing adjustment function g(x) is used, each component s in the relationship matrix S is ji By applying the adjustment function g(x) to each component w of the adjusted matrix W, ji The value of approaches a normal distribution. By applying the adjustment function g(x) in this way to obtain the adjusted matrix W, it becomes possible to emphasize the cluster separability.

[0065] Moreover, the adjusted matrix generating means 23 executes processing in accordance with the adjustment function g(x) shown in the following (Equation 18) instead of the adjustment function g(x) shown in the above (Equation 17), and calculates each component w of the adjusted matrix W. ji may be calculated.

[0066] (Equation 18)

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[0067] In (Equation 18), a = 2 / σ. In (Equation 18), x is the relationship index value s. ji Substituting f(x), we get the component w ji As is clear from comparing (Equation 16) and (Equation 18), the adjustment function g(x) is 1 minus the monotonically increasing adjustment function f(x) shown in (Equation 16). In (Equation 18), μ is also the average of the elements of the triangular matrix in the relationship matrix S. The variance σ of the elements of the triangular matrix in the relationship matrix S is 2is not used. In this way, the monotonically decreasing adjustment function g(x) shown in (Equation 18) is a function generated based on the relationship matrix S. a is a coefficient obtained by dividing 2 by the standard deviation σ, and a=2 / σ. (Equation 18) is a sigmoid function.

[0068] By using the monotonically increasing adjustment function f(x) of (Formula 15) and (Formula 16) and the monotonically decreasing adjustment function g(x) of (Formula 17) and (Formula 18), the relationship component s in the relationship matrix S is ji After adjusting the relationship component w ji The adjustment functions shown in (Formula 15), (Formula 16), (Formula 17), and (Formula 18) all use the standard deviation σ of the elements of the triangular matrix in the relationship matrix S and the mean μ of the elements of the triangular matrix in the relationship matrix S. In this way, by adjusting the values ​​of the relationship components using the adjustment function, it is possible to emphasize the cluster separability of each item.

[0069] In this embodiment, in order to further emphasize the cluster separability, the adjusted matrix generating means 23 executes the process according to the following (Equation 19) to recalculate the variables.

[0070] (Equation 19)

number

[0071] In (Equation 19), r is a coefficient that satisfies r≧1, and s is a reduction coefficient that satisfies s0≦s≦1. Both r and s are real values.

[0072] Execute the process according to (Equation 19), and substitute the recalculated variables σ' and μ' into (Equation 15) and (Equation 17) respectively to calculate each element w of the adjusted matrix W. ji In addition, the recalculated variables a' and μ' are substituted into (Equation 16) and (Equation 18) to calculate each element w of the adjusted matrix W. jiIn this way, by recalculating the variables, it is possible to further emphasize the separation of the clusters.

[0073] FIG. 7 is a diagram showing the relationship between the reduction coefficient s and the adjustment function f(x). FIG. 7 shows the corresponding adjustment function f(x) when only the reduction coefficient s is changed. The example in FIG. 7 shows the adjustment function f(x) for three types of s = 1, 1 / 2, and 1 / 4. By setting the reduction coefficient s to a number less than 1, it is possible to further emphasize the cluster separability.

[0074] When distance is used as an element of the relationship matrix S, each element w of the adjusted matrix W is adjusted by applying a monotonically increasing adjustment function f(x). ji In other words, in this case, the adjusted matrix W is an adjusted distance matrix. When similarity is used as an element of the relationship matrix S, each element w of the adjusted matrix W is adjusted by applying a monotonically increasing adjustment function f(x). ji In other words, in this case, the adjusted matrix W is the adjusted similarity matrix.

[0075] When distance is used as an element of the relationship matrix S, each element w of the adjusted matrix W is adjusted by applying a monotonically decreasing adjustment function g(x). ji is the similarity. In other words, in this case, the adjusted matrix W is the adjusted similarity matrix. When similarity is used as an element of the relationship matrix S, each element w of the adjusted matrix W is adjusted by applying the monotonically decreasing adjustment function g(x). ji is the distance. In other words, in this case, the adjusted matrix W is the adjusted distance matrix.

[0076] Next, coordinate values ​​are calculated based on the adjusted matrix W (step S50). Specifically, the coordinate value calculation means 24 calculates coordinate values ​​for arranging each item in the k-dimensional space based on the adjusted matrix W. A specific processing method is as follows: ji is a distance or a similarity, that is, the adjusted matrix W is an adjusted distance matrix or an adjusted similarity matrix.

[0077] First, each element w of the adjusted matrix W ji is the distance, that is, the case where the adjusted matrix W is the adjusted distance matrix will be described. When the adjusted matrix W is the adjusted distance matrix, the coordinate value calculation means 24 performs a Young-Householder transformation on the adjusted matrix W, which is the adjusted distance matrix, to obtain a matrix Y, and then performs a calculation using multidimensional scaling to decompose the matrix Y into the form Y=XTX. In this way, coordinate values ​​for arranging each item in a k-dimensional space are calculated.

[0078] In this case, first, the coordinate value calculation means 24 performs Young-Householder transformation on the adjusted matrix W, which is the adjusted distance matrix. The Young-Householder transformation is a transformation that uses a centering matrix Cn on an n-by-n square matrix to obtain a matrix Y according to the following (Equation 20).

[0079] (Equation 20) Y=-1 / 2·CnDCn

[0080] When n=3, Cn is expressed as follows (Equation 21).

[0081] (Equation 21)

number

[0082] 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.

[0083] Next, each element w of the adjusted matrix W ji is the similarity, that is, the adjusted matrix W is the adjusted similarity matrix.

[0084] If the adjusted matrix W is an adjusted similarity matrix, in step S50, the coordinate value calculation means 24 generates a graph Laplacian matrix P from the adjusted matrix W, which is the adjusted similarity matrix, 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 n items are obtained.

[0085] As explained above, when the components of the relationship matrix S obtained in step S30 are distances, if a monotonically increasing adjustment function f(x) is used in step S40, the components of the adjusted matrix W become distances. Conversely, when the components of the relationship matrix S are distances, if a monotonically decreasing adjustment function g(x) is used in step S40, the components of the adjusted matrix W become similarities. On the other hand, when the components of the relationship matrix S obtained in step S30 are similarities, if a monotonically increasing adjustment function f(x) is used in step S40, the components of the adjusted matrix W become similarities. Conversely, when the components of the relationship matrix S are similarities, if a monotonically decreasing adjustment function g(x) is used in step S40, the components of the adjusted matrix W become distances.

[0086] Then, in step S50, each component w of the adjusted matrix W is ji If the distance is the adjusted distance matrix, the Young-Householder transformation is performed on the adjusted matrix W to obtain the matrix Y, and then a calculation is performed using multidimensional scaling to decompose the matrix Y into the form Y = XTX to calculate the coordinate values ​​for arranging each item in k-dimensional space. On the other hand, each component w of the adjusted matrix W is ji is the similarity, a graph Laplacian matrix P is generated from the adjusted matrix W, which is the adjusted similarity matrix, and then the coordinate values ​​for arranging each item in k-dimensional space are calculated based on the graph Laplacian matrix P.

