JP2017004493A - Data analysis method, data analysis apparatus, and program - Google Patents

Abstract

[Problem] To enable clustering that reflects a variety of information. [Solution] A data distribution method decomposes a fundamental matrix of N rows and M columns that indicates the degree of association between each of N first objects and each of M second objects into three matrices, and clusters at least one of the first objects and the second objects. A data analysis method includes an acquisition step of acquiring a fundamental matrix in which a value indicating the degree of association is input for each element of the fundamental matrix, a setting step of setting K indicating the number of clusters of the first object and L indicating the number of clusters of the second object, a decomposition step of decomposing the three matrices into a first matrix of N rows and K columns, a second matrix of a matrix of K rows and L columns, and a third matrix of L rows and M columns, such that the product of the first matrix, the second matrix, and the third matrix approximates the fundamental matrix, and an output step of outputting a clustering result by outputting at least one of the first matrix, the second matrix, and the third matrix. [Selected Figure] FIG.

Description

  The present invention relates to a data analysis method, a data analysis apparatus, and a program.

  In recent years, networking has progressed, and various data has been collected and accumulated via various devices. The various data are access information of the WEB site, customer purchase history, program recording / viewing history, customer age / sex information, and the like. Among them, recommendation services such as recommending merchandise by clustering users according to attributes such as preferences using purchase histories and recording histories are performed. As a currently known clustering method, NMF and a matrix decomposition method called Tri-NMF obtained by further expanding the NMF have been proposed (for example, Non-Patent Document 1). In Non-Patent Document 1, clustering is performed using one of the three matrices by performing matrix decomposition that can approximate a matrix serving as input data by the product of three matrices.

Orthogonal Nonnegative Matrix Tri-Factorizations for Clustering

  Clustering that reflects more diverse information is required.

  Therefore, the present invention provides a data analysis method, data analysis apparatus, and program capable of clustering reflecting various information.

  In the data analysis method according to an aspect of the present invention, a basic matrix of N rows and M columns indicating the degree of association between each of the N first objects and each of the M second objects is represented by three matrices. Is a data analysis method for clustering at least one of the first object and the second object by decomposing the basic matrix into which the values indicating the degree of association are input for each element of the basic matrix An acquisition step, a setting step for setting K indicating the number of clusters of the first object, and an L indicating the number of clusters of the second object, three matrices, a first matrix of N rows and K columns, A second matrix in which at least one element in one specific row and one specific column stores numerical values that fall within a predetermined range, and a third matrix of L rows and M columns. And the product of the first matrix, the second matrix, and the third matrix approximates the fundamental matrix And outputting at least one of the first matrix, the second matrix, and the third matrix by decomposing into the first matrix, the second matrix, and the third matrix, and the first object and the second object An output step of outputting at least one clustering result.

  Note that these comprehensive or specific aspects may be realized by a system, a method, an integrated circuit, a computer program, or a recording medium such as a computer-readable CD-ROM, and the system, method, integrated circuit, and computer program. And any combination of recording media.

  The data analysis method, data analysis apparatus, and program of the present invention enable clustering reflecting various information.

1 is a block diagram showing a schematic configuration of a data analysis system for executing a data analysis method according to Embodiment 1. FIG. 6 is an explanatory diagram illustrating an example of a basic matrix according to Embodiment 1. FIG. FIG. 10 is an explanatory diagram illustrating a modification of the basic matrix according to the first embodiment. 1 is a block diagram illustrating a schematic configuration of a data analysis apparatus according to a first embodiment. 6 is an explanatory diagram illustrating concepts of a basic matrix, a first matrix, a second matrix, and a third matrix according to Embodiment 1. FIG. 3 is a flowchart showing a flow of a data analysis method according to the first embodiment. 3 is a flowchart showing a flow of decomposition processing according to the first embodiment. 6 is an explanatory diagram illustrating an example of a basic matrix according to Embodiment 1. FIG. It is explanatory drawing which shows an example of the 1st matrix, the 2nd matrix, and the 3rd matrix which were obtained by performing the data analysis method based on the basic matrix of FIG. 10 is a flowchart showing a flow of decomposition processing according to the second embodiment. 10 is a flowchart showing a flow of deletion processing according to the second embodiment. It is a block diagram which shows the modification of a data analyzer.

(Knowledge that became the basis of the present invention)
The inventor has found that the following problems occur with respect to the method described in the “Background Art” column.

  When collecting purchase history, recording history, etc., the only data that can be collected is the information that a person has purchased a product or recorded a program. Information that “not recorded” or “not recorded” has not been collected directly. Hereinafter, for convenience of explanation, a case where collected data is data related to a recording history will be described as an example. That is, since the information “recorded” is accumulated, the information “not recorded” is obtained by reverse calculation such that “not recorded” = “not recorded”. In other words, the information “recorded” can be thought of as “recorded because the user likes the program”, but the information “not recorded” includes “recording because the user dislikes the program”. There are two types of meanings: the meaning of “not present” and the meaning of “the user does not know the existence of the program in the first place”. However, in the method of Non-Patent Document 1, the two types of information “not recorded” are not considered, and clustering is performed considering only the information “recorded” = “I like the program”. ing. That is, the information that the program is “disliked” is not considered at all.

  For this reason, by enabling clustering in consideration of the information “I hate”, it is possible to perform clustering reflecting various information.

