JP2009048575A - Clustering device, clustering method, program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a clustering device capable of reducing a lack of balance in the number of vectors included in each cluster, a clustering method, a program and a recording medium. <P>SOLUTION: A dimension degenerating means 11 converts multidimensional vector data into two-dimensional vector data, and an imaging means 12 converts the two-dimensional vector data into binary image data. An area extracting means 13 extracts an initial area composed of adjacent pixels among pixels corresponding to a two-dimensional vector out of pixels composing an image which the binary image data shows. A cluster range determining means 14 extracts two-dimensional normal distribution from the frequency distribution of pixels for every initial areas, and determines a cluster range based on the average and standard deviation of every extracted two-dimensional normal distribution. A cluster determining means 15 classifies the pixels into clusters according to an evaluation value H and whether the pixels are included in the cluster range. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a clustering device, a clustering method, a program, and a recording medium that divide a set of a plurality of elements into clusters that are subsets. More specifically, the present invention relates to a set of multidimensional vectors based on similarity between vectors. The present invention relates to a clustering apparatus, a clustering method, a program, and a recording medium that divide into clusters.

  Finding similar elements from a set of a plurality of elements and dividing the set into several subsets is called clustering. Clustering is applied to classification of a large amount of information used on the web (Web) or in a company, and a large amount of information can be divided into similar information by clustering. Clustering makes it possible to quickly find necessary information and to show similar information features as an outline of the information, so that it can be used for information retrieval.

  Clustering of a set of vectors includes hierarchical clustering and non-hierarchical clustering.

  In the hierarchical clustering, for example, when N sets are included in a set, N clusters composed of individual vectors are first formed. Next, based on the distance between the two vectors, a distance between two clusters each including each vector is calculated, and two clusters having the smallest distance between the clusters are merged into one. This merging is sequentially repeated until all the clusters are merged into one cluster to form a cluster hierarchical structure. For example, a vector can be classified into k clusters by determining the number of clusters as k and dividing the hierarchy by a hierarchy of k clusters.

  Non-hierarchical clustering is clustering that classifies vectors without using a hierarchical structure. As a typical non-hierarchical clustering, there is a k-means method (hereinafter referred to as “k-means method”). The k-means method classifies into k clusters according to the distance between vectors. The procedure of clustering by the k-means method when the number of vectors included in the set is N and the number of clusters is k is shown.

  In the procedure 1, any k vectors among the N vectors are set as initial values of vectors indicating the centers of the k clusters. In the procedure 2, the N vectors are classified into clusters having the closest cluster center vector. In procedure 3, the average of the vectors included in each cluster is set as the center of the new cluster. In step 4, step 2 and step 3 are repeated until the center of the cluster no longer changes, and the process ends when the center of the cluster no longer changes.

  In the above-described hierarchical clustering and non-hierarchical clustering by the k-means method, it is necessary to manually specify the number k of clusters.

  As an example of a conventional technique that does not require manually specifying the number of clusters k, there is an automatic document classification method. In this document automatic classification method, the number of clusters is determined so that the processing time is within an allowable time, and the document is expressed as a vector and classified according to the strength of the semantic element expressing the content of the document (for example, Patent Document 1).

Japanese Patent Laid-Open No. 10-171823

  However, in the above-described prior art example, there is a problem that even if the number of clusters can be automatically determined, the number of vectors included in each cluster may be biased. For example, hierarchical clustering is classified into a cluster including 2% of all vectors and a cluster including 40% of all vectors, depending on the number of clusters. Numbers may be biased.

  When this hierarchical clustering is used for information retrieval and the retrieval result is displayed, if there are many vectors classified into one cluster, the number of similar documents increases, and thus a desired document is found. It takes a lot of time. Or when there are few documents displayed, a desired document may not be contained in it.

  To correct this bias, use a dendrogram or tree diagram to illustrate the hierarchical structure, and manually divide clusters with a large number of vectors into lower layers, or clusters with a small number of vectors to a higher level. Need to merge in hierarchy.

  In the non-hierarchical clustering by the k-means method, the result of clustering differs depending on how the initial value of the center of the cluster is determined in step 1. For example, if the center of the initial value of a cluster is concentrated in a specific area, and the center of the initial value of one cluster is far from that area, the number of vectors contained in each cluster is biased, as in hierarchical clustering. Occurs. In order to correct this bias, it is necessary to manually correct the clustering result.

  An object of the present invention is to provide a clustering device, a clustering method, a program, and a recording medium that can reduce the deviation of the number of vectors included in each cluster.

The present invention provides an input means for inputting multidimensional vector data representing a multidimensional vector;
Dimension conversion means for converting the multidimensional vector data input by the input means into two-dimensional vector data representing a two-dimensional vector by a predetermined dimension conversion method;
Image data representing an image composed of pixels to which the two-dimensional vector data converted by the dimension conversion means is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and to which a frequency indicating the number of the corresponding two-dimensional vector is given. Imaging means for converting to
A region extracting unit that extracts a region constituted by adjacent pixels from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels represented by the image data converted by the imaging unit; ,
From the frequency distribution given to the pixels included in each region extracted by the region extraction means, a normal distribution constituting the distribution is extracted, and for each extracted normal distribution, the average of each normal distribution is centered, and Cluster range determining means for determining a range determined based on the standard deviation as a cluster range;
A clustering apparatus comprising: a cluster whose range is determined by a cluster range determination unit according to a predetermined classification condition for equalizing the number of pixels classified into clusters; and a pixel classification unit that classifies each pixel. It is.