[0087] Whether the components of the relationship matrix calculated in step S30 are distance or similarity, and whether the adjustment function used in step S40 is a monotonically increasing adjustment function f(x) or a monotonically decreasing adjustment function g(x), can be set appropriately depending on the type of data being handled, the purpose of visualization, etc. Furthermore, whether to use the Young-Householder transformation or the graph Laplacian matrix in step S50 is set depending on the type of components of the adjusted matrix W obtained in step S40.

[0088] <3. Details of Step S30> As described above, in this embodiment, the number of common elements m ji and the number of common elements m ij From the relationship index value s ji The function f(m jj, m ii, m ji ) are mainly used asymmetric normalized self-information of the joint probability distribution of two variables, asymmetric normalized mutual information of the joint probability distribution of two variables, and regression coefficients of the joint probability distribution of two variables. Among these, asymmetric normalized self-information and asymmetric normalized mutual information are used to determine the number of common elements m ji and the number of common elements m ij From the relationship index value s ji The way of thinking to find this is explained below.

[0089] In this specification, we define "relationship" as the property that indicates whether two objects are similar or not, and "similarity" as the degree to which two objects are similar to each other. Therefore, "distance" and "similarity," which are mutually inverse concepts, are sub-concepts of "relationship," which indicates the property that two objects are similar or not. First, in general terms, we list several distance and similarity indices between two given finite sets A and B. We also explain how they can be derived. Indices can be classified into the following six types depending on whether they are distance (dissimilarity) or similarity, and whether they are symmetric or asymmetric.

[0090] (A1) Distance index, symmetry (A2) Similarity index, symmetric (A3) Distance index, asymmetric (from set A to set B) (A4) Distance index, asymmetric (from set B to set A) (A5) Similarity index, asymmetric (from set A to set B) (A6) Similarity index, asymmetric (from set B to set A)

[0091] However, (A4) can be mechanically obtained by swapping sets A and B in (A3), and (A6) can be similarly obtained from (A5), so they can essentially be seen as four types.

[0092] There are many possible indicators for each category, and there is no single definitive answer.

[0093] (B1) Indicators derived from self-information (B2) Indicators derived from mutual information (B3) Other various indicators

[0094] From here, we will explain the methods for deriving (B1) "indicators derived from self-information" and (B2) "indicators derived from mutual information." As a preparation for this, we will define "self-information," which is the premise of (B1), and "entropy," which is the premise of (B2). For both, we will explain the cases with one random variable and two random variables.

[0095] Let us consider the universal set U (for example, all words recorded in the word database 10) as a finite set, and two subsets of U, A (words appearing in one document) and B (words appearing in the other document), as given. Based on the number of elements in each of the sets U, A, B, and A∩B (words appearing in both documents), the joint probability distribution of the random variables X and Y can be defined. Therefore, the normalized index generated from the self-information of the set can be used as an index of the distance and similarity between A and B. (B2) Regarding mutual information, by using "mutual information" instead of "self-information" in (B1), six types of indexes between two sets can be created through a similar derivation process.

[0096] Here, we introduce random variables X and Y corresponding to sets A and B, respectively. When a certain α is an element of set A, the random variable X takes the value 1, and otherwise it takes the value 0. That is, α ∈A → X =1 If α ∈A is not true, then X =0 Similarly, we introduce a random variable Y for set B. Each variable can take on a binary value of 0 or 1, but in the following, for generality, we will assume that each variable takes on m and q values. Six types of indices can be created based on self-information and mutual information, resulting in a total of 12 types of indices ((Indicator 1) to (Indicator 12) described below). These 12 types of indices are indices of the relationship between sets.

[0097] First, we will explain the self-information and entropy (one variable). For this purpose, we set them as follows:

[0098] ·Suppose there is a finite set X whose elements are x1, x2, x3,...,xm. X={x1, x2, x3,...,xm} ·Let the random variable X take the elements of X as its values. ·Let x represent one element of X. x∈X ·The probability that the value of random variable X is x is written as P(X=x).

[0099] The information "an event occurred in which the random variable X takes the value x" carries a certain amount of information, h(X=x), which is defined as follows: h(X=x)=-log(P(X=x))

[0100] This h(X=x) is called "self-information" (or "selection information" or "self-entropy"). · It is customary to use 2 as the base of logarithms. Although h(X=x) is an absolute number, if you use 2 as the base of the logarithm, you can add the unit [bit]. Here, the unit is omitted. For example, the information "an event with a probability of 1 / 8 occurred" has an informational content of 3.

[0101] If the average (or expected) value of self-information h(X=x) over all x∈X is H(X), then H(X)= Σ x∈X P(X=x)h(X=x). When calculating the average, weights are assigned based on the probability of each event occurring. Expanding h(X=x) gives the following:

[0102] H(X)=-Σ x∈X P(X=x)log(P(X=x))

[0103] H(X) is called the "average information" (or "Shannon information" or "entropy of information") of X. So far, we have defined the self-information and entropy for the case of one variable. Next, we will discuss the case of two variables.

[0104] Given two sets X and Y, where X={x1, x2, x3,···, xm} and Y={y1, y2, y3,···, yq;}, the set Z shown below is called the "Cartesian product" of sets X and Y, and is expressed as follows:

[0105] Z=X×Y Z=[(x,y);x∈X,y∈Y]

[0106] In the Cartesian product set Z of sets X and Y, the probability that random variable X takes value x(∈X) and random variable Y takes value y(∈Y) will be denoted as P(X=x,Y=y). This is called simultaneous probability or joint probability. If P(X=x,Y=y)=P(X=x)P(Y=y) holds for all x(∈X) and y(∈Y), then the random variables X and Y are said to be independent of each other, however, independence will not be assumed below.

[0107] Here, we can say the following (Equation 22-1) (Equation 22-2). This is called "marginalization."

[0108] P(X=x)=Σ y∈Y P(X=x, Y=y)…… (Equation 22-1) P(Y=y)=Σ x∈X P(X=x, Y=y)…… (Equation 22-2)

[0109] In marginalization, each term in the sum is a non-negative value, so the following "marginalization inequalities" hold: (Equation 22-3) (Equation 22-4).

[0110] 0≦P(X=x,Y=y)≦P(X=x)…… (Formula 22-3) 0≦P(X=x,Y=y)≦P(Y=y)…… (Formula 22-4)

[0111] If we consider the Cartesian product Z=X×Y of sets X and Y as a one-dimensional set with m×q elements, then we can naturally define the self-information and average information. When the random variable X takes on a value x∈X and the random variable Y takes on a value y∈Y, the self-information h(X=x,Y=y) can be defined as h(X=x,Y=y)=-log(P(X=x,Y=y)).