  In order to solve such a problem, the data analysis method according to one aspect of the present invention provides N rows M indicating the degree of association between each of the N first objects and each of the M second objects. A data analysis method for decomposing a matrix of columns into three matrices and clustering at least one of a first object and a second object and indicating a degree of relevance for each element of the matrix An acquisition step of acquiring a basic matrix to which values are input, a setting step of setting K indicating the number of clusters of the first object, and L indicating the number of clusters of the second object, and three matrices N A first matrix of rows and K columns, and a second matrix of K rows and L columns, in which numerical values that fall within a predetermined range are stored in each element of at least one specific row and one specific column; , A third matrix of L rows and M columns, a first matrix, a second matrix and a third matrix A decomposition step for decomposing the first matrix, the second matrix, and the third matrix so that the product of the columns approximates the base matrix, and outputting at least one of the first matrix, the second matrix, and the third matrix And outputting the clustering result of at least one of the first object and the second object.

  Thereby, it becomes possible to perform clustering in consideration of the factor that the user did not acquire the object. Therefore, clustering reflecting various information becomes possible.

  For example, numerical values that fall within a predetermined range may be stored in each element of a specific row and a specific column.

  As a result, numerical values that fall within a predetermined range are stored in each element of a specific row and a specific column of the second matrix, so that different information (well-known level of the object, user acquisition frequency) is reflected. Clustering is possible.

  For example, a numerical value falling within a predetermined range may be a positive value that is substantially zero.

  Thereby, since the numerical value falling within the predetermined range is a positive value that is substantially 0, the degree of association with the cluster can be almost eliminated, and a value specialized for various information can be obtained.

  For example, the sum of the elements in each row of the first matrix may be substantially the same value in all rows.

  Thereby, since the sum total of each element in each row of the first matrix is substantially the same value in all rows, the values of the respective columns of the first matrix can be easily compared.

  For example, the sum of the elements in each column of the third matrix may be substantially the same value in all columns.

  Thereby, since the sum total of each element in each column of the third matrix is substantially the same value in all columns, it is possible to easily compare the values of each row of the third matrix.

  For example, the decomposition step repeats updating the first matrix, the second matrix, and the third matrix so that a difference between a product of the first matrix, the second matrix, and the third matrix and a base matrix is reduced. It may be.

  As a result, the first matrix, the second matrix, and the third matrix are updated so that the difference between the product of the first matrix, the second matrix, and the third matrix and the basic matrix becomes small. It can be done smoothly.

  For example, the decomposition step deletes the k-th row in the second matrix when each element in the k-th row is a numerical value that falls within a predetermined range in a row other than the specific one row of the second matrix, By deleting the k-th column in the matrix, the first matrix with N rows and K-1 columns, the second matrix with K-1 rows and L columns, and the third matrix with L rows and M columns are updated. Also good.

  Thereby, it is possible to increase the processing speed and the accuracy of clustering.

  For example, the decomposition step deletes the l-th column in the second matrix when each element in the l-th row is a numerical value that falls within a predetermined range in a column other than the specific one column of the second matrix, By deleting the l-th row in the matrix, updating to the first matrix of N rows and K columns, the second matrix of K rows and L-1 columns, and the third matrix of L-1 rows and M columns may be performed. Good.

  Thereby, it is possible to increase the processing speed and the accuracy of clustering.

  For example, the first object may be a user, and the relevance level for each element of the basic matrix of N rows and M columns may indicate whether or not N users are interested in each of the M second objects.

  In addition, the data analysis apparatus according to one aspect of the present invention provides a basic matrix of N rows and M columns indicating the degree of association between each of the N first objects and each of the M second objects. A data analysis apparatus that decomposes into one matrix and clusters at least one of the first object and the second object, and a basic matrix in which a value indicating the degree of association is input to each element of the basic matrix A setting unit that sets K indicating the number of clusters of the first object, and L indicating the number of clusters of the second object, and three matrices, the first matrix of N rows and K columns A second matrix in which numerical values that fall within a predetermined range are stored in each element of at least one of a specific row and a specific column, and a third matrix of L rows and M columns A matrix, and the product of the first matrix, the second matrix, and the third matrix approximates the basic matrix, A decomposition unit that decomposes the first matrix, the second matrix, and the third matrix; and outputs at least one of the first matrix, the second matrix, and the third matrix, so that the first object and the second object And an output unit that outputs at least one clustering result.

  Thereby, it becomes possible to perform clustering in consideration of the factor that the user did not acquire the object. Therefore, clustering reflecting various information becomes possible.

  A program according to one embodiment of the present invention is a program for causing a computer to execute the data analysis method described above.

  Thereby, it becomes possible to perform clustering in consideration of the factor that the user did not acquire the object. Therefore, clustering reflecting various information becomes possible.

  Note that these comprehensive or specific aspects may be realized by a system, a method, an integrated circuit, a computer program, or a recording medium such as a computer-readable CD-ROM, and the system, method, integrated circuit, and computer program. And any combination of recording media.

(Embodiment 1)
Hereinafter, a data analysis method according to an embodiment will be specifically described with reference to the drawings. It should be noted that each of the embodiments described below shows a comprehensive or specific example. Numerical values, shapes, materials, components, arrangement positions and connection forms of components, steps, order of steps, and the like shown in the following embodiments are merely examples, and are not intended to limit the present invention. In addition, among the constituent elements in the following embodiments, constituent elements that are not described in the independent claims indicating the highest concept are described as optional constituent elements.