In the present invention, the predetermined classification condition is:
If the frequency given to a pixel is a frequency that constitutes only one normal distribution, classify the pixel to which the frequency is given into a cluster corresponding to the normal distribution that the frequency constitutes,
When a part of the frequency assigned to a pixel is a frequency that forms a plurality of normal distributions, the pixel to which the frequency is assigned is selected from the normal distributions that are part of the frequency. Classify the cluster into the cluster corresponding to the normal distribution with the largest evaluation value divided by the mean,
When the frequency given to a pixel is a frequency that does not constitute any normal distribution, the evaluation value is the highest among the clusters in the range closest to the pixel to which the frequency is assigned. It is characterized by classifying into large clusters.

The present invention also includes an input step of inputting multidimensional vector data representing a multidimensional vector;
A dimension conversion step of converting the multidimensional vector data input in the input step into two-dimensional vector data representing a two-dimensional vector according to a predetermined dimension conversion condition;
Image data representing an image made up of pixels to which the two-dimensional vector data converted in the dimension conversion step is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and to which a frequency representing the number of the corresponding two-dimensional vector is given An imaging step to convert to
An area extraction step for extracting an area constituted by adjacent pixels from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted in the imaging step; ,
From the frequency distribution given to the pixels included in each region extracted in the region extraction step, a normal distribution that constitutes the distribution is extracted, and for each extracted normal distribution, the average of each normal distribution is centered, and A cluster range determining step for determining a range determined based on the standard deviation as a cluster range;
A clustering method comprising: a pixel classification step for classifying each pixel into a cluster whose range is determined in the cluster range determination step according to a predetermined classification condition for equalizing the number of pixels classified into clusters. It is.

The present invention also includes an input step of inputting multidimensional vector data representing a multidimensional vector;
A dimension conversion step of converting the multidimensional vector data input in the input step into two-dimensional vector data representing a two-dimensional vector according to a predetermined dimension conversion condition;
Image data representing an image made up of pixels to which the two-dimensional vector data converted in the dimension conversion step is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and to which a frequency representing the number of the corresponding two-dimensional vector is given. An imaging step to convert to
An area extraction step for extracting an area constituted by adjacent pixels from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted in the imaging step; ,
From the frequency distribution given to the pixels included in each region extracted in the region extraction step, a normal distribution that constitutes the distribution is extracted, and for each extracted normal distribution, the average of each normal distribution is centered, and A cluster range determining step for determining a range determined based on the standard deviation as a cluster range;
In order to cause a computer to execute a pixel classification step for classifying each pixel in a cluster whose range is determined in a cluster range determination step according to a predetermined classification condition for equalizing the number of pixels classified into clusters. It is a program.
The present invention is also a computer-readable recording medium on which the program is recorded.

  According to the present invention, multi-dimensional vector data representing a multi-dimensional vector is input by the input means, and the multi-dimensional vector data input by the input means is converted into a two-dimensional vector according to a predetermined dimensional conversion condition by the dimension conversion means. It is converted into two-dimensional vector data to be represented.

  Then, a pixel to which the two-dimensional vector data converted by the dimension converting unit is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and a frequency indicating the number of the corresponding two-dimensional vector is given by the imaging unit. Among the pixels represented by the image data converted to image data representing the image and converted by the image extraction unit by the region extraction unit, the pixel is represented by a value indicating that there is a corresponding two-dimensional vector. A region constituted by adjacent pixels is extracted.

  Further, a normal distribution constituting the distribution is extracted from the frequency distribution given to the pixels included in each region extracted by the region extracting unit by the cluster range determining unit, and for each extracted normal distribution, each normal distribution is extracted. A range centered on the average of the normal distribution and determined based on the standard deviation is determined as the cluster range, and according to a predetermined classification condition for equalizing the number of pixels classified into clusters by the pixel classification unit, Each pixel is classified into a cluster whose range is determined by the cluster range determining means.

  That is, by classifying pixels into clusters, multi-dimensional vectors corresponding to the pixels can be classified into clusters. Therefore, according to a predetermined classification condition for equalizing the number of pixels classified into clusters, the pixels are classified. By classifying into clusters, the number of vectors included in each cluster can be reduced. If the document data is expressed as multidimensional vector data and applied to the search, the document data can be searched faster.

  According to the invention, in the input step, multidimensional vector data representing a multidimensional vector is input. In the dimension conversion step, the multidimensional vector data input in the input step is converted into two-dimensional vector data representing a two-dimensional vector according to a predetermined dimension conversion condition. In the imaging step, the two-dimensional vector data converted in the dimension conversion step is represented by a pixel which is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and is given a frequency indicating the number of the corresponding two-dimensional vector. Convert to image data representing an image.

