JP2008250848A - Clustering method, data processor, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform accurate clustering of data based on a self organizing map. <P>SOLUTION: Self organizing map processing to fit input data to a code vector using the self organizing map, determination processing to determine whether the code vector obtained by the above process is converged into a predetermined state, and separation/bind processing to compare the distance between the respective code vectors with a set threshold, if determined not converged, separate the cases of longer distances than the threshold value, and bind the cases of shorter than the threshold value are performed. Processes to perform self organizing map processing to the code vector clustered by separation/bind in the separation/bind processing and to acquire the code vector are repeated, and the clustering state determined to be converged into the predetermined state in the determination processing is output. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a clustering method for performing a process of classifying various data using a self-organizing map (SOM), a data processing apparatus for performing the clustering process, and a process such as a computer apparatus. The present invention relates to a program that is implemented in a data processing apparatus.

Conventionally, k-means method, fuzzy-c average method, etc. are known as methods for clustering various data. These methods are based on the assumption that the distribution of data to be clustered is a normal distribution. On the other hand, an arbitrary shape clustering method has been proposed as a method for performing clustering with high accuracy even if the distribution of data to be clustered has an arbitrary shape. However, in the conventionally proposed arbitrary shape clustering, the accuracy of the clustering is not so good. That is, when different clusters are close to each other, even if an arbitrary shape clustering method is used, different clusters may be classified into the same cluster.
“Arbitrary Shape Clustering Robust to Noise Based on Labeling by Ascending Order of Intercluster Distance”, Journal of the Institute of Image Information, Vol.60, N0.4, pp.618-620, 2006

The inventor of the present application has proposed a clustering method for solving the above problem in Non-Patent Document 1.
In this proposed clustering method, a code vector is randomly generated, and then the generated code vector is fitted to data using a self-organizing map (SOM). Based on the continuity of the code vector, clustering is performed. It is a technique to do. In this method, first, code vectors are divided and labeled each time the angle connecting the fitted code vectors changes greatly. Next, each data is clustered by searching for a coat vector in which each data has a minimum distance and assigning a label of the code vector to the data.

  FIG. 8 and FIG. 9 show an example of processing by a clustering method using this conventional self-organizing map. The example of FIG. 8 assumes a case where clustering is successful. To explain in order, it is assumed that a plurality of data are distributed two-dimensionally as shown at the left end of FIG. Here, as a distribution, it is assumed that the [u] -shaped distribution and the [n] -shaped distribution are close to each other in the vertical direction and can be seen as an [x] -shaped.

  At this time, each data is fitted to the code vector using the self-organizing map, and the code vector data shown in the center of FIG. 8 is obtained. Next, every time the angle connecting the fitted code vector changes greatly, the code vector is divided and labeled, and the label is assigned to the data. If the assignment is appropriate, as shown at the right end of FIG. The upper [u] -shaped distribution cluster (indicated by a black circle) and the lower [n] -shaped distribution cluster (indicated by a triangle) are clustered into different ones.

  On the other hand, in the example shown in FIG. 9, the code vector is fitted to each data using the self-organizing map for the same data shown at the left end of FIG. 9, and the code vector data shown in the center of FIG. This is an example obtained as a result of being divided into three clusters of black circles, triangles and squares as shown at the right end of FIG. In this example, the clusters indicated by triangles are in a state straddling up and down, and data that are originally different clusters are clustered as the same cluster. Separately, the data is classified into a cluster indicated by a black circle and a cluster indicated by a square, and originally the same cluster is classified into different clusters.

8 and 9 do not particularly indicate what data is to be clustered. For example, each data indicated by a circle at the left end of FIGS. 8 and 9 is data of a face image. Assuming that personal authentication is possible using the face image. For example, among the data indicated by the circles at the left end of FIGS. 8 and 9, the data distributed in the upper [u] shape is various face images taken of Mr. A, and the lower [n] ] Suppose that the data distributed in a letter shape are various face images taken of Mr. B. At this time, when Mr. A and Mr. B are identified from the image data, it is only necessary to perform clustering as shown in FIG. 8, but when clustering is performed as shown in FIG. It cannot be identified and a personal authentication error occurs. The fact that there are multiple face images of a person can be attributed to various factors such as changes due to changes in facial expressions of one person, changes due to shooting conditions such as lighting, etc. Clustering is required.
The description here shows the principle of clustering, and in the case of an actual face image, it is data of a higher number of dimensions different from the two-dimensional data as shown in FIGS. Probability is high.