[Overall system configuration]
FIG. 1 is a block diagram showing a schematic configuration of a data analysis system for executing the data analysis method according to the first embodiment.

  The data analysis system 1 executes a data analysis method that decomposes a basic matrix of N rows and M columns indicating whether or not N users are interested in each of M objects into three matrices, and clusters users. . The object is an object that the user is interested in, and examples thereof include products purchased or rented by the user and programs such as TV programs and radio programs that are viewed or recorded / recorded by the user. As for the presence / absence of interest, when the object is a product, “purchased” means “purchased” and “not interested” means not purchased. On the other hand, when the target is a program, “interested” means that the program has been viewed or recorded / recorded, and “not interested” means that the program has not been viewed or recorded / recorded.

  FIG. 2 is an explanatory diagram illustrating an example of a basic matrix.

  In the basic matrix shown in FIG. 2, N users U1, U2, U3, U4, U5... Indicate whether or not there are interests in each of the M objects O1, O2, O3, O4, O5, O6. . A value indicating the interest is input to each element of the basic matrix. Specifically, “1” is assigned to an element of interest, and “0” is assigned to an element of no interest. For example, when the target is a program and the presence / absence of recording on the program is determined to be interested, “1” is input to the program recorded by the user, and the program is not recorded by the user. On the other hand, “0” is input. Note that the data values and formats are merely examples, and the present invention is not limited to these. The value input to each element may be a non-negative value.

  FIG. 3 is an explanatory diagram showing a modification of the basic matrix.

  In the example of FIG. 3, the case where the presence or absence of interest with respect to a program is shown by 5-step evaluation is shown. Even in this case, the value of each element may be normalized so that the maximum value “5” becomes “1”.

  Then, the data analysis system 1 clusters users or objects by decomposing the basic matrix into three matrices.

  Specifically, the data analysis system 1 includes an input device 200, a display device 300, and a data analysis device 400, as shown in FIG. The input device 200, the display device 300, and the data analysis device 400 are communicably connected via a network 500.

  The network 500 is a wired network such as Ethernet (registered trademark), a wireless network such as a wireless LAN, a public network, or a network in which these networks are combined. A public network is a communication line provided by a telecommunications carrier for communication of an unspecified number of users, and includes, for example, a general telephone line or ISDN.

  The input device 200 is a device to which a basic matrix of N rows and M columns is input. The input device 200 is, for example, a personal computer, a smartphone, a feature phone, a tablet terminal, or the like provided with an input unit 210 such as a keyboard, a touch panel, or a pointing device. When the basic matrix of N rows and M columns is input, the input device 200 transmits the basic matrix to the data analysis device 400 via the network 500.

  When at least one of the basic matrix and the three matrices is input from the data analysis device 400, the display device 300 is a device that displays the at least one matrix. The display device 300 is, for example, a personal computer, a smartphone, a feature phone, a tablet terminal, or the like provided with a display unit 310 such as a display. The analyst views at least one matrix displayed on the display unit 310 of the display device 300, so that the clustered result can be analyzed.

  In this embodiment, the case where the input device 200 and the display device 300 are independent and different terminals is illustrated, but the input device 200 and the display device 300 may be a single terminal.

[Data analysis equipment]
The data analysis device 400 is a processing device that decomposes a basic matrix of N rows and M columns into three matrices. The data analysis device 400 is, for example, a server, a personal computer, a smartphone, a feature phone, a tablet terminal, or the like.

  FIG. 4 is a block diagram illustrating a schematic configuration of the data analysis apparatus 400.

  As illustrated in FIG. 4, the data analysis device 400 includes an acquisition unit 410, a processing unit 420, and an output unit 430.

  The acquisition unit 410 acquires a basic matrix input from the input device 200 via the network 500 and outputs the basic matrix to the processing unit 420.

  The processing unit 420 is a processing unit that decomposes the basic matrix input from the acquisition unit 410 into three matrices, and includes a CPU, a RAM, a ROM, and the like. The processing unit 420 includes a storage unit 421, a setting unit 422, and a decomposition unit 423.

  The storage unit 421 is a storage area for storing the basic matrix recorded from the acquisition unit 410, and is, for example, a nonvolatile memory or a volatile memory.

  The setting unit 422 stores setting items used in the disassembling process in the disassembling unit 423. Examples of setting items include K and L, which are values that determine the sizes of the three matrices. In addition, examples of the setting item include a convergence determination condition at the time of decomposition processing. The setting unit 422 sets the setting item by outputting the setting item to the decomposition unit 423 when the decomposition process is performed by the decomposition unit 423.

  Note that the setting item may not be stored in the setting unit 422 in advance, but may be a setting value input from the input device 200 as the setting item. In this case, the setting unit 422 stores the setting item received from the input device 200 via the acquisition unit 410.

  The decomposition unit 423 divides the three matrices into a first range of N rows and K columns and a matrix of K rows and L columns, and each element in at least one of one specific row and one specific column is within a predetermined range. The first matrix, the second matrix, and the third matrix with L rows and M columns, the first matrix, the second matrix, and the third matrix are approximated to the basic matrix. Decompose into two and third matrices.