  In the region extraction step, a region constituted by adjacent pixels is extracted from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted in the imaging step. To do. In the cluster range determination step, a normal distribution constituting the distribution is extracted from the frequency distribution given to the pixels included in each region extracted in the region extraction step, and each normal distribution is extracted for each extracted normal distribution. A range centered on the average and determined based on the standard deviation is determined as the cluster range. In the pixel classification step, each pixel is classified into the cluster whose range is determined in the cluster range determination step in accordance with a predetermined classification condition for equalizing the number of pixels classified into the cluster.

  In other words, by applying the clustering method according to the present invention, it is possible to classify pixels into clusters, thereby classifying multi-dimensional vectors corresponding to pixels into clusters, so that the number of pixels classified into clusters is made uniform. By classifying pixels into clusters in accordance with predetermined classification conditions for performing the above, it is possible to further reduce the bias of the number of vectors included in each cluster. If the document data is expressed as multidimensional vector data and applied to the search, the document data can be searched faster.

According to the present invention, an input step for inputting multidimensional vector data representing a multidimensional vector;
A dimension conversion step of converting the multidimensional vector data input in the input step into two-dimensional vector data representing a two-dimensional vector according to a predetermined dimension conversion condition;
Image data representing an image made up of pixels to which the two-dimensional vector data converted in the dimension conversion step is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and to which a frequency representing the number of the corresponding two-dimensional vector is given. An imaging step to convert to
An area extraction step for extracting an area constituted by adjacent pixels from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted in the imaging step; ,
From the frequency distribution given to the pixels included in each region extracted in the region extraction step, a normal distribution that constitutes the distribution is extracted, and for each extracted normal distribution, the average of each normal distribution is centered, and A cluster range determining step for determining a range determined based on the standard deviation as a cluster range;
A program for causing a computer to execute a pixel classification step for classifying each pixel into a cluster whose range is determined in a cluster range determination step according to a predetermined classification condition for equalizing the number of pixels classified into clusters. Can be offered as.

  The present invention can also be provided as a computer-readable recording medium on which the program is recorded.

  FIG. 1 is a block diagram showing a functional configuration of a clustering automation apparatus 1 according to an embodiment of the present invention. The clustering method according to the present invention is processed by the clustering automation apparatus 1.

  A clustering automation apparatus 1 which is a clustering apparatus includes a multidimensional vector data input means (hereinafter referred to as input means) 10, a dimension reduction means 11, an imaging means 12, a region extraction means 13, a cluster range determination means 14 and a cluster determination means 15. It is comprised including.

  The clustering automation apparatus 1 is configured by a computer, for example. The computer constituting the clustering automation apparatus 1 receives information via an input device such as a keyboard and a mouse, an output device including a display device such as a display or a printing device such as a printer, and a communication line such as a LAN (Local Area Network). A communication device that transmits and receives, a semiconductor memory or a hard disk device, a storage device that stores programs and data, and a central point that controls the input device, the output device, and the communication device by executing a program stored in the storage device And a processing device (Central Processing Unit: hereinafter referred to as “CPU”). The program is a program for controlling the clustering automation apparatus 1 and may include an OS (Operating System) and an application program. The computer may be a generally known computer and will not be described in detail.

  The input means 10 reads out the multidimensional vector data stored in the multidimensional vector data storage device 2 and inputs it to the clustering automation device 1. Multidimensional vector data is data representing a multidimensional vector. A multidimensional vector represents, for example, document data as a multidimensional vector depending on its contents.

  The multidimensional vector data storage device 2 is a storage device connected to a communication line such as a LAN, and information stored in the multidimensional vector data storage device 2 can be read out by a communication device included in a computer. In the configuration shown in FIG. 1, the multidimensional vector data storage device 2 is configured as an independent device different from the clustering automation device 1, but the multidimensional vector data storage device 2 may be included in the clustering automation device 1. .

The dimension reduction means 11 which is a dimension conversion means converts the multidimensional vector data input by the input means 10 into two-dimensional vector data representing a two-dimensional vector by a predetermined dimension conversion method. The predetermined dimension conversion method is, for example, a multi-dimensional scale construction method (Multi-
Dimensional Scaling (hereinafter abbreviated as “MDS”).

  MDS is classified into a metric multidimensional scaling method (Metric MDS: hereinafter referred to as “metric MDS”) and a non-metric multidimensional scaling method (hereinafter referred to as “non-metric MDS”). The metric MDS is a method of spatially arranging objects based on the distance data between the objects, and the non-metric MDS is a method for spatially locating the objects based on the distance data between the objects or dissimilarity data corresponding to the distance data. (See, for example, Yasuyuki Saitoh, Hiroshi Sukuhisa, “Analysis Method of Related Data”, first edition, Kyoritsu Publishing Co., Ltd., September 10, 2006, p37-p123).