As image authentication for personal authentication, in addition to facial images, various types of authentication that are made by imaging fingerprints, irises, blood vessels, etc. have been proposed and are being put into practical use. Accurate clustering of a large number of images is very important for accurate authentication. In addition to images, for example, even when performing personal authentication from speech, it is possible to perform personal authentication by clustering the frequency characteristics of the input speech. In such cases, the principle of clustering is also the case where clustering is performed. The same. Further, the same applies when authentication is performed using handwriting.
In the conventional clustering method using the self-organizing map, as described above, appropriate clustering is not necessarily performed, and there is a problem that the reliability of the clustering result is not high. For example, taking a face image as an example, even if there is a change in facial expression, in order to accurately determine whether or not they are the same person, very high-level clustering is required. It wasn't.

  The present invention has been made in view of such a point, and an object thereof is to perform data clustering based on a self-organizing map with higher accuracy.

  The present invention provides a code vector setting process for setting a code vector on a coordinate axis on which a plurality of data is arranged, and a code vector setting thereof, when clustering a plurality of input data based on a self-organizing map algorithm A self-organizing map process that fits the code vector set in the process to data using a self-organizing map, and a judgment that determines whether the code vector obtained by the self-organizing map process has converged to a predetermined state When it is determined that the process and the determination process have not converged, the distance between the code vectors of each code vector obtained by the self-organizing map process is compared with the set threshold value, and the distance is larger than the distance by the threshold value. Separation is performed when separation is longer, and separation is performed when the distance is shorter than the threshold. Repeat the process of obtaining the code vector by performing the self-organizing map process on the code vector clustered by the combination and the plurality of input data based on the clustering state determined to have converged to the predetermined state by the determination process Clustering.

  According to the present invention, data can be appropriately clustered by performing separation / combination based on the distance between code vectors. For example, by applying to the image data as data to be clustered, it becomes possible to accurately identify a person or object indicated by the image data. For example, when performing personal authentication from a face image indicated by image data, it is possible to accurately classify who the face is of which image data is taken. Alternatively, when the character indicated by the image data is recognized, the character recognition can be accurately performed.

Hereinafter, an embodiment of the present invention will be described with reference to FIGS. In the present invention, various data are applied to data that is classified using a self-organizing map.
FIG. 1 is a flowchart showing an example of processing according to the present embodiment, and FIG. 2 is a diagram showing an example of an apparatus configuration for performing the processing.

  The apparatus is composed of, for example, a computer apparatus and its peripheral devices, and the image capturing section 11 configured by a camera, video capture, etc. connected to the computer apparatus is used to input data by capturing the image data. The identification result based on the clustered result is displayed on the display 21. Software (program) for causing the computer device to function as an image identification device is installed. The software executes the operation process shown in the flowchart of FIG. For the operation, for example, a keyboard 17 connected to a computer device is used.

  The image data captured by the image capturing unit 11 is sent to the data processing unit 12 and is used as data for clustering under the control of the control unit 15.

  Data for clustering is stored in the data memory 13 and clustering is performed under the control of the control unit 15. When each clustered cluster is output as an identification result, it may be output as clustered data as it is. For example, whether each cluster is the same cluster as the reference image stored in the database 14. It may be determined whether or not, and various authentication processes may be performed. The recognition processing result is sent to, for example, the display control unit 18 to display the recognition result on the display 21.

Next, details of the clustering process of this example executed by the data processing apparatus configured as described above will be described.
First, the outline of the clustering process of this example will be described with reference to the flowchart of FIG. 1. When a plurality of data to be clustered are input, the plurality of data are arranged on n-dimensional (n is an integer of 2 or more) coordinate axes. A code vector is randomly generated for the data on the coordinate axes. The number of code vectors to be generated is a preset number. Alternatively, the number of code vectors may be set according to the number of input data. In the case of this example, in order to separate and combine clusters as will be described later, a value called a label is set and the label value is updated.