  FIG. 5 is an explanatory diagram showing the concept of the basic matrix, the first matrix, the second matrix, and the third matrix according to the present embodiment.

  For example, if the basic matrix of N rows and M columns is a matrix of 14 rows and 20 columns, and K = 3 and L = 3, the first matrix of N rows and K columns becomes a matrix of 20 rows and 3 columns, and the first matrix of K rows and L columns. The 2 matrix is a matrix of 3 rows and 3 columns, and the third matrix of L rows and M columns is a matrix of 3 rows and 14 columns.

  K is the value of the number of user clusters. L is the value of the number of object clusters. However, the elements (clusters) that are not directly related to the user cluster (cluster of the first object) and the object cluster (second object cluster) include the first matrix, the second matrix, and the first matrix corresponding to one column or one row. Included in 3 matrices.

  In the case of FIG. 5, K indicating the number of clusters of the first object is set to “3”, and L indicating the number of clusters of the second object is set to “3”. Of these, two are described as being directly related to the respective clusters of the first object and the second object, and one being a cluster not directly related to each cluster. When the analyst inputs only the number of user clusters and the number of object clusters that are directly related to each of the clusters to be classified, the setting unit 422 or the decomposition unit 423 determines the number of clusters. A value obtained by adding 1 (a value obtained by adding an element not directly related) may be K and L.

  Here, the numerical value that falls within the predetermined range is a positive value that is substantially 0, specifically, a value that falls within the range of 0 to 0.1, preferably 0 to 0.01. The value is within the range. In addition, the value of each element in at least one specific row and specific column in the second matrix may not be the same as long as it is a numerical value falling within a predetermined range. In the present embodiment, a case where the value of each element in the K-th row and the L-th column in the second matrix is 0 will be described as an example. However, the value of one element of the Kth row and the Lth column in the second matrix may be a numerical value that falls within a predetermined range. The specific row may be a row other than the Kth row, and the specific column may be a column other than the Lth column.

  Further, when each element of a specific column of the second matrix is set to a numerical value that falls within a predetermined range, the third matrix gives a condition that the sum of the elements in each column is the same value in all the columns. On the other hand, when each element in a specific row of the second matrix is a numerical value that falls within a predetermined range, the first matrix gives a condition that the sum of the elements in each row is the same value in all rows. The “same value” may not be a completely matching value, but may be a substantially “same value” having a slight tolerance. The “same value” may be any value, but “1”, “100”, or the like may be used to make it easy to recognize the relationship between the user, the object, and each cluster.

  A more specific description of the first matrix, the second matrix, and the third matrix will be described later.

  The decomposition unit 423 repeatedly updates the first matrix, the second matrix, and the third matrix so that the error between the product of the first matrix, the second matrix, and the third matrix and the basic matrix becomes small. When the convergence determination condition stored in the unit 422 is satisfied, the update is terminated. For example, a method for determining that the convergence determination condition is satisfied when a predetermined number of times (1000 times or more) is repeated, and an error between the product of the first matrix, the second matrix, and the third matrix and the base matrix is a predetermined value. (E.g., 1e-6) or less, a method of determining that the convergence determination condition is satisfied, and the error of the product of the first matrix, the second matrix, and the third matrix before and after one update is a predetermined value (e.g., 1e-6) A method of determining that the convergence determination condition is satisfied when the value is equal to or less than 1e-6) can be given. Each method may be used alone or in combination. The error may be a sum of values obtained by subtraction of each matrix element, or may be a sum of squares of values obtained by subtraction of each element.

  As illustrated in FIG. 4, the output unit 430 outputs at least one of the basic matrix, the first matrix, the second matrix, and the third matrix to the display device 300. The output unit 430 may output the basic matrix, the first matrix, the second matrix, and the third matrix in a lump, or may output them in combination. The output unit 430 may also output an error between the final product of the first matrix, the second matrix, and the third matrix and the basic matrix to the display device 300.

[Data analysis method]
Next, a data analysis method according to the present embodiment will be described.

  FIG. 6 is a flowchart showing the flow of the data analysis method according to the present embodiment.

  In the input device 200, a value indicating the interest is input to each element of the basic matrix. In the input device 200, K, L, and convergence determination conditions are also input. After these inputs, the input device 200 outputs the basic matrix, K, L, and convergence determination conditions to the data analysis device 400. Note that if the setting item has already been set in the setting unit 422 of the data analysis device 400 and is used for the subsequent processing, it is not necessary to input the setting item with the input device 200.

  The acquisition unit 410 of the data analysis device 400 acquires the basic matrix, K, L, and convergence determination condition input from the input device 200 via the network (step S1). After the acquisition, the acquisition unit 410 stores the basic matrix in the storage unit 421.

  Further, the setting unit 422 stores K and L acquired by the acquisition unit 410 and the convergence determination condition as setting items (steps S2 and S3).

  The decomposition unit 423 of the data analysis device 400 executes the decomposition process based on the basic matrix and the setting items.

  FIG. 7 is a flowchart showing the flow of the disassembling process according to the present embodiment.

  The decomposition unit 423 generates the first matrix, the second matrix, and the third matrix based on N, M, K, and L. At this time, the decomposing unit 423 substitutes random values for each element of the first matrix, the second matrix, and the third matrix, and initializes them (step S11).

  Next, the decomposition unit 423 sets i to 0 (step S12).