  In both methods of the metric MDS and the non-metric MDS, the distance relationship between the vectors, that is, the similarity relationship is maintained as much as possible by reducing the number of dimensions of the space in which the object is placed than the number of dimensions of the object. The dimension can be reduced. For the distance, for example, the Euclidean distance may be used. As a method for reducing the dimension, besides MDS, other methods for reducing the dimension to a lower-dimensional vector while maintaining the distance relationship between the multi-dimensional vectors indicated by the multi-dimensional vector data as much as possible, Component analysis may be used.

  FIG. 2 is a diagram showing an example of the XY coordinate system 21 indicating the position of the two-dimensional vector converted by the dimension reduction means 11. The position of the two-dimensional vector indicated by the two-dimensional vector data is represented by coordinates (x, y) in the XY coordinates. The position of “x” indicates the position of the tip of each two-dimensional vector when the start point is the coordinate (0, 0).

  The imaging means 12 converts the two-dimensional vector data converted by the dimension reduction means 11 into binary image data. The binary image data is data representing an image composed of pixels having a value of either “0” or “1”. The imaging unit 12 converts the two-dimensional vector data into binary image data according to the following procedure.

  In the procedure 1, when the position in the XY coordinates of the two-dimensional vector indicated by the two-dimensional vector data is the coordinates (x, y), the maximum value Xmax of x, the maximum value Ymax of y, the minimum value Xmin of x, and the value of y The minimum value Ymin is obtained, and the x range Lx = Xmax−Xmin and the y range Ly = Ymax−Ymin are obtained.

  In the procedure 2, when the resolution of the image indicated by the binary image data is m × n, m and n are natural numbers, and the number of two-dimensional vectors indicated by the two-dimensional vector data is N, the minimum satisfying the conditions 1 and 2 Find m and n. Condition 1 is m: n = (Lx + 1) :( Ly + 1), and Condition 2 is m × n ≧ N. By satisfying Condition 1 and Condition 2, the two-dimensional vector data can be converted into binary image data while maintaining the distance relationship between the two-dimensional vectors indicated by the two-dimensional vector data, that is, the similarity relationship as much as possible. .

  In the procedure 3, when the position of the pixel in the XY coordinates is the coordinate (X, Y), the two-dimensional vector data is represented by the conversion formulas X = x × m / (Lx + 1) and Y = y × n / (Ly + 1). The coordinates (x, y) of the two-dimensional vector are converted into the coordinates (X, Y) of the pixels. After conversion, the value of the pixel at the coordinate where the two-dimensional vector is converted is “1”, and the value of the pixel not at the coordinate where the two-dimensional vector is converted is “0”.

  By the procedures 1 to 3, the two-dimensional vector data can be converted into the binary image data while maintaining the distance relationship between the two-dimensional vectors indicated by the two-dimensional vector data, that is, the similarity relationship as much as possible.

  FIG. 3 is a diagram illustrating an example of the image 22 converted by the imaging unit 12. Each rectangle of each square represents one pixel 221, a white rectangle is a pixel having a pixel value of “0”, and a hatched rectangle is a pixel having a pixel value of “1”.

  FIG. 4 is a diagram illustrating an example of the data structure 31 of the pixel converted by the imaging unit 12. Each pixel is represented by a data structure of a structure type array G [i] [j] where i and j are natural numbers. Each G [i] [j] is a pixel value, cluster information, status information, and frequency. including. The frequency is the number of two-dimensional vectors having the same pixel coordinates (X, Y) for each pixel when the two-dimensional vector data is converted into binary image data, and is also referred to as “distribution frequency”. . For example, if the number of two-dimensional vectors converted to a pixel whose pixel position is the coordinate (1, 1) is four, the frequency of the pixel is “4”. The cluster information and status information will be described later.

  In the data structure 31 shown in FIG. 4, the pixel value of the pixel G [1] [1] is “1”, status information to be described later is “unprocessed”, and the frequency is “4”. Similarly, the pixel value of the pixel G [2] [1] is “1”, the status information is “unprocessed”, and the frequency is “5”. The pixel value of the pixel G [3] [1] is “1”, the status information is “unprocessed”, and the frequency is “7”. The pixel value of the pixel G [m] [n] is “0”, the status information is “unprocessed”, and the frequency is “0”.

  FIG. 5 is a diagram showing an example of an image 23 in which the initial area extracted by the area extracting unit 13 is shown. The area extraction unit 13 sets adjacent pixels as one area from among the pixels constituting the image indicated by the binary image data converted by the imaging unit 12 among the pixels having the pixel value “1”. Extraction is performed, and the extracted area is set as an initial area. Adjacent means that the pixels are adjacent in the X-axis direction, that is, the width direction of the mesh shown in FIG. 5, or in the Y-axis direction, that is, the height direction of the mesh shown in FIG. In the image 23 shown in FIG. 5, four initial regions 23 a to 23 d are shown. The initial region 23a is composed of four pixels, the initial region 23b is composed of one pixel, the initial region 23c is composed of three pixels, and the initial region 23d is composed of two pixels.

  FIG. 6 is a diagram illustrating an example of the pixel data structure 32 after the region extraction processing by the region extraction unit 13. The cluster information is a number for identifying the initial area. The status information is information indicating the state of the pixel used when extracting the initial region. “Unprocessed” indicates that it has not been extracted as any initial region, and “Processed” has already been selected. Indicates that it has been extracted as the initial region.