  When the code vector is generated, a self-organizing map process (SOM process) for fitting the generated code vector to a plurality of input data is performed (step S1). In the self-organizing map process, a code vector that satisfies a certain condition is set as a victory vector, and a process of updating the code vector is performed based on the relationship between the victory vector and its surrounding code vectors. The self-organizing map processing is a processing method that has already been performed in the past, and is processing for bringing a code vector closer to data.

Then, in the self-organizing map process, it is determined whether or not the code vector has sufficiently converged (step S2). If the code vector has converged, the code vector process is terminated, and based on the code vector label Each data is clustered (step S6), and the clustering process is terminated. Convergence here means a state in which the code vector is a vector that approximates the input data.
If the code vectors have not converged, a threshold Th is set based on the value between the current code vectors (step S3). Although the setting of the threshold Th will be described later, for example, an appropriate value is set using the maximum value and the average value of the length of the current code vector.

  When the threshold Th is set, the current distance between the respective code vectors is compared with the set threshold Th. In the comparison, when the distance is larger than the threshold Th (including the case where the distance is equal in the formula described later), the two code vectors determined at that time are separated into different clusters (step S4). Set different label values by separating into different clusters. If the distance is smaller than the threshold Th, the two code vectors determined at that time are combined into the same cluster (step S5). By binding to the same class, it has the same label value.

  Then, with respect to the code vector of each cluster subjected to the separation in step S4 and the combination in step S5, the process returns to step S1, self-organizing map processing is performed, the code vector is updated, and further input is performed. Fit the data. Thereafter, until it is determined in step S2 that the code vector has sufficiently converged, the separation / combination processing in steps S4 and S5 is repeated from the self-organizing map processing in step S1.

  In step S6, as a process of clustering each data based on the code vector label, the code vector closest to the data on the coordinate axes is determined. Then, a cluster corresponding to the label value of the code vector is set. Therefore, for example, if there are two label values, the data is clustered into two, and if there are three label values, the data is clustered into three.

  Next, examples of actual clustering are shown in FIGS. FIGS. 3 and 5 are examples of clustering by the processing of this example, and FIGS. 4 and 6 are examples of clustering by the conventional processing on the same data as FIGS.

  First, the example of FIG. 3 will be described. FIG. 3A shows a distribution of input data artificially generated on a two-dimensional coordinate axis. In this example, as can be seen from FIG. 3A, the data is divided into two groups. FIG. 3B shows a code vector randomly generated on the coordinate axis where this data is arranged. In the initial state of FIG. 3B, the code vectors are connected to one. From the state shown in FIG. 3B, a self-organizing map process is performed to update the code vector so as to approach the input data point.

  By repeating this self-organizing map process, the data is sequentially approached as shown in FIGS. 3C and 3D. In this example, the code is changed according to the distance of each code vector. Vector separation and combination processing is performed. In the example of FIG. 3D, the example is separated into two, but the separation state is still incomplete.

On the other hand, in the state at the end of the calculation when the code vector is sufficiently updated, the code vector is set in a shape that almost connects the data points on the coordinate axes as shown in FIG. ing. The code vector is divided into two corresponding to the data arrangement state.
By clustering each data based on the code vector labeled in the state shown in FIG. 3 (e), each data is accurately clustered into two as shown in FIG. 3 (f). It becomes. FIG. 3F shows a state where data is clustered into data indicated by ◯ and data indicated by X.

On the other hand, the example of FIG. 4 in which the conventional processing is performed on the same data as FIG. 3 will be described. FIG. 4A shows the distribution of input data artificially generated on a two-dimensional coordinate axis. Yes, as in FIG. FIG. 4B shows a code vector randomly generated on the coordinate axis where this data is arranged. From the state shown in FIG. 4B, the self-organizing map process is performed to update the code vector so as to approach the data point, as shown in FIGS. 4C, 4D, and 4E. In order, the data points are brought closer to each other. In this conventional process, the code vector is connected to one while the self-organizing map process is performed, and the code vector is connected to one even at the end of the repetitive calculation shown in FIG. ing.
When the code vectors shown in FIG. 4 (e) are obtained, the process of dividing the code vectors is performed according to the angle forming each code vector. As shown in FIG. 4 (f), the data is clustered into four completely different from the actual data distribution. The state of FIG. 4 (f) shows a state divided into a circle mark, a cross mark, a triangle mark, and a square mark.