  Next, the decomposing unit 423 determines whether i is equal to or greater than the predetermined number of convergence determination conditions. If it is smaller than the predetermined number, the process proceeds to step S14. If i is equal to or greater than the predetermined number, the decomposing process is performed. finish.

  In step S14, the decomposition unit 423 updates the first matrix, the second matrix, and the third matrix.

  At the time of updating, the decomposing unit 423 updates the initialized first matrix, second matrix, and third matrix using a predetermined matrix updating formula, so that the first matrix, the second matrix, and the second matrix are updated. A first matrix, a second matrix, and a third matrix are obtained in which the product of the three matrices approximates the basic matrix. At this time, the decomposing unit 423 updates the values of the elements in the Kth row and the Lth column of the second matrix to be 0.

  An example of the matrix update formula is shown below.

In the following matrix updating formula (1) and the fundamental matrix is X, the first matrix is F, the second matrix is S, the third matrix is G ^T. Α, β, and γ are constants. S ^* is a matrix in which a value (0 in the present embodiment) that falls within a predetermined range is inserted into the value of each element of at least one specific row and specific column of S.

  The decomposition unit 423 updates the first matrix, the second matrix, and the third matrix so that the matrix update formula (1) is minimized.

但し、Ｆ_ｗ,ｋは、Ｆのｗ行ｋ列の要素の値示す（１≦ｗ≦Ｎ、１≦ｋ≦Ｋ）。
Ｓ_ｋ,ｌは、Ｓのｋ行ｌ列の要素の値を示す（１≦ｋ≦Ｋ、１≦ｌ≦Ｌ）。
Ｇ_ｔ,ｌは、Ｇのｔ行ｌ列の要素の値の値を示す（１≦ｔ≦Ｍ、１≦ｌ≦Ｌ）。
Ｆ^Ｔは、Ｆの転置行列を示す。
Ｇ^Ｔは、Ｇの転置行列を示す。
Ｓ^Ｔは、Ｓの転置行列を示す。
Ｘ^Ｔは、Ｘの転置行列を示す。
Ａ^Ｔは、Ａの転置行列を示す。 An example of a mathematical expression showing details of the matrix update equation (1) is shown below.

Here, F _{w, k} indicates the value of the element of F in w rows and k columns (1 ≦ w ≦ N, 1 ≦ k ≦ K).
S _{k, l} indicates the value of an element of k rows and l columns of S (1 ≦ k ≦ K, 1 ≦ l ≦ L).
G _{t, l} represents the value of the element of G row t column l (1 ≦ t ≦ M, 1 ≦ l ≦ L).
F ^T indicates the transposed matrix of F.
G ^T denotes a transposed matrix of G.
S ^T indicates a transposed matrix of S.
X ^T represents a transposed matrix of X.
^AT represents the transpose matrix of A.

  The decomposing unit 423 can update the first matrix, the second matrix, and the third matrix so as to reduce the error by using the equations (2) to (4).

  Next, the decomposing unit 423 calculates an error between the product of the updated first matrix, second matrix, and third matrix and the base matrix (step S15).

  Next, the decomposing unit 423 determines whether or not the error obtained in step S15 is equal to or smaller than a predetermined value. If the error is equal to or smaller than the predetermined value, the process proceeds to step S17. .

  In step S17, the disassembling unit 423 adds 1 to i and proceeds to step S13. Thereby, the update of the first matrix, the second matrix, and the third matrix is repeated until the error becomes equal to or smaller than the predetermined value or until i reaches the predetermined number of times. At the end of the decomposition process, the first matrix, the second matrix, and the third matrix with almost no error between the product of the first matrix, the second matrix, and the third matrix and the basic matrix are obtained.

  When the disassembly process ends and the process proceeds to step S5 in FIG. 5, the output unit 430 outputs the basic matrix, the first matrix, the second matrix, and the third matrix to the display device 300. Since the basic matrix, the first matrix, the second matrix, and the third matrix are displayed on the display device 300, an analyst can analyze them to analyze the clustered result.

[An example of each matrix]
Next, an example of the basic matrix used in the data analysis method and the first matrix, the second matrix, and the third matrix obtained by the data analysis method will be described.

  FIG. 8 is an explanatory diagram illustrating an example of a basic matrix.

  The basic matrix shown in FIG. 8 is a matrix with 20 rows and 14 columns. The basic matrix of FIG. 7 shows whether or not 20 users U1 to U20 have recorded 14 programs P1 to P14. “1” is input for a program recorded by each user, and “0” is input for a program not recorded. These “1” and “0” are values indicating the presence or absence of interest.

  FIG. 9 is an explanatory diagram illustrating an example of the first matrix, the second matrix, and the third matrix obtained by performing the data analysis method based on the basic matrix of FIG. Even if the same basic matrix is used, the final first matrix, second matrix, and third matrix differ depending on the value of each element at the time of initialization, the convergence determination condition, and the matrix update expression.

  In the example of FIG. 8, K is 3, and the third column (K column) of the second matrix is a specific column. That is, the first column and the second column of the second matrix are columns related to the user clusters UC1 and UC2. Further, L is 3, and the third row (L row) of the second matrix is a specific one row. That is, the first row and the second row of the second matrix are columns related to the program clusters PC1 and PC2.