[0112] If the average value of the self-information h(X=x, Y=y) over all x(∈X) and y(∈Y) is H(X, Y), then H(X, Y)=Σ x∈X Σ y∈Y P(X=x,Y=y)h(X=x,Y=y). If we write the sum as a whole, it becomes H(X, Y)=Σ (x, y)∈X×Y It can also be written as P(X=x,Y=y)h(X=x,Y=y). Expanding H(X=x,Y=y), we get H(X, Y)=-Σ (x, y)∈X×Y P(X=x,Y=y) log(P(X=x,Y=y)), which is called "joint entropy."

[0113] So far, we have defined self-information and entropy for the cases of one variable and two variables, respectively. From here, we will discuss the index derived from self-information, which corresponds to (B1) of the above (B1) to (B3). As a preparation for this, we will first introduce the assumption of non-negative correlation and explain how to derive three inequalities related to self-information that hold under this assumption.

[0114] First, the properties of self-information will be explained. The following (Equation 23-1) (Equation 23-2) hold as the "first inequality regarding self-information."

[0115] h(X=x, Y=y)≧h(X=x)…… (Equation 23-1) h(X=x,Y=y)≧h(Y=y)…… (Formula 23-2)

[0116] We prove the "first inequality on self-information." As mentioned above, the following inequality related to marginalization holds.

[0117] 0≦P(X=x,Y=y)≦P(X=x) …… (Formula 22-3) 0≦P(X=x,Y=y)≦P(Y=y)…… (Formula 22-4)

[0118] Due to the monotonically increasing property of logarithmic functions, the same inequality holds even if we take the logarithms of each side, as shown below.

[0119] log(P(X=x,Y=y))≦log(P(X=x)) log(P(X=x,Y=y))≦log(P(Y=y))

[0120] Multiplying both sides by (-1) reverses the inequality sign, giving us the following:

[0121] -log(P(X=x,Y=y))≧-log(P(X=x)) -log(P(X=x,Y=y))≧-log(P(Y=y))

[0122] Proof complete. Therefore, the following formula holds:

[0123] h(X=x, Y=y)≧h(X=x) h(X=x,Y=y)≧h(Y=y)

[0124] Here, we consider only the case where there is a non-negative correlation between event X = x and event Y = y (non-negative correlation assumption). P(X=x,Y=y)≧P(X=x)P(Y=y)…… (Formula 23-3)

[0125] Under the assumption of non-negative correlation (Equation 23-3), by taking the logarithm of each side and multiplying by (-1), the inequality is reversed, and the following (Equation 23-4) holds as the "second inequality for self-information."

[0126] h(X=x,Y=y)≦h(X=x)+h(Y=y)…… (Formula 23-4)

[0127] The relationship regarding self-information is summarized. Re-listing (Equation 23-1), (Equation 23-2), and (Equation 23-4), we get: h(X=x, Y=y)≧h(X=x)…… (Equation 23-1) h(X=x,Y=y)≧h(Y=y)…… (Formula 23-2) h(X=x,Y=y)≦h(X=x)+h(Y=y)…… (Formula 23-4) However, (Equation 23-4) is based on the non-negative correlation assumption (Equation 23-3). This holds true if P(X=x, Y=y)≧P(X=x)P(Y=y)≧0.

[0128] So far, we have derived three inequalities related to self-information under the assumption of non-negative correlation. Using these, we can derive symmetric and asymmetric normalized self-information, but we will first explain how to derive the symmetric one. The above relationships related to self-information (Equation 23-1), (Equation 23-2), and (Equation 23-4) indicate the lower and upper limits of the possible values ​​of self-information h(X=x, Y=y). These can be summarized as follows:

[0129] max(h(X=x,Y=y))≦h(X=x,Y=y)≦h(X=x)+h(Y=y)

[0130] When combining them into one, you can also do it like this:

[0131] min(h(X=x,Y=y))≦h(X=x,Y=y)≦h(X=x)+h(Y=y)

[0132] However, the summarization of min(h(X=x,Y=y)) is an inequality that is "too broad" with too much leeway in the lower limit. In what follows, we will use max(h(X=x,Y=y)). However, using the latter, it is possible to derive the Google Distance described in the following non-patent document. In other words, the index derived from (B1) self-information, which will be described below, is a different thing.

[0133] Non-patent literature: Rudi L. Cilibrasi and Paul MB Vitanyi. "The google similarity distance." IEEE Transactions on Knowledge and Data Engineering, Vol. 19, pp.370-383, 2007.

[0134] We can define r by regarding h(X=x, Y=y) as a point that divides the lower and upper limits internally in the ratio r:1-r. Alternatively, by looking at the internal division ratio in reverse, we can define r' by regarding h(X=x, Y=y) as a point that divides the lower and upper limits internally in the ratio 1-r':r'. Then, clearly, r and r' satisfy the following equation.

[0135] 0≦r≦1,0≦r′≦1,r+r´=1

[0136] The above formula can be rewritten as follows:

[0137] r=(h(X=x,Y=y)-max(h(X=x,Y=y))) / min(h(X=x,Y=y)) r´=(h(X=x)+h(Y=y)-h(X=x,Y=y)) / min(h(X=x,Y=y))

[0138] r represents the distance and r' represents the similarity. Under the assumption of non-negative correlation, both r and r' take values ​​between 0 and 1, but when there is negative correlation, r'>1 and r'<0. If the joint probability is made infinitely close to 0, it can become arbitrarily large or small. Here, r and r' are called "normalized self-information" and are respectively defined as d NSI (X=x,Y=y), sim NSI Let us express this as (X=x, Y=y).

[0139] To summarize the normalized self-information (symmetric), d NSI (X=x,Y=y), sim NSI (X=x, Y=y) can be expressed as follows:

[0140] d NSI (X=x,Y=y)=(h(X=x,Y=y)-max(h(X=x,Y=y))) / min(h(X=x),h(Y=y)) sim NSI (X=x,Y=y)=(h(X=x)+h(Y=y)-h(X=x,Y=y)) / min(h(X=x,Y=y))

[0141] where d NSI is the distance, sim NSI represents the similarity. The above non-negative correlation assumption (Equation 23-3) Under the condition that P(X=x, Y=y)≧P(X=x)P(Y=y)≧0, the following holds:

[0142] 0≦d NSI (X=x,Y=y)≦1 0≦sim NSI (X=x,Y=y)≦1

[0143] When there is a negative correlation, it looks like this:

[0144] d NSI (X=x,Y=y)>1 sim NSI (X=x,Y=y)<0

[0145] Up to this point, we have discussed symmetric indices derived from (B1) self-information. Next, we will discuss asymmetric indices. The relationships regarding self-information in (Equation 23-1), (Equation 23-2), and (Equation 23-4) above indicate the lower and upper limits of the possible values ​​of h (X = x, Y = y). In the above example, symmetry was maintained by combining them into one using max(), but here we will treat them separately.