  FIG. 5 is another example in which the processing of this example is performed. FIG. 5A shows a distribution of input data artificially generated on a two-dimensional coordinate axis. In this example, as can be seen from FIG. 5A, the data is divided into three groups. FIG. 5B shows a code vector randomly generated on the coordinate axis where this data is arranged. In the initial state of FIG. 5B, the code vectors are connected to one. From the state shown in FIG. 5B, the self-organizing map process is performed to update the code vector so as to approach the input data point.

By repeating this self-organizing map process, the data is sequentially approached as shown in FIGS. 5C and 5D. In this example, according to the distance between the code vectors, Vector separation and combination processing is performed. For this reason, in the state at the end of the calculation when the code vector is sufficiently updated, the code vector is set in a shape that substantially connects the data points on the coordinate axes as shown in FIG. At the same time, the code vector is divided into three corresponding to the data arrangement state.
By clustering each data based on the code vector labeled in the state shown in FIG. 5 (e), each data is accurately clustered into three as shown in FIG. 5 (f). It becomes. FIG. 3F shows a state in which data indicated by a circle, data indicated by a cross, and data indicated by a triangle are clustered.

In contrast, the example of FIG. 6 in which the conventional processing is performed on the same data as FIG. 5 will be described. FIG. 6A shows the distribution of input data artificially generated on a two-dimensional coordinate axis. Yes, as in FIG. FIG. 6B shows a code vector randomly generated on the coordinate axis on which this data is arranged. From the state shown in FIG. 6B, the self-organizing map process is performed to update the code vector so as to approach the data point, as shown in FIGS. 6C, 6D, and 6E. In order, the data points are brought closer to each other. In this conventional process, the code vector is connected to one while the self-organizing map process is performed, and the code vector is connected to one even at the end of the repetitive calculation shown in FIG. ing.
When the code vector shown in FIG. 6 (e) is obtained, the code vector is divided according to the angle forming each code vector. In this example, there is no difference in the angle that can be divided. As shown in FIG. 6 (f), the clustering state of the data obtained in a typical manner is a state that is completely different from the actual data distribution and is all classified into the same cluster.

Next, details of the algorithm of this example will be described using mathematical expressions. Here, primary self-organizing map processing is used.
[1. First, a k-dimensional code vector m ^p _l is randomly generated in the domain. The k dimension here is a dimension number indicating that it is an [n × n] dimension when the data is the number of pixels of [n × n], for example. The code vector m ^p _l represents the code vector at the p (1 ≦ p ≦ num _l ) th in the class l (1 ≦ l ≦ C _l ).
[2. The following update process of the code vector m ^p _l is repeated for t = 1, 2,..., T;
[3. The code vector m ^p _l satisfying the expression (1) is obtained.

This equation (1) is assumed to be a victory code vector for the data xj.
[4. ] The winning code vector and its surrounding code vectors are updated by equation (2).

  However, (alpha) (t) and Nc (t) are calculated | required from Formula (3) and Formula (4).

[Q] represents the maximum integer not exceeding q.
The steps so far correspond to the self-organizing map process in step S1 in the flowchart of FIG.

[5. ] 1 ₁ = 1, 2,..., C ₁ ; p = 1, 2 _,. num _l1 is the number of code vectors included in Class _{l 1.} Further, d _totai = 0 and d _cnt = 0. d _totai is the sum of the differences from the next to the code vector in the class. d _cnt is the number of code vectors in the class (that is, the number of code vectors −1).

[5.1] If m ^l1 _{p + 1} exists, the equation (5) is calculated and d _totai = d _totai + d _diff and d _cnt = d _cnt +1.

[5.2] If d _cnt ≠ 0, the threshold value Th = (d _totai / d _cnt ) + αd ^(max) _diff is set. However, d ^(max) _diff is the maximum value of d _diff . Further, as _[d totai / d _cnt], that are divided by the number of total code vector, thus seeking the average of each code vector. As described above, the threshold value Th is set by adding the value obtained by multiplying the maximum value by the coefficient α to the average of the code vectors.
[6. ] 1 ₁ = 1, 2,..., C ₁ ; p = 1, 2,..., Num ₁₁ , [5.1] is repeated.
This is the process of setting the threshold value Th in step S3.