  In the first matrix, the respective degrees of association between the 20 users U1 to U20, the user clusters UC1 and UC2, and the recording frequency are stored in each element. In the second matrix, the degree of association between the user clusters UC1 and UC2 and the recording frequency and the program clusters PC1 and PC2 and the degree of familiarity is stored in each element. In the third matrix, the program clusters PC1 and PC2, the degree of familiarity, and the degree of association between each of the 14 programs P1 to P14 are stored in each element.

  Here, the present inventor stores a numerical value (a numerical value falling within a predetermined range) indicating that there is almost no degree of association with the user clusters UC1 and UC2 for a specific column of the second matrix. As a result, it was found that a row indicating the degree of familiarity of the program (object) (the third row in the third matrix shown in FIG. 9) is generated. In the case of the third matrix in FIG. 9, the degree of familiarity is small when each value of the row (third line) indicating the degree of familiarity is large, and the degree of familiarity is large when each value is small. The degree of familiarity is an index indicating how much the program (object) is known, and may be used as the popularity of the program. A user who does not record a program with a high level of familiarity can estimate that he does not record because he does not know the program, but does not record. Since it is considered that “a popular program is not recorded intentionally”, it can be inferred that “this user does not like this program”. Since the row indicating the degree of familiarity is generated in the third matrix, the first matrix, the second matrix, and the third matrix are updated by reflecting the degree of familiarity in the decomposition process. Therefore, clustering considering information “dislike” is possible.

  Furthermore, the present inventor stores a numerical value (a numerical value falling within a predetermined range) indicating that there is almost no degree of association with the program clusters PC1 and PC2 with respect to a specific row of the second matrix. It was found that a row indicating the recording frequency of the user (the third column in the first matrix shown in FIG. 9) is generated. In the case of the first matrix in FIG. 9, if each value in the row (third column) indicating the recording frequency is large, the user's recording frequency is low, and if each value is small, the recording frequency is high. The recording frequency is an index indicating the degree to which the user records a program. Then, when the column indicating the recording frequency is generated in the first matrix, the present inventor includes each of the users U1 to U20 and the user clusters UC1 and UC2 in the other columns of the first matrix after the decomposition process. It was found that the relevance is stored as a value excluding the influence of the recording frequency as much as possible. This allows clustering of users with similar preferences regardless of the recording frequency.

  In this embodiment, since the object is a program, the recording frequency appears in one row of the first matrix by storing a numerical value falling within a predetermined range in a specific row of the second matrix. Became. However, when the object is a product, the purchase frequency at which the user purchases (or rents) the product appears in one row of the first matrix. Since both the purchase frequency and the recording frequency are indices indicating the degree to which the user acquires an object, these may be collectively referred to as an acquisition frequency.

  Moreover, in this Embodiment, since each user U1-U20 respond | corresponds to each row in a 1st matrix, and each program P1-P14 respond | corresponds to each column of a 3rd matrix, specific 1 column of a 2nd matrix Corresponds to the degree of familiarity, and one specific line corresponds to the recording frequency. Conversely, when each user U1 to U20 corresponds to each column in the third matrix and each program P1 to P14 corresponds to each row of the first matrix, a specific one row of the second matrix is known. And one specific column corresponds to the recording frequency. In other words, depending on the relationship between the target to be clustered and the first matrix, the second matrix, and the third matrix, the element corresponding to the degree of familiarity and the recording frequency becomes one row or one column of the second matrix. Or If clustering is performed in consideration of only one of the degree of familiarity and the recording frequency (acquisition frequency), each element in one specific row and one specific column of the second matrix is considered in consideration of the above-described relationship. On the other hand, a numerical value that falls within a predetermined range may be stored.

[Effects]
As described above, according to the present embodiment, the first matrix of N rows and K columns and the matrix of K rows and L columns, each element of at least one specific row and specific column, The first matrix, the second matrix, and the third matrix are such that the product of the three matrices of the second matrix storing numerical values falling within a predetermined range and the third matrix of L rows and M columns approximates the basic matrix. The matrix is decomposed. Thereby, it becomes possible to perform clustering in consideration of the factor that the user did not acquire the object (program, product). Therefore, clustering reflecting various information becomes possible.

  In the case of the present embodiment, information such as “dislike” can be inferred from the user's recording history. However, if there is no data analysis method described above, information “dislike” must also be collected. In other words, if clustering reflecting a variety of information can be performed, energy consumption related to information collection can be reduced accordingly.

  In addition, since numerical values that fall within a predetermined range are stored in each element of a specific row and a specific column of the second matrix, clustering that reflects the familiarity of the object and the user's acquisition frequency is possible. It becomes.

  In addition, since the numerical value falling within the predetermined range is a positive value that is substantially 0, the degree of association with the user cluster or the program cluster can be almost eliminated, and a value specialized for the degree of familiarity and acquisition frequency is obtained. be able to.

  Further, since the sum of the elements in each row of the first matrix is substantially the same value in all rows, the value of each column indicating the acquisition frequency can be calculated based on the same value. Therefore, the values of the respective columns can be easily compared.

  In addition, since the sum of the elements in each column of the third matrix is substantially the same value in all columns, the value of each row indicating the degree of familiarity can be calculated based on the same value. Therefore, the values of the respective rows can be easily compared.