[0146] h(X=x)≦h(X=x,Y=y)≦h(X=x)+h(Y=y) h(Y=y)≦h(X=x,Y=y)≦h(X=x)+h(Y=y)

[0147] From this, if a normalized index is created by an internal division ratio, as in the symmetric case, the following asymmetric formula is obtained as the asymmetric normalized self-information:

[0148] d NSI (X=x→Y=y)=h(X=x,Y=y)-h(X=x) / h(Y=y) d NSI (Y=y→X=x)=h(X=x,Y=y)-h(Y=y) / h(X=x) sim NSI (X=x→Y=y)=(h(X=x)+h(Y=y)-h(X=x,Y=y)) / h(Y=y) sim NSI (Y=y→X=x)=(h(X=x)+h(Y=y)-h(X=x,Y=y)) / h(X=x)

[0149] Here, dNSI represents distance and simNSI represents similarity. Under the above non-negative correlation assumption (Equation 23-3) P(X=x, Y=y)≧P(X=x)P(Y=y)≧0, the following holds:

[0150] 0≦d NSI (X=x→Y=y)≦1 0≦d NSI (Y=y→X=x)≦ 0≦sim NSI (X=x→Y=y)≦1 0≦sim NSI (Y=y→X=x)≦1

[0151] Up to this point, we have explained how to derive the index derived from self-information, which corresponds to (B1) of the aforementioned (B1) to (B3). Next, we will explain how to derive the index derived from mutual information, which corresponds to (B2). This can be done in a roughly equivalent manner by using entropy instead of self-information in (B1). As a prelude, we will first explain how to derive the three inequalities related to entropy. Regarding joint entropy, the "first inequality related to joint entropy" shown in (Equation 24-1) and (Equation 24-2) holds.

[0152] H(X, Y)≧ H(X)…… (Equation 24-1) H(X, Y)≧ H(Y)…… (Equation 24-2)

[0153] We prove the "first inequality regarding joint entropy." In (Equation 24-1), we prove that the value obtained by subtracting the right side from the left side is non-negative.

[0154] H(X, Y)-H(X)=-Σ (x,y)∈X×Y P(X=x,Y=y)log(P(X=x,Y=y))+Σ x∈X P(X=x)log(X=x)

[0155] Here, by marginalization (Equation 22-1), P(X=x)=Σ y∈Y Since P(X=x, Y=y), the following equation holds:

[0156] H(X, Y)-H(X) =-Σ (x,y)∈X×Y P(X=x,Y=y)log(P(X=x,Y=y))+Σ x∈X [Σ y∈Y P(X=x,Y=y)]log(P(X=x)) =-Σ (x,y)∈X×Y P(X=x,Y=y)log(P(X=x,Y=y))+Σ (x,y)∈X×Y P(X=x,Y=y)log(P(X=x)) =-Σ (x,y)∈X×Y P(X=x,Y=y)log(P(X=x,Y=y) / P(X=x))+Σ x∈X [Σ y∈Y P(X=x,Y=y)]log(P(X=x))

[0157] Here, by marginalization (Equation 22-3), 0≦P(X=x, Y=y)≦P(X=x). Therefore, all terms are non-negative. Therefore, the following equation holds:

[0158] H(X, Y)-H(X)≧0

[0159] The same is true for (Equation 24-2) when X and Y are swapped. This completes the proof. Regarding the joint entropy, the "second inequality for joint entropy" shown in (Equation 24-3) holds.

[0160] H(X, Y)≦H(X)+H(Y)…… (Equation 24-3)

[0161] The equality holds if and only if X and Y are independent random variables, i.e., P(X=x,Y=y)=P(X=x)P(Y=y). We will prove this next.

[0162] From marginalization (Equation 22-1) and (Equation 22-2), P(X=x)=Σ y∈Y P(X=x, Y=y)…… (Equation 22-1) P(Y=y)=Σ x∈X P(X=x, Y=y)…… (Equation 22-2) Therefore, the following formula holds:

[0163] H(X)=-Σ (x,y)∈X×Y P(X=x,Y=y)log(P(X=x)) H(Y)=-Σ (x,y)∈X×Y P(X=x,Y=y)log(P(Y=y))

[0164] Therefore, the following further equation holds:

[0165] H(X)+H(Y)-H(X, Y)=-Σ (x,y)∈X×Y P(X=x,Y=y)log((P(X=x)P(Y=y) / P(X=x,Y=y))

[0166] Here, for any u>0, log(u)≦u−1, i.e., −log(u)≧1−u, and therefore the following equation holds.

[0167] H(X)+H(Y)-H(X, Y)≧ Σ (x,y)∈X×YP(X=x,Y=y)(1-P(X=x)P(Y=y) / P(X=x,Y=y))=0

[0168] This completes the proof. We will now explain "mutual information." If the random variables X and Y are not independent of each other, H(X, Y) and H(X) + H(Y) do not coincide. As shown in (Equation 24-3) above, H(X, Y) ≦ H(X) + H(Y)... (Equation 24-3). The difference between the information amounts of both in (Equation 24-3) ((right side) - (left side)) is called "mutual information," and is expressed as follows: Mutual information is always a non-negative value.

[0169] I(X, Y)=H(X)+H(Y)-H(X, Y)... (Formula 24-4)

[0170] Let us explain "conditional entropy." The conditional self-information of event A under the condition that event B occurs, h(A|B), is defined as follows:

[0171] h(A|B)=-log(P(A|B))

[0172] Given a random variable X, the expected value of the conditional self-information h(X = x|B) = -log(P(X = x|B)) of the event X = x given the event B is called the "conditional entropy" and is expressed as follows:

[0173] H(X |B)=-Σ x∈X P(X = x|B)log(P(X = x|B))

[0174] Furthermore, given a random variable Y, the expected value of the conditional entropy H(X | Y=y) of the event X = x with respect to y, given that the event Y = y has occurred, can be expressed as follows. This is also called "conditional entropy".

[0175] H(X | Y)=Σ y∈Y P(Y=y) H(X | Y=y)

[0176] The following equations (Equation 24-5) and (Equation 24-6) hold true as equations that hold for conditional entropy.