  In the data structure 32 shown in FIG. 6, the cluster information of the pixel G [1] [1] is “1”, the status information is “processed”, and the frequency is “4”. Similarly, the cluster information of the pixel G [2] [1] is “1”, the status information is “processed”, and the frequency is “5”. The cluster information of the pixel G [3] [1] is “1”, the status information is “processed”, and the frequency is “7”. The cluster information of the pixel G [m] [n] is “k”, the status information is “processed”, and the frequency is “2”.

  The cluster range determining unit 14 determines the cluster range based on the frequency distribution of the pixels included in each initial region extracted by the region extracting unit 13. That is, the dimension reduction means 11 and the imaging means 102 set adjacent pixels as an initial area, thereby making data with high similarity into one area, and the cluster range determination means 14 performs clustering based on the frequency distribution. By determining the range, data having higher similarity are aggregated into one cluster.

  The frequency distribution of the pixels included in each initial region extracted by the region extracting unit 13 can be regarded as a two-dimensional mixed normal distribution in which a plurality of two-dimensional normal distributions that are normal distributions are mixed. That is, it is assumed that the frequency distribution of the pixels constituting each initial region is a two-dimensional mixed normal distribution in which a plurality of peaks are formed, and each of the plurality of peaks is a two-dimensional normal distribution. A two-dimensional normal distribution constituting a two-dimensional mixed normal distribution can be extracted.

As a method for extracting a two-dimensional normal distribution from a two-dimensional mixed normal distribution, for example, EM (
There is a method using the Expectation Maximization algorithm. The EM algorithm repeats an E step (Expectation Step) for obtaining the expected value of likelihood and an M step (Maximization Step) for maximizing the expected value of likelihood, thereby including observation data containing uncertain information. (See, for example, Shotaro Ako, “Geometry of the EM Algorithm”, Information Processing Vol. 37, No. 1, 1996).

  The cluster range determining means 14 extracts a two-dimensional normal distribution from the two-dimensional mixed normal distribution in the following procedure. An example of the procedure using the EM algorithm is shown assuming that the distribution of each initial region is a two-dimensional mixed normal distribution and each mountain of each initial region is one two-dimensional normal distribution.

  In the procedure 1, a two-dimensional normal distribution is extracted using the EM algorithm for the frequency distribution of each initial region c. Here, c is a natural number of 1 to U, and U is the number of initial regions. In step 2, for each two-dimensional normal distribution extracted for each initial region c, the average xct in the X-axis direction, the average yct in the Y-axis direction, the standard deviation σxct in the X-axis direction, and the standard deviation σyct in the Y-axis direction are calculated. calculate. Here, t is a natural number of 1 to R, and R is the number of two-dimensional normal distributions extracted in the initial region.

  In the procedure 3, the range in the ellipse having the coordinates (xct, yct) as the center, the radius in the X-axis direction as p × σxct, and the radius in the Y-axis direction as q × σyct is determined as the cluster range. Here, p and q are positive real numbers of “3” or less, and a desired cluster range can be obtained by changing p and q. For example, when considering a normal distribution in the X-axis direction, if p = 1, 68.3% of pixels can be included in the cluster range. Furthermore, if p = 2, 95.4% of pixels can be included, and if p = 3, 99.7% of pixels can be included.

  FIG. 7 is a diagram illustrating an example of the two-dimensional normal distribution 24 extracted by the cluster range determining unit 14. The two-dimensional normal distribution 24 is a two-dimensional normal distribution on the straight line 241 of Y = X + a, and the height indicates the frequency 242 of each pixel.

  FIG. 8 is a diagram illustrating an example of the two-dimensional normal distribution 25 extracted by the cluster range determining unit 14. The two-dimensional normal distribution 25 is a two-dimensional normal distribution in the X-axis direction. The range 251 is a range in the X-axis direction of the cluster, and the length of the range 251 corresponds to the diameter in the X-axis direction of an ellipse whose radius in the X-axis direction is p × σxct.

  FIG. 9 is a diagram illustrating an example of the pixel data structure 33 after the cluster range determination processing by the cluster range determination unit 14. After the cluster range is determined by the cluster range determining unit 14, the cluster information is a number for identifying the cluster, and indicates the number of the cluster in the cluster range in which each pixel is included.

  In the data structure 33 shown in FIG. 9, the cluster information of the pixel G [1] [1] is “1”, the cluster information of the pixel G [2] [1] is “1” and “2”, The cluster information of the pixel G [3] [1] is “2”, and the cluster information of the pixel G [m] [n] is “k ′”. The pixel G [2] [1] is in the cluster range where the cluster information is “1” and the cluster range where the cluster information is “2”. The status information and the frequency are the same as those in the data structure 32 shown in FIG. 6, and a description thereof is omitted to avoid duplication.

  The cluster determining unit 15 classifies the pixels into clusters according to the following procedure depending on whether or not the pixel is within the cluster range determined by the cluster range determining unit 14. In step 1, the cluster information of each pixel is checked. If there is only one cluster number, that is, if the frequency of a pixel is a frequency that constitutes only one normal distribution, the cluster information indicates that pixel. Classify into numbered clusters.