  In addition, since the first matrix, the second matrix, and the third matrix are updated so that the difference between the product of the first matrix, the second matrix, and the third matrix and the basic matrix becomes small, the matrix decomposition is smoothly performed. Can be done.

(Embodiment 2)
In the data analysis method exemplified in the first embodiment, when K and L are set to some extent, a row similar to a specific row is generated or a column similar to a specific column is generated at the time of update. It is assumed that In this case, since the accuracy of clustering may be reduced, in the second embodiment, when the data analysis method is executed, a row having the same property as a specific one row is generated in the second matrix. Alternatively, when a column having the same property as a specific column occurs in the second matrix, a method of deleting a row or column having the same property will be described.

  FIG. 10 is a flowchart showing the flow of the disassembling process according to the second embodiment.

  In the flowchart shown in FIG. 10, step S18 for performing a deletion process is added between steps S14 and S15 of the decomposition process according to the first embodiment. For this reason, only step S18 is demonstrated here and description is abbreviate | omitted about another step.

  In the deletion process in step S18, the decomposition unit 423 generates a column having the same property as the specific one row in the second matrix or a column having the same property as the specific one column in the second matrix. In some cases, rows or columns that have the same properties are deleted.

  FIG. 11 is a flowchart showing the flow of the deletion process.

  The decomposition unit 423 calculates a difference between each value of a specific first column (Lth column) in the second matrix and each value of each other column (step S21).

  Next, the decomposing unit 423 determines whether or not there is a column (the l-th column) in which the absolute value of the difference is less than or equal to a certain value for all elements (step S22). The process proceeds to S23, and if there is no l-th column, the process proceeds to Step S24.

  In step S23, the decomposition unit 423 deletes the 1st column of the second matrix and the 1st row of the third matrix, so that the first matrix of N rows and K columns and the K row of L-1 columns are deleted. Update to the second matrix and the third matrix of L-1 rows and M columns.

  In step S24, the decomposing unit 423 calculates the difference between each value of a specific first row (Kth row) in the second matrix and each value of each other row.

  Next, the decomposing unit 423 determines whether or not there is a row (k-th row) in which the absolute value of the difference is less than or equal to a certain value for all elements (step S25). The process proceeds to S26, and if there is no k-th row, the deletion process is terminated.

  In step S26, the decomposition unit 423 deletes the k-th row of the second matrix and the k-th column of the first matrix, so that the first matrix of N rows and K-1 columns and the K-1 row L Update to the second matrix of columns and the third matrix of L rows and M columns, and the deletion process ends.

  The constant value is, for example, a value of 0.1 or less. Moreover, the process from step S21 to step S23 and the process from step S24 to step S26 may be reversed. Furthermore, in steps S22 and S25, the determination is made based on the absolute value of the difference. If each element in a specific row or a specific column is close to 0, each row or column The determination may be made based on whether or not the sum of elements is equal to or less than a certain value.

[Effects]
As described above, according to the present embodiment, k rows in the second matrix are obtained when the elements in the kth row are values that fall within a predetermined range in the rows other than the specific one row of the second matrix. By deleting the eyes and deleting the k-th column in the first matrix, the first matrix of N rows and K-1 columns, the second matrix of K-1 rows and L columns, and the third matrix of L rows and M columns And update. Thereby, it is possible to increase the speed of the division process and the accuracy of clustering.

  In addition, in the columns other than the specific one column of the second matrix, when each element in the l-th row is a numerical value that falls within a predetermined range, the l-th column in the second matrix is deleted, and the l-th row in the third matrix By deleting the eye, the first matrix with N rows and K columns, the second matrix with K rows and L-1 columns, and the third matrix with L-1 rows and M columns are updated. Thereby, it is possible to increase the speed of the division process and the accuracy of clustering.

(Other embodiments)
As described above, Embodiments 1 and 2 have been described as examples of the technology disclosed in the present application. However, the technology in the present embodiment is not limited to this, and can be applied to an embodiment in which changes, replacements, additions, omissions, and the like are appropriately performed. Moreover, it is also possible to combine each component demonstrated by each said embodiment into a new embodiment.

  In the following description, the same parts as those in the above embodiment may be denoted by the same reference numerals and the description thereof may be omitted.

  For example, in the above embodiment, the case where the basic matrix is input to the data analysis device 400 via the network 500 has been described as an example. However, the basic matrix may be directly input (created) to the data analysis device. .

  FIG. 12 is a block diagram showing a modification of the data analysis apparatus.

  As shown in FIG. 12, the data analysis apparatus 400A is provided with an input unit 450, a processing unit 420, and a display unit 460. The input unit 450 is an input device such as a keyboard, a touch panel, or a mouse, and a basic matrix is input (created) when an analyst operates the input unit 450. That is, the input unit 450 is an acquisition unit. The display unit 460 is a display, and displays and outputs at least one of a basic matrix, a first matrix, a second matrix, and a third matrix. That is, the display unit 460 is an output unit. Furthermore, the data analysis device 400A may include a storage unit such as a hard disk or a memory that stores the basic matrix, the first matrix, the second matrix, and the third matrix.

  In each of the above embodiments, each component may be configured by dedicated hardware or may be realized by executing a software program suitable for each component. Each component may be realized by a program execution unit such as a CPU or a processor reading and executing a software program recorded on a recording medium such as a hard disk or a semiconductor memory. Here, the software that realizes the image decoding apparatus of each of the above embodiments is the following program.