[0177] H(X | Y)=H(X,Y)-H(Y)…… (Formula 24-5) H(Y | X) = H(X,Y) - H(X)... (Equation 24-6)

[0178] The relationship between the average information H and the mutual information I so far can be summarized as follows:

[0179] H(X,Y) ≧ H(Y) …… (Equation 24-1) H(X,Y) ≧ H(Y) …… (Equation 24-2) H(X,Y) ≦ H(X)+H(Y) …… (Equation 24-3) I(X,Y) =H(X) +H(Y)-H(X,Y) …… (Formula 24-4) H(X|Y) =H(X,Y) -H(Y) …… (Formula 24-5) H(Y|X) = H(X,Y) - H(X) …… (Equation 24-6)

[0180] Up to this point, we have derived three inequalities related to entropy. Using these, we can derive symmetric and asymmetric normalized mutual information, but first we will explain how to derive the symmetric one. (Equation 24-1) to (Equation 24-3) are shown again. H(X, Y)≧H(X) …… (Equation 24-1) H(X, Y)≧H(Y) …… (Equation 24-2) H(X, Y)≦H(X)+H(Y) …… (Equation 24-3)

[0181] (Equation 24-1) to (Equation 24-3) show the lower and upper limits of the values ​​that H(X, Y) can take. These can be combined and written as follows:

[0182] max(H(X), H(Y))≦H(X, Y)≦H(X)+H(Y)

[0183] We can define r by viewing H(X, Y) as a point that divides the lower and upper limits internally in the ratio r:1-r. Alternatively, by reversing the internal division ratio, we can define r' by viewing H(X, Y) as a point that divides the lower and upper limits internally in the ratio 1-r':r'. Clearly, then, 0≦r≦1, 0≦r'≦1, and r+r'=1. The above equation can be rewritten as follows:

[0184] r=[H(X, Y)-max(H(X), H(Y))] / min(H(X),H(Y)) r´=[H(X)+H(Y)-H(X, Y)] / min(H(X),H(Y))

[0185] The numerator of r' is the mutual information I(X, Y), but it can be normalized by having a denominator. Here, r represents distance and r' represents similarity. It is very similar to the normalized index of self-information, but in the case of mutual information, the assumption of non-negative correlation is not required. r and r' are generally called "normalized mutual information" and are respectively expressed as d NMI (X, Y), sim NMI It is expressed as (X, Y).

[0186] To summarize the symmetric normalized mutual information, we can write "normalized mutual information" d NMI (X, Y), sim NMI (X, Y) can be expressed as follows: In this case, the non-negative correlation assumption is not required.

[0187] d NMI =[H(X, Y)-max(H(X), H(Y)) / min(H(X), H(Y)) sim NMI =(H(X)+H(Y )-H(X, Y)) / min(H(X), H(Y))

[0188] The above d NMI (X, Y), sim NMI For (X, Y), 0≦d NMI (X, Y) ≤ 1, 0 ≤ sim NMI (X, Y)≦1. Here, d NMI is the distance, sim NMI represents the similarity. However, when X and Y are uncorrelated, d NMI takes the maximum value of 1, and sim NMI takes a minimum value of 0, and when there is a negative correlation, it starts to decrease and increase again. NMI and sim NMI represents how well information from X has been transmitted to Y, and is considered to be not transmitted at all when there is no correlation, and to be transmitted when there is a negative correlation. Up to this point, we have discussed symmetric indices derived from (B2) entropy (mutual information). Next, we will discuss asymmetric indices.

[0189] (Equation 24-1) to (Equation 24-3) are shown again. H(X, Y)≧H(X) …… (Equation 24-1) H(X, Y)≧H(Y) …… (Equation 24-2) H(X, Y)≦H(X)+H(Y) …… (Equation 24-3)

[0190] This indicates the lower and upper limits of the values ​​that H(X, Y) can take. In the above example, symmetry was maintained by combining them into one using max(), but here we will treat them separately.

[0191] H(X)≦H(X, Y)≦H(X)+H(Y) H(Y)≦H(X, Y)≦H(X)+H(Y)

[0192] From this, if a normalized index is created by the internal division ratio, as in the above example, the following asymmetric formula is obtained as the asymmetric normalized mutual information.

[0193] d NMI (X→Y)=(H(X, Y)-H(X)) / H(Y) d NMI (Y→X)=(H(X, Y)-H(Y)) / H(X) sim NMI (X→Y)=(H(X)+H(Y)-H(X, Y)) / H(Y) sim NMI (Y→X)=(H(X)+H(Y)-H(X, Y)) / H(X)

[0194] Here, the non-negative correlation assumption is not required, so the following holds: d NMI is the distance, sim NMI represents the degree of similarity.

[0195] 0≦d NMI (X→Y)≦1 0≦d NMI (Y→X)≦1 0≦sim NMI (X→Y)≦1 0≦sim NMI (Y→X)≦1

[0196] So far, we have explained how to derive the index derived from entropy, which corresponds to (B2) in the above-mentioned (B1) to (B3). Up to this point, (B1) and (B2) in the above-mentioned (B1) to (B3) have been defined using general random variables X and Y, but to finally reduce them to an index between two sets, we do the following.

[0197] The universal set U is a finite set, and its two subsets are set A and set B (A⊂U, B⊂U). Here, we define the probability distribution associated with the set. Set X and set Y are defined as follows:

[0198] X={0,1} Y={0,1}

[0199] Let X be the set of possible values ​​x of random variable X, and Y be the set of possible values ​​y of random variable Y.

[0200] X=x(x∈X) Y=y(y∈Y)

[0201] Now, suppose the joint probability distribution of variables X and Y is as follows:

[0202] P(X=0,Y=0)=[n(U)-n(A)-n(B)+n(A∩B)] / n(U) P(X=1,Y=0)=[n(A)-n(A∩B)] / n(U) P(X=0,Y=1)=[n(B)-n(A∩B)] / n(U) P(X=1,Y=1)=n(A∩B] / n(U)

[0203] This means that we can naturally define the joint distribution P(X, Y) of random variables X and Y from sets A and B. The distance and similarity between sets A and B can be defined as the following (Indicator 1) to (Indicator 12) using the distance and similarity between X and Y derived from the joint probability distribution P(X, Y) of random variables X and Y.

[0204] (Indicator 1) d NSI (A,B)=d NSI (X=1, Y=1) (Indicator 2) sim NSI (A,B)=sim NSI (X=1, Y=1) (Indicator 3) d NSI (A→B)=d NSI (X=1→Y=1) (Indicator 4) d NSI (B→A)=d NSI (Y=1→X=1) (Indicator 5) sim NSI (A→B)=sim NSI (X=1→Y=1) (Indicator 6) sim NSI (B→A)=sim NSI (Y=1→X=1) (Indicator 7) d NMI (A,B)=d NMI (X,Y) (Indicator 8) sim NMI (A,B)=sim NMI (X,Y) (Indicator 9) d NMI (A→B)=d NMI (X→Y) (Indicator 10) d NMI (B→A)=d NMI (Y→X) (Indicator 11) sim NMI (A→B)=sim NMI (X→Y) (Indicator 12) sim NMI (B→A)=sim NMI (Y→X)

[0205] As mentioned above, d NSI , d NMI is the distance, sim NSI , sim NMI represents similarity. Therefore, among the above (Index 1) to (Index 12), (Index 1), (Index 3), (Index 4), (Index 7), (Index 9), and (Index 10) are indices of distance between two sets, and (Index 2), (Index 5), (Index 6), (Index 8), (Index 11), and (Index 12) are indices of similarity between two sets. The larger the distance index, the greater the difference, and the smaller the value, the smaller the difference. The larger the similarity index, the smaller the difference, and the smaller the value, the greater the difference. In other words, both the distance index and the similarity index are indices of relationship as a broad concept. For example, if the distance index value is small, it can be determined that the similarity is high, so the distance index can also be used as an index of relationship. Here, (Index 1) and (Index 2) will be rewritten and the details will be shown. (Index 1) can be rewritten as follows.