  In step 2, if the cluster information of the pixel does not have a cluster number, that is, if the frequency of the pixel is a frequency that does not constitute any normal distribution, the cluster within the cluster range closest to the pixel is selected. Classify. When there are a plurality of clusters having the closest distance, the clusters having the largest evaluation value H are classified from the plurality of clusters having the closest distance. The evaluation value H is the average of the standard deviation in the X-axis direction and the standard deviation in the Y-axis direction of the secondary normal distribution corresponding to each cluster, and the average in the X-axis direction and the average in the Y-axis direction of each secondary normal distribution. And is calculated by the equation H = ((σxct + σyct) / 2) / ((xct + yct) / 2) = (σxct + σyct) / (xct + yct). Here, xct is an average in the X-axis direction, yct is an average in the Y-axis direction, σxct is a standard deviation in the X-axis direction, and σyct is a standard deviation in the Y-axis direction.

  In the procedure 3, when there are a plurality of cluster numbers in the pixel cluster information, that is, when a part of the frequency of the pixel is a frequency constituting a plurality of normal distributions, the evaluation value of the plurality of clusters is determined. Classify pixels into clusters where H is maximum.

  FIG. 10 is a diagram illustrating an example of an image 26 in which pixels are classified into clusters by the cluster determination unit 15. In the image 26, three clusters 26a to 26c are shown.

  Since the cluster determination unit 15 classifies the pixels using the evaluation value H, a normal distribution cluster having a smaller frequency and a larger variance is used for pixels that do not fall within any cluster range and pixels that fall within a plurality of cluster ranges. Can be classified. That is, by classifying pixels into clusters, multidimensional vectors corresponding to pixels can be classified into clusters, so the number of vectors classified into clusters of normal distribution with a lower peak height and wider spread The number of vectors in each cluster can be further reduced.

  In this way, multidimensional vector data representing a multidimensional vector is input by the input means 10, and the multidimensional vector data input by the input means 10 by the dimension reduction means 11 is converted into a two-dimensional vector according to a predetermined dimension conversion condition. Is converted into two-dimensional vector data.

  Then, the imaging unit 12 represents the two-dimensional vector data converted by the dimension reduction unit 11 with a value indicating the presence or absence of the corresponding two-dimensional vector, and a frequency indicating the number of the corresponding two-dimensional vectors is given. The pixel data is converted into image data representing an image composed of pixels, and is represented by a value indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted by the image extraction unit 12 by the region extraction unit 13. An initial region composed of adjacent pixels is extracted from the pixels.

  Further, a normal distribution constituting the distribution is extracted from the distribution of frequencies given to the pixels included in each initial region extracted by the region extracting unit 13 by the cluster range determining unit 14, and each extracted normal distribution is extracted. In addition, a range centered on the average of each normal distribution and determined based on the standard deviation is determined as a cluster range, and the cluster determining unit 15 determines in advance the number of pixels classified into clusters. According to the classification condition, each pixel is classified into a cluster whose range has been determined by the cluster range determination means 14.

  That is, by classifying pixels into clusters, multi-dimensional vectors corresponding to the pixels can be classified into clusters. Therefore, according to a predetermined classification condition for equalizing the number of pixels classified into clusters, the pixels are classified. By classifying into clusters, the number of vectors included in each cluster can be reduced. If the document data is expressed as multidimensional vector data and applied to the search, the document data can be searched faster.

  Furthermore, when the predetermined classification condition is that the frequency given to a pixel is a frequency that constitutes only one normal distribution, the pixel to which the frequency is given is assigned to a cluster corresponding to the normal distribution that the frequency constitutes. If the frequency that is classified and a part of the frequency given to the pixel constitutes a plurality of normal distributions, the pixel to which the frequency is given is out of the plurality of normal distributions that constitute a part of the frequency, If the standard distribution of the normal distribution is divided into clusters corresponding to the normal distribution with the largest evaluation value divided by the average, and the frequency assigned to the pixel is a frequency that does not constitute any normal distribution, that frequency is assigned. Is classified into the cluster having the largest evaluation value among the clusters in the range closest to the pixel to which the frequency is given.

  Therefore, by using the evaluation value obtained by dividing the standard deviation of the normal distribution by the average, the frequency pixels that do not constitute the normal distribution and the frequency pixels that constitute the plurality of normal distributions are classified into clusters with less frequency and greater variance. Thus, the deviation of the number of pixels, that is, the number of vectors included in each cluster can be further reduced.

  FIG. 11 is a flowchart showing the processing procedure of the imaging process executed by the imaging unit 12. After the multidimensional vector data is converted into two-dimensional vector data by the dimension reduction means 11, the process proceeds to step A1.