[6.1] In comparison with the threshold value Th, if the condition of the equation (6) is satisfied, e ^l1 _p = 2 and e ^l1 _p + 1 = 1, and p + 1 to luml ₁ included in l ₁ are set. Increment the code vector label by one.

[7. _{] L 1 = 1,2, ···,} C l; l 2 = l 1 +2, ···, C l; p = 1,2, ···, mun l1; q = 1,2, ·· .. Repeat the following processing for num _l2 . However, _{mun l1} and _{num l2} is the number of code vectors respectively included in the class _{l 1} and _{l 2.}

[7.1] If e ^l1 _p = 1 or 2 and e ^l2 _p = 1 or 2, the equation (7) is calculated.

In the equation (7), if the relationship between the distance d between code vectors and the threshold Th is d <Th,
If e ^l1 _p = 1 and e ^l2 _p = 1,

age,

As a result, the order of the code vectors having the label value of l ₂ is changed. further,

Thus, the code vectors included in the classes l ₁ and l ₂ are combined, and the process proceeds to [7].
If e ^l1 _p = 2 and e ^l2 _p = 2,

age,

And further,

age,

Thus, the code vectors included in the classes l ₁ and l ₂ are combined, and the process proceeds to [7].
If e ^l1 _p = 1 and e ^l2 _p = 2

age,

And further,

age,

Thus, the code vectors included in the classes l ₁ and l ₂ are combined, and the process proceeds to [7].
If e ^l1 _p = 2 and e ^l2 _p = 1,

age,

And further,

age,

Thus, the code vectors included in the classes l ₁ and l ₂ are combined, and the process proceeds to [7].

  In the algorithm described so far, [4] is a process of updating the code vector. In [5], processing for calculating the threshold Th is performed, and in [6], code vectors are separated according to the threshold. In [7], code vectors are combined according to a threshold value.

  By performing the processing in this way, the self-organizing map processing is performed while the separation and combination shown in FIG. 3 or FIG. 5 is performed, and data can be clustered satisfactorily.

In the examples of FIGS. 3 and 5, the example in which data is arranged on two-dimensional coordinates has been described. However, more complicated data such as image data is arranged on coordinate axes having a high number of dimensions, and the arrangement is performed. A similar method can be applied when clustering data.
For example, in the case of an image in which the letter “A” is shown in the dot arrangement as shown in FIG. 7, a large number of sets of vectors are generated based on the horizontal and vertical pixel arrangement of the image, and the vector Is processed as input data, and the above-described self-organizing map processing is performed while performing separation and combination, thereby enabling accurate clustering of image data.

  The image data can be applied to a process for identifying an individual from, for example, an image obtained by photographing a face. In this case, an image obtained by photographing each individual is stored as a database, and the face image in the database is compared with the photographed image data, and the photographed image data is the same as any face image in the database. Accurate clustering is possible by clustering whether or not it belongs to a cluster. For example, even if the facial expression of the photographed face image is different from the face image in the database, or the brightness and shadowing conditions at the time of photographing are different from the face image in the database, Personal authentication is possible. When there are a plurality of images having different facial expressions and photographing conditions for each individual person as the face images to be databased, the personal authentication accuracy is further improved.

  Further, as another application example of image recognition, for example, the present invention can be applied to a case where an image obtained by photographing (inputting) a handwritten character is compared with a character pattern prepared in a database. By applying it to handwritten character recognition, the recognition rate of handwritten characters can be improved.

Furthermore, the present invention may be applied to clustering for identifying data other than face images and handwritten characters.
For example, as an image for authenticating an individual, in addition to a face, an image obtained by photographing a specific part of a body such as a fingerprint, an iris, or a blood vessel (vein) may be clustered by the method of the present invention and authenticated.
Further, the results of analyzing voice characteristics such as speech (frequency characteristics and the like) may be clustered by the method of the present invention to perform personal authentication.

  In the above-described embodiment, the data processing device for performing clustering is configured using a personal computer device, which is a general-purpose information processing device, as shown in FIG. You may make it comprise as this information processing apparatus. Alternatively, the processing according to the present invention can be configured as a device that performs the processing according to the present invention by programming the processing of the present invention and installing the program (software) in various information processing apparatuses. The program of the present invention may be downloaded via a transmission means such as the Internet, in addition to being distributed by being stored in a storage medium such as an optical disk or a semiconductor memory.