[0206] (Indicator 1) d NSI (A,B)=d NSI (X=1, Y=1) =((h(X=1,Y=1)-max(h(X=1,Y=1))) / min(h(X=1),h(Y=1)) =(-log(P(X=1,Y=1))-max(-log(P(X=1)),-log(P(Y=1))) / min(-log(P(X=1)),-log(P( Y=1)))=(-log(n(A∩B))+log(min(n(A),n(B)))) / (-log(max(n(A),n(B)))+log(n(U)))

[0207] Also, (index 2) can be rewritten as follows:

[0208] (Indicator 2) sim NSI (A,B)=sim NSI (X=1, Y=1) =((h(X=1+h(Y=1)-h(X=1,Y=1)) / min(h(X=1),h(Y=1)) =(-log(P(X=1)-log(P(Y=1))+log(P(X=1,Y=1))) / min(-log(P(X=1)),-log(P(Y=1))) =(-log(n(A))-log(n(B))+log(n(A∩B))+log(n(U))) / (-log(max(n(A),n(B)))+log(n(U)))

[0209] As a result, (Indicator 1) to (Indicator 6) can be derived as follows:

[0210] (Indicator 1) d NSI (A,B) =(-log(n(A∩B))+log(min(n(A),n(B)))) / (-log(max(n(A),n(B)))+log(n(U))) (Indicator 2) sim NSI (A,B) =(-log(n(A))-log(n(B))+log(n(A∩B))+log(n(U))) / (-log(max(n(A),n(B)))+log(n(U))) (Indicator 3) d NSI (A→B) =(-log(n(A∩B))+log(n(A))) / (-log(n(B)))+log(n(U))) (Indicator 4) d NSI (B → A) =(-log(n(A∩B))+log(n(B))) / (-log(n(A)))+log(n(U))) (Indicator 5) sim NSI (A→B) =(-log(n(A))-log(n(B))+log(n(A∩B))+log(n(U))) / (-log(n(B))+log(n(U))) (Indicator 6) sim NSI (B → A) =(-log(n(A))-log(n(B))+log(n(A∩B))+log(n(U))) / (-log(n(A))+log(n(U)))

[0211] The above (Index 1) to (Index 6) are normalized self-information of the joint probability distribution of two variables. Among them, (Index 1) and (Index 2) are indices of a symmetric relationship, and (Index 3) to (Index 6) are indices of an asymmetric relationship. Therefore, any of (Index 3) to (Index 6), which are asymmetric normalized self-information of the joint probability distribution of two variables, can be used as an index of an asymmetric relationship between two sets.

[0212] Since indicators 7 to 12 are complicated, we will express them indirectly. First, we define probability as follows: A' is the complement of A, and B' is the complement of B.

[0213] P(A)=n(A) / n(U) P(B)=n(B) / n(U) P(A´)=(n(U)-n(A)) / n(U) P(B´)=(n(U)-n(B)) / n(U) P(A´∩B´)=(n(U)-n(A)-n(B)+n(A∩B)) / n(U) P(A∩B´)=(n(A)-n(A∩B)) / n(U) P(A´∩B)=(n(B)-n(A∩B)) / n(U) P(A∩B)=n(A∩B) / n(U)

[0214] Moreover, entropy is defined as follows. H(A)=-P(A´)log(P(A´))-P(A)log(P(A)) H(B)=-P(B´)log(P(B´))-P(B)log(P(B)) H(A,B)=-P(A´∩B´)log(P(A´∩B´))-P(A∩B´)log(P(A∩B´))-P(A´∩B)log(P(A´∩B))-P(A∩B)log(P(A∩B))

[0215] (Indicators 7) to (Indicators 12) can be defined as follows using the average information content:

[0216] (Indicator 7) d NSI (A,B) =(H(A,B)-max(H(A),(H(B))) / min(H(A),(H(B)) (Indicator 8) sim NMI (A,B) =(H(A)+H(B)-H(A,B)) / min(H(A),(H(B)) (Indicator 9) d NMI (A→B) =(H(A,B)-H(A)) / H(B) (Indicator 10) d NMI (B → A) =(H(A,B)-H(B)) / H(A) (Indicator 11) sim NMI (A→B) =(H(A)+H(B)-H(A,B)) / H(B) (Indicator 12) sim NMI (B → A) =(H(A)+H(B)-H(A,B)) / H(A)

[0217] The above (Indicator 7) to (Indicator 12) are normalized mutual information of the joint probability distribution of two variables. Among them, (Indicator 7) and (Indicator 8) are indices of a symmetric relationship, and (Indicator 9) to (Indicator 12) are indices of an asymmetric relationship. Therefore, any of (Indicator 9) to (Indicator 12), which are asymmetric normalized mutual information of the joint probability distribution of two variables, can be used as an index of an asymmetric relationship between two sets.

[0218] Up to this point, (B1) and (B2) of (B1) to (B3) mentioned above have been defined using sets A and B. Next, we will discuss the Pearson coefficient and regression coefficient as one of the various other indices in (B3).

[0219] Relationships sim P (A,B)=(n(A∩B)n(U)-n(A)n(B)) / (n(A)(n(U)-n(A))n(B)(n(U)-n(B))) 1 / 2

[0220] The Pearson coefficient uses n(U), the number of elements in the universal set U. The Pearson coefficient is the correlation coefficient ρ of the probability distribution of the direct product of the random variables X and Y. The Pearson coefficient takes a real value between -1 and 1. The Pearson coefficient takes a value of 0 when there is no correlation (independence). There is an asymmetric version of the Pearson coefficient. The asymmetric version is the regression coefficient, which is defined as follows:

[0221] (Indicator 13) sim RC (A→B) =(n(A∩B)n(U)-n(A)n(B)) / (n(A)(n(U)-n(A)) (Indicator 14) sim RC (B → A) =(n(A∩B)n(U)-n(A)n(B)) / (n(B)(n(U)-n(B))

[0222] The asymmetric versions of the Pearson coefficient, (Indicator 13) and (Indicator 14), are the normalized mutual information of the joint probability distribution of two variables. Therefore, the asymmetric version of the Pearson coefficient, which is the regression coefficient of the joint probability distribution of two variables, can be used as an indicator of the asymmetric relationship between two sets.

[0223] As described above, the indices of the asymmetric relationship between two sets have been described, but in this embodiment, any of the asymmetric normalized self-information of the joint probability distribution of two variables (Indicator 3) to (Indicator 6), the asymmetric normalized mutual information of the joint probability distribution of two variables (Indicator 9) to (Indicator 12), and the normalized mutual information of the joint probability distribution of two variables (Indicator 13) and (Indicator 14) can be used as an index of the asymmetric relationship between two sets. In particular, when the sets (A → B) and (B → A) are paired with their orientations reversed, the mutual dependency between the two items becomes clear.