  In step A1, when the position in the XY coordinates of the two-dimensional vector indicated by the two-dimensional vector data is the coordinate (x, y), the maximum value Xmax of x, the maximum value Ymax of y, the minimum value Xmin of x, and the value of y From the minimum value Ymin, an x range Lx = Xmax−Xmin and a y range Ly = Ymax−Ymin are obtained. In step A2, the minimum m and n satisfying the conditions 1 and 2 are obtained when the resolution of the image indicated by the binary image data is m × n and the number of document data, that is, the number of two-dimensional vectors is N. Condition 1 is m: n = (Lx + 1) :( Ly + 1), and Condition 2 is m × n ≧ N. Here, m and n are natural numbers.

  In step A3, coordinates (x, y) indicating the position of the two-dimensional vector indicated by the two-dimensional vector data are expressed as 2 by the formula X = x × m / (Lx + 1) and the formula Y = y × n / (Ly + 1). Conversion is made to the coordinates (X, Y) of the pixel on the image indicated by the value image data. After conversion, the pixel value corresponding to the two-dimensional vector indicated by the two-dimensional vector data is “1”, and the pixel value not corresponding to the two-dimensional vector indicated by the two-dimensional vector data is “0”. The process ends. Steps A1 to A3 are imaging steps.

  FIG. 12 is a flowchart showing a processing procedure of region extraction processing executed by the region extraction means 13. When the imaging unit 12 finishes the imaging process shown in FIG. 11, the process proceeds to step B1.

  In step B1, for each pixel G [i] [j], the pixel value is set to “0” or “1” based on the result of the imaging process by the imaging unit 12, and “unprocessed” is set with the status information as an initial value. As an initial value of coordinates (i, j), that is, the structure type array G [i] [j], i = 1 and j = 1. In step B2, pixels are sequentially checked with i = i + 1 and j = 1. However, this process is passed when i = 1 and j = 1.

  In step B3, it is determined whether i = m + 1. If i = m + 1, the process proceeds to step B11. If i = m + 1 is not satisfied, the process proceeds to step B4. In step B4, it is determined whether or not the status information is “unprocessed”. If the status information is unprocessed, the process proceeds to step B5. If the status information is not processed, the process returns to step B2. In step B5, the status information is set to “processed”. In Step B6, it is determined whether or not the pixel value is “1”. If the pixel value is “1”, the process proceeds to step B7. If the pixel value is not “1”, the process returns to step B2.

  In step B7, it is examined whether or not the pixel value of the pixel adjacent to the pixel at coordinates (i, j) is “1” sequentially. In step B8, it is determined whether there is an adjacent pixel having a pixel value “1” and status information “unprocessed”. If there is an adjacent pixel whose pixel value is “1” and status information is “unprocessed”, the process proceeds to step B9, where the adjacent pixel has a pixel value of “1” and status information is “unprocessed”. If there is nothing, the process proceeds to step B13.

  In step B9, the pixel moves to the adjacent pixel. That is, the coordinates (i, j) are set to the coordinates of the adjacent pixels. In step B10, the status information of the moved pixel is set to “processed”, and the process returns to step B7. In step B11, i = 1 and j = j + 1. In step B12, it is determined whether j = n + 1. If j = n + 1, the region extraction process is terminated. If j = n + 1 is not satisfied, the process returns to step B2.

  In step B13, it is determined whether or not four adjacent directions have been checked. If the adjacent four directions are checked, the process proceeds to step B14. If the adjacent four directions are not checked, the process returns to step B7. In step B14, it is determined whether or not it is the first movement source. If it is the first movement source, the process proceeds to step B16, and if it is not the first movement source, the process proceeds to step B15. For example, when moving to an adjacent pixel in step B9, the coordinates (i, j) of the pixel before the movement are sequentially stored in step B9, and the coordinates before the first movement are determined in step B14. It is determined whether or not the same.

  In step B15, the process returns to the previous pixel of the movement source. That is, the pixel coordinate is returned to the coordinate (i, j) of the pixel before the movement that was moved one before. In step B16, an adjacent pixel whose pixel value is “1” is determined as one initial region, and the process returns to step B2. Steps B1 to B16 are region extraction steps.

  FIG. 13 is a flowchart showing a processing procedure of cluster range determination processing executed by the cluster range determination means 14. When the area extracting unit 13 finishes the area extracting process shown in FIG. 12, the process proceeds to step C1.

  In step C1, for each initial region c, a two-dimensional normal distribution constituting the distribution is obtained from the two-dimensional mixed normal distribution of each initial region using the EM algorithm. Here, c is a natural number of 1 to U, and U is the number of initial regions. In step C2, the average xct and yct of each two-dimensional normal distribution obtained for each initial region c and the standard deviations σxct and σyct are obtained. Here, t is a natural number of 1 to R, and R is the number of two-dimensional normal distributions obtained from each two-dimensional mixed normal distribution.

  In step C3, the cluster range determination process is terminated with the ellipse range having the radius p × σxct in the X-axis direction centered on the point (xct, yct) and the radius p × σyct in the Y-axis direction as the cluster range. Steps C1 to C3 are cluster range determination steps.

  FIG. 14 is a flowchart showing a processing procedure of cluster determination processing executed by the cluster determination means 15. When the cluster range determining means 14 finishes the cluster range determining process shown in FIG. 13, the process proceeds to step D1.