  That is, the program decomposes a basic matrix of N rows and M columns indicating the degree of association between each of the N first objects and each of the M second objects into three matrices. A data analysis method for clustering at least one of the first object and the second object, and acquiring a basic matrix in which a value indicating the degree of association is input for each element of the basic matrix A setting step for setting a step, K indicating the number of clusters of the first object, and L indicating the number of clusters of the second object, and three matrices: a first matrix of N rows and K columns; A matrix of rows and L columns, a second matrix in which numerical values falling within a predetermined range are stored in each element of at least one specific row and a specific column, and a third matrix of L rows and M columns , The first matrix, the second matrix and the third matrix are the basic rows The first object is output by decomposing into a first matrix, a second matrix, and a third matrix, and outputting at least one of the first matrix, the second matrix, and the third matrix so as to approximate to And an output step of outputting a clustering result of at least one of the second objects.

  Moreover, in each said embodiment, another process part may perform the process which a specific process part performs. Further, the order of the plurality of processes may be changed, and the plurality of processes may be executed in parallel.

  As described above, the data analysis method according to one or more aspects has been described based on the embodiment, but the present invention is not limited to this embodiment. Unless it deviates from the gist of the present invention, various modifications conceived by those skilled in the art have been made in this embodiment, and forms constructed by combining components in different embodiments are also within the scope of one or more aspects. May be included.

  The present invention is useful as a data analysis method, data analysis apparatus, and program used for clustering. That is, the present invention can be applied in various fields that require clustering, such as a recommendation system and sentence classification.

DESCRIPTION OF SYMBOLS 1 Data analysis system 200 Input device 300 Display apparatus 400 Data analysis device 410 Acquisition part 420 Processing part 421 Storage part 422 Setting part 423 Decomposition part 430 Output part 500 Network

Claims (11)

A basic matrix of N rows and M columns indicating the degree of association between each of the N first objects and each of the M second objects is decomposed into three matrices, and the first object and the first object are decomposed. A data analysis method for clustering at least one of two objects,
An acquisition step of acquiring the basic matrix in which a value indicating the degree of association is input for each element of the basic matrix;
A setting step of setting K indicating the number of clusters of the first object and L indicating the number of clusters of the second object;
The three matrices are a first matrix of N rows and K columns, and a matrix of K rows and L columns, and numerical values that fall within a predetermined range are stored in each element of one specific row and one specific column. The first matrix, so that the product of the first matrix, the second matrix, and the third matrix approximates the basic matrix, A decomposing step of decomposing the second matrix and the third matrix;
An output step of outputting at least one clustering result of the first object and the second object by outputting at least one of the first matrix, the second matrix, and the third matrix;
Data analysis method including. The data analysis method according to claim 1, wherein a numerical value that falls within the predetermined range is stored in each element of the specific row and the specific column. The data analysis method according to claim 1, wherein the numerical value falling within the predetermined range is a positive value that is substantially zero. The data analysis method according to any one of claims 1 to 3, wherein the first matrix has a sum of elements in each row that is substantially the same in all rows. The data analysis method according to any one of claims 1 to 4, wherein the third matrix has a sum of elements in each column that is substantially the same in all columns. The decomposition step includes
Repeat updating the first matrix, the second matrix, and the third matrix so that a difference between a product of the first matrix, the second matrix, and the third matrix and the basic matrix is reduced. The data analysis method as described in any one of Claims 1-5. The decomposition step includes
In each row other than the specific one row of the second matrix, when each element in the k-th row is a numerical value that falls within the predetermined range, the k-th row in the second matrix is deleted, and the first matrix To update the first matrix of N rows and K-1 columns, the second matrix of K-1 rows and L columns, and the third matrix of L rows and M columns by deleting the k-th column in The data analysis method according to any one of 1 to 6. The decomposition step includes
In each column other than the specific column of the second matrix, if each element in the l-th row is a numerical value that falls within the predetermined range, the l-th column in the second matrix is deleted, and the third matrix The first row of N rows and K columns, the second matrix of K rows and L-1 columns, and the third matrix of L-1 rows and M columns are updated by deleting the 1st row in The data analysis method as described in any one of 1-7. The first object is a user, and the degree of association with each element of the basic matrix indicates whether or not N users are interested in each of the M second objects. The data analysis method according to one item. A basic matrix of N rows and M columns indicating the degree of association between each of the N first objects and each of the M second objects is decomposed into three matrices, and the first object and the A data analysis device for clustering at least one of the second objects,
An acquisition unit that acquires the basic matrix in which a value indicating the degree of association is input for each element of the basic matrix;
A setting unit for setting K indicating the number of clusters of the first object and L indicating the number of clusters of the second object;
The three matrices are a first matrix of N rows and K columns and a matrix of K rows and L columns, and numerical values that fall within a predetermined range are stored in at least one element of a specific row and a specific column. The first matrix, the third matrix, and the third matrix with L rows and M columns, and the product of the first matrix, the second matrix, and the third matrix approximates the basic matrix. A decomposition unit that decomposes the second matrix and the third matrix;
An output unit for outputting at least one clustering result of the first object and the second object by outputting at least one of the first matrix, the second matrix, and the third matrix;
A data analysis apparatus.   A program for causing a computer to execute the data analysis method according to claim 1.

Images