[0224] As an index of the asymmetric relationship between two sets, not only the index obtained as described above but also other indexes can be used. In this embodiment, three types of indexes are used, which are generated when the number of elements in the universal set that includes the sets related to all items is n(U), the number of elements in the set related to one item is n(A), the number of elements in the set related to the other item is n(B), and the number of elements in the intersection of these two sets is n(A∩B).

[0225] The first type is the asymmetric normalized self-information of the two-variable joint probability distribution generated by the numbers of elements in the set, n(U), n(A), n(B), and n(A∩B), as shown in (Indicator 3) to (Indicator 6). The second type is the asymmetric normalized mutual information of the two-variable joint probability distribution generated by the numbers of elements in the set, n(U), n(A), n(B), and n(A∩B), as shown in (Indicator 9) to (Indicator 12). The third type is the regression coefficient of the two-variable joint probability distribution generated by the numbers of elements in the set, n(U), n(A), n(B), and n(A∩B), as shown in (Indicator 13) and (Indicator 14).

[0226] As the asymmetric normalized self-information of the first type of joint probability distribution, (index 5) (index 6) (or (index 3) (index 4)) can be used. For example, when (index 5) (index 6) is used, the relationship matrix generation means 22 executes the process according to the above (index 5) (index 6) in step S30. Specifically, based on the words extracted from the word database 10, the number of common elements m jj Let n(A) be the number of common elements, m ii Let n(B) be the number of common elements m. ji (=m ij ) is set as n(A∩B), and the total number of words set in the word database 10 is set as n(U), and the processing is performed according to the above (Index 5) and (Index 6). Then, the sim calculated according to (Index 5) and (Index 6) is NSI (A→B), sim NSI (B→A) is the relationship index value s ji , s ij This gives the relationship matrix S=[s ji ](j=1,2,3,···,n;i=1,2,3,···,n) is calculated.

[0227] As the asymmetric normalized mutual information of the second type of joint probability distribution, (index 11) (index 12) (or (index 9) (index 10)) can be used. For example, when (index 11) (index 12) is used, the relationship matrix generation means 22 executes the process according to the above (index 11) (index 12) in step S30. Specifically, based on the words extracted from the word database 10, the number of common elements m jj Let n(A) be the number of common elements, m ii Let n(B) be the number of common elements m. ji (=m ij) is set to n(A∩B), and the total number of words set in the word database 10 is set to n(U), and processing is performed according to the above (index 11) (index 12). However, since (index 11) (index 12) are actually formulas using the average information amounts H(A), H(B) and H(A,B), the formulas for defining probability and entropy on the previous page are used to use formulas using the numbers of elements n(U), n(A), n(B), and n(A∩B). In other words, the relationship matrix generation means 22 performs processing according to the formula for calculating the asymmetric normalized mutual information of the joint probability distribution using the numbers of elements n(U), n(A), n(B), and n(A∩B), and calculates the calculated sim NMI (A→B), sim NMI (B→A) is the relationship index value s ji , s ij This gives the similarity matrix S=[s ji ](j=1,2,3,···,n;i=1,2,3,···,n) is calculated.

[0228] As the regression coefficients of the third type of joint probability distribution, (index 13) and (index 14) can be used. In this case, the relationship matrix generating means 22 executes the process according to the above (index 13) and (index 14) in step S30. Specifically, based on the words extracted from the word database 10, the number of common elements m jj Let n(A) be the number of common elements, m ii Let n(B) be the number of common elements m. ji (=m ij ) is set as n(A∩B), and the total number of words set in the word database 10 is set as n(U), and the processing according to (Index 13) and (Index 14) is executed. Then, the sim calculated according to (Index 13) and (Index 14) is RC (A→B), sim RC (B→A) is the relationship index value s ji , s ij This gives the relationship matrix S=[s ji ](j=1,2,3,···,n;i=1,2,3,···,n) is generated.

[0229] After the relationship matrix generation means 22 generates the relationship matrix S in step S30, the adjusted matrix generation means 23 generates the adjusted matrix W in step S40, and the coordinate value calculation means 24 calculates coordinate values ​​based on the adjusted matrix W in step S50. Then, in step S60, the item placement means 27 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.

[0230] <4. Specific examples> Next, an example using specific data will be explained. 36 novels were used as documents. These 36 documents are registered in the document database 11 in association with document IDs that identify the documents. In step S10, the morphological analysis means 25 executes morphological analysis and extracts words. In this state, the extracted words are registered in the word database 10 in association with word IDs that identify the words and the document IDs of the documents in which they appear.

[0231] By identifying a document ID from the information stored in this word database 10, it is possible to identify the words that appear in the document with that document ID. In step S20, the relationship matrix generation means 22 extracts two documents from the 36 documents and calculates the number of words that the two documents have in common as the number of common elements. This is calculated by referencing the word database 10 with the two document IDs and identifying the number of word IDs that are stored in common association with the two document IDs. By calculating this for all combinations of two documents from the 36 documents, a 36 x 36 common element number matrix with the number of common elements as its components is obtained.

[0232] Then, after the relationship matrix generation means 22 generates the relationship matrix S in step S30, the adjusted matrix generation means 23 generates the adjusted matrix W in step S40, and the coordinate value calculation means 24 calculates the coordinate values ​​based on the adjusted matrix W in step S50.

[0233] In step S60, the item placement means 27 generates a spatial perspective view projecting the three-dimensional space onto a two-dimensional plane, and three two-dimensional projection views projecting all two-dimensional combinations of the three dimensions, in the form of a scatter diagram. In the spatial perspective view, each item is displayed as a small circle to save space, and in the two-dimensional projection views, the author's name and work title are displayed on the item. Such a scatter diagram is shown in Figure 8.

[0234] By creating a scatter diagram like the one shown in Figure 8, the positional relationships between the works become clear at a glance. It is possible to understand which works are close to each other and to grasp the overall structure showing the relationships between all the works.

[0235] As shown in Figure 8, by extracting the relationships between items based on the data related to each item in the category of interest and displaying a scatter plot with each item as a node, it is possible to get a bird's-eye view of the overall distribution of items in the category of interest and understand the structure of the category. Nodes on the graph that correspond to similar items are placed close to each other.

[0236] By focusing on one item, it is possible to find conceptually similar items by extracting one or more other items placed nearby. Also, by looking at the overall picture, it is possible to distinguish between central and peripheral items in a category. Another advantage is that if the overall structure consists of multiple clusters, the cluster configuration can be visually grasped.

[0237] 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, the asymmetric normalized autoinformation of the joint probability distribution of two variables, the asymmetric normalized mutual information of the joint probability distribution of two variables, and the regression coefficient of the joint probability distribution of two variables are used as indices of the relationship between sets related to two items, but various indices of the relationship can be used.