It is a flowchart which shows the process example by one embodiment of this invention. It is a block diagram which shows the structural example of the apparatus which performs the process by one embodiment of this invention. It is explanatory drawing which shows the process example (Example 1) by one embodiment of this invention. It is explanatory drawing which shows the example which performed the conventional process with respect to the same data as the example of FIG. It is explanatory drawing which shows the process example (Example 2) by one embodiment of this invention. It is explanatory drawing which shows the example which performed the conventional process with respect to the same data as the example of FIG. It is explanatory drawing which shows the example which applied the process of one embodiment of this invention with respect to image data. It is a principle figure which shows the example of the clustering based on the conventional self-organization map. It is a principle figure which shows the example of the clustering based on the conventional self-organization map.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 11 ... Image acquisition part, 12 ... Data processing part, 13 ... Data memory, 14 ... Database, 15 ... Control part, 16 ... Program memory, 17 ... Keyboard, 18 ... Display control part, 19 ... Display

Claims (6)

In a clustering method for clustering a plurality of input data based on a self-organizing map,
A code vector setting process for setting a code vector on a coordinate axis in which the plurality of data are arranged;
A self-organizing map process for fitting the code vector set in the code vector setting process to the plurality of data using a self-organizing map algorithm;
A determination process for determining whether the code vector obtained by the self-organizing map process has converged to a predetermined state;
When it is determined in the determination process that it has not converged, the distance between each code vector obtained by the self-organizing map process is compared with a set threshold value, and separated when the distance is longer than the threshold value, Separation / combination processing that combines when the distance is shorter than the threshold,
The process of performing the self-organizing map process on the code vectors clustered by the separation and combination in the separation / combination process to fit the plurality of data is repeated, and the determination process determines that the code vector has converged to a predetermined state. A clustering method comprising clustering the plurality of data based on a clustering state. In the clustering method according to claim 1,
The threshold value is a value calculated by calculation using a maximum value and an average value of distances between code vectors. In the clustering method according to claim 1,
A clustering method, wherein the plurality of input data is image data for personal identification, and an individual is specified from an image by clustering based on the self-organizing map. In the clustering method according to claim 1,
A clustering method, wherein the plurality of input data is character image data, and character recognition is performed from an image by clustering based on the self-organizing map. In a data processing apparatus that clusters a plurality of input data based on a self-organizing map,
Code vector setting means for setting a code vector on a coordinate axis in which the plurality of data are arranged;
Self-organizing map processing means for fitting the code vector set by the code vector setting means to the plurality of data using a self-organizing map algorithm;
Determining means for determining whether the code vector obtained by the processing in the self-organizing map processing means has converged to a predetermined state;
When it is determined in the determination process by the determination means that it has not converged, the distance between each code vector obtained by the self-organizing map process is compared with a set threshold value, and the distance is longer than the threshold value And separation / combination processing means for combining when the distance is shorter than the threshold,
It repeats the process of obtaining the code vector by performing the self-organizing map processing in the self-organizing map processing means on the code vectors clustered by the separation and combining in the separation / combination processing means, and the determination in the determination means A data processing apparatus that outputs a result of clustering the plurality of data based on a clustering state determined to have converged to a predetermined state by processing. In a program for implementing a process for clustering a plurality of input data based on a self-organizing map on a data processing apparatus,
A code vector setting process for setting a code vector on a coordinate axis in which the plurality of data are arranged;
A self-organizing map process for fitting the code vector set in the code vector setting process to the plurality of data using a self-organizing map algorithm;
A determination process for determining whether the code vector obtained by the self-organizing map process has converged to a predetermined state;
When it is determined that the convergence is not achieved in the determination process, the distance between the code vectors of each code vector obtained by the self-organizing map process is compared with a set threshold value, and the distance is longer than the threshold value. Separating and performing separation / combination processing to combine when the distance is shorter than the threshold,
Repeat the process of obtaining the code vector by performing the self-organizing map process on the code vectors clustered by the separation and combination in the separation / combination process, and the clustering state determined to have converged to a predetermined state in the determination process A program for executing a process of clustering the plurality of data based on the data.

Images