[0238] In the above embodiment, documents written in natural language are used as each item belonging to a category of interest, and these documents are used as input data to perform morphological analysis of each item to extract morphemes, and a set of the extracted morphemes is used as a set related to each item. However, sets related to each item may be prepared in advance. For example, in the above embodiment, it is possible to prepare only the word database 10 in advance without using the document database 11, and use only the information recorded in the word database 10 to calculate effective coordinate values ​​for use in creating a scatter diagram or the like.

[0239] In the above embodiment, a group of documents is used as the category of interest, documents written in natural language are used as each item, and a set of words contained in the documents is used as input data. However, various other applications are possible. For example, a group of articles related to multiple companies can be collected, and these articles can be used as the category of interest, monthly articles for each company can be used as items, and a set of words contained in each article can be used as input data, to display the relationships between articles from different companies. Also, for example, descriptions of multiple products can be collected, and these descriptions can be used as the category of interest, each product can be used as an item, and a set of words contained in each product description can be used as input data, to display the relationships between different products.

[0240] Alternatively, an image of a painting or the like may be used as each item belonging to a category of interest, and the image may be used as input data to perform image analysis of each item, thereby identifying words that express the content of the image, and a set of identified words may be used as a set related to each item. In this case, the information processing device may be configured to include an image database instead of the document database 11, and an image analysis means instead of the morphological analysis means 25.

[0241] The image analysis means, like the morphological analysis means 25, is included in the arithmetic processing unit 20 and is realized by the CPU 1 executing a program. The image analysis means performs image analysis on each image to identify words to be tagged as content that represents the image. Various known image analysis methods can be used as the image analysis method performed by the image analysis means. For example, image tagging software called "Clarifai" from Clarifai, Inc., USA, can be used as image analysis software. The identified words are associated with the image IDs of the images and registered in a word database. This word database stores words and the image IDs of images to which the words are assigned as tags that represent content, in association with word IDs, which are word identification information that identify the words. This word database is treated similarly to the word database 10 in the above embodiment. The information processing device then calculates coordinate values ​​corresponding to each item (image) based on the information registered in the word database and creates a scatter diagram. [Explanation of symbols]

[0242] 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 20. Processing unit 21...Common element number matrix generation means 22. Relationship matrix generation method 23...Adjusted matrix generation means 24. Coordinate value calculation means 25...Morphological analysis means 27. Item placement method 30. Output means 100 Information processing device

Claims

1. 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 between two items by calculating an index value of a relationship between sets related to the two items for each item belonging to the category of interest; an adjusted matrix generating means for generating an adjustment function that changes monotonically using a mean μ of elements of a triangular matrix in the relationship matrix, and for generating an adjusted matrix by applying the adjustment function to each element of the relationship matrix; 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 adjusted matrix; An information processing device having the above.

2. The information processing device according to claim 1 , wherein the adjustment function is a monotonically increasing function, which is a sigmoid function shown in Equation (1) configured using an average μ of elements of a triangular matrix in the relationship matrix S. [0013] ・・・（１）

3. The information processing device according to claim 1 , wherein the adjustment function is a monotonically decreasing function, which is a sigmoid function shown in Equation (2) configured using an average μ of elements of a triangular matrix in the relationship matrix S. [0014] ・・・（２）

4. The adjustment function is a monotonically increasing function and is configured using the mean μ and standard deviation σ of the elements of the triangular matrix in the relationship matrix S, and is expressed by the normal distribution N(μ, σ) shown in Equation (3). 2 2. The information processing apparatus according to claim 1, wherein the cumulative probability density function is a cumulative probability density function of [Equation 15] ・・・（３）

5. The adjustment function is a monotonically decreasing function and is configured using the mean μ and standard deviation σ of the elements of the triangular matrix in the relationship matrix S, and is expressed by the normal distribution N(μ, σ) shown in Equation (4). 2 2. The information processing apparatus according to claim 1, wherein the cumulative probability density function is a cumulative probability density function of [0016] ・・・（４）

6. 4. The information processing device according to claim 2, wherein the adjustment function uses a coefficient r that satisfies r≧1 and a reduction coefficient s that satisfies 0≦s≦1, and uses coefficients a′ and μ′ obtained by the following equation (5) instead of the coefficient a and the coefficient μ. [Equation 17] ・・・（５）

7. 6. The information processing device according to claim 4, wherein the adjustment function uses coefficients σ′ and μ′ obtained by the following equation (6) using a coefficient r that satisfies r≧1 and a reduction coefficient s that satisfies 0≦s≦1, instead of the coefficient σ and the coefficient μ. [Equation 18] ・・・（６）

8. 8. The information processing device according to claim 1, wherein the relationship matrix generation means calculates, as an index value of the relationship, a normalized self-information of a joint probability distribution of two variables generated based on the number of elements of a universal set that includes sets related to two items, the number of elements of a set related to one item, the number of elements of a set related to the other item, and the number of elements of an intersection of a set related to one item and a set related to the other item.

9. 8. The information processing device according to claim 1, wherein the relationship matrix generation means calculates, as an index value of the relationship, a normalized mutual information of a joint probability distribution of two variables generated based on the number of elements of a universal set that includes sets related to two items, the number of elements of a set related to one item, the number of elements of a set related to the other item, and the number of elements of an intersection of a set related to one item and a set related to the other item.

10. The method further comprises 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, The information processing apparatus according to claim 1 , wherein the relationship matrix generating means generates the relationship matrix using the set of extracted morphemes.

11. further comprising image analysis means for performing image analysis on the images to identify words when each item belonging to the category of interest is an image; The information processing device according to claim 1 , wherein the relationship matrix generating means generates the relationship matrix using the set of identified words.

12. 1. An information processing method in which a computer calculates coordinate values ​​for locating each item in a k-dimensional space using a set associated with each item belonging to a category of interest, the method comprising: The computer generating a relationship matrix by calculating, for each item in the category of interest, an index value of the relationship between sets related to the two items; generating a monotonically varying adjustment function using the average μ of the elements of the triangular matrix in the relationship matrix, and generating an adjusted matrix by applying the adjustment function to each element of the relationship matrix; An information processing method for calculating coordinate values ​​for locating each item in k-dimensional space by performing a predetermined transformation on an adjusted matrix.

13. A program that causes a computer to calculate coordinate values ​​for locating each item in k-dimensional space using a set associated with each item belonging to a category of interest, the program comprising: Computer, a relationship matrix generating means for generating a relationship matrix between two items by calculating, for each item belonging to the category of interest, an index value of the relationship between sets related to the two items; an adjusted matrix generating means for generating a monotonically varying adjustment function using the average μ of the elements of the triangular matrix in the relationship matrix, and for generating an adjusted matrix by applying the adjustment function to each element of the relationship matrix; coordinate value calculation means for performing a predetermined transformation on the adjusted matrix to calculate coordinate values ​​for arranging each item in a k-dimensional space; A program that functions as a

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