  In step D1, it is determined whether there is one corresponding cluster. If there is only one cluster number in the cluster information, it is determined that there is only one corresponding cluster, and the process proceeds to step D6. If there is not only one cluster number in the cluster information, it is determined that there is not one corresponding cluster, and the process proceeds to step D2. In step D2, it is determined whether or not there is a corresponding cluster. If there is no cluster number in the cluster information, it is determined that there is no corresponding cluster, and the process proceeds to step D3. If there is a cluster number in the cluster information, it is determined that there is a corresponding cluster, and the process proceeds to step D7.

  In step D3, it is determined whether or not there is one shortest distance cluster. If there is one shortest distance cluster, the process proceeds to step D6, and if there is not one shortest distance cluster, the process proceeds to step D4. In step D4, the pixel is classified into a cluster having the largest evaluation value H among a plurality of shortest distance clusters. The evaluation value H is calculated by the equation H = (σxct + σyct) / (xct + yct). Here, xct is an average in the X-axis direction, yct is an average in the Y-axis direction, σxct is a standard deviation in the X-axis direction, and σyct is a standard deviation in the Y-axis direction.

  In step D5, it is determined whether or not all the pixels have been classified. When all the pixels are classified, the cluster determination process is terminated. When all the pixels are not classified, the process returns to step D1 to process the next pixel. In step D6, the pixel is classified into the cluster, and the process proceeds to step D5. In step D7, the pixel is classified into a cluster having the largest evaluation value H among the corresponding clusters, and the process proceeds to step D5. Steps D1 to D7 are pixel classification steps.

By classifying pixels into clusters, multidimensional vectors corresponding to the pixels can be classified into clusters. Since the pixels are classified using the evaluation value H, the pixels that do not fall within any cluster range and the pixels that fall within a plurality of cluster ranges can be classified into normal distribution clusters with smaller frequency and greater variance. . Therefore, it is possible to increase the number of vectors classified into clusters of normal distribution having a lower peak height and wider spread, and it is possible to further reduce the bias in the number of vectors of each cluster.
Thus, in the step processed by the input means 10, multidimensional vector data representing a multidimensional vector is input. In the step processed by the dimension reduction means 11, the multidimensional vector data input in the step processed by the input means 10 is converted into two-dimensional vector data representing a two-dimensional vector according to a predetermined dimension conversion condition.

  In step A1 to step A3 of the flowchart shown in FIG. 11, the two-dimensional vector data converted in the step processed by the dimension reduction means 11 is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and corresponds. Conversion into image data representing an image composed of pixels to which a frequency representing the number of two-dimensional vectors is given. Steps B1 to B16 in the flowchart shown in FIG. 12 are values indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted in steps A1 to A3 in the flowchart shown in FIG. A region constituted by adjacent pixels is extracted from the represented pixels.

  In Step C1 to Step C3 of the flowchart shown in FIG. 13, the distribution is configured from the distribution of the frequencies given to the pixels included in each region extracted in Step B1 to Step B16 of the flowchart shown in FIG. A normal distribution is extracted, and for each extracted normal distribution, a range determined based on the average of each normal distribution and based on the standard deviation is determined as a cluster range. Then, in steps D1 to D7 of the flowchart shown in FIG. 14, the range is set in steps C1 to C3 of the flowchart shown in FIG. 13 according to a predetermined classification condition for equalizing the number of pixels classified into clusters. Each pixel is classified into the cluster in which is determined.

  In other words, by applying the clustering method according to the present invention, it is possible to classify pixels into clusters, thereby classifying multi-dimensional vectors corresponding to pixels into clusters, so that the number of pixels classified into clusters is made uniform. By classifying pixels into clusters in accordance with predetermined classification conditions for performing the above, it is possible to further reduce the bias of the number of vectors included in each cluster. If the document data is expressed as multidimensional vector data and applied to the search, the document data can be searched faster.

  The program for controlling the clustering automation apparatus 1 is also a program for causing a computer to execute each step of the clustering method according to the present invention. Therefore, the present invention can be provided as a program for causing a computer to execute each step of the clustering method.

  In the above-described embodiment, the program is stored in a storage device of a computer such as a semiconductor memory or a hard disk device. However, the program is not limited to these storage devices, and a computer-readable recording medium. May be recorded. The recording medium may be a recording medium that can be read by providing a program reading device as an external storage device (not shown) and inserting the recording medium therein, or may be a storage device of another device. .

  Any recording medium may be used as long as the stored program is accessed from a computer and executed. Alternatively, any recording medium may be configured such that the program is read, the read program is stored in the program storage area of the storage device, and the program is executed. Further, it may be downloaded from another device via a communication network and stored in the program storage area. The download program is stored in advance in a storage device of a computer, or installed in a program storage area from another recording medium.

The recording medium configured to be separable from the main body is, for example, a tape-based recording medium such as a magnetic tape / cassette tape, a magnetic disk such as a flexible disk / hard disk, or a CD-ROM (Compact Disk Read Only Memory) / MO (Magneto Optical). disk) / MD (Mini Disc) / DVD (Digital Versatile Disk) and other optical disk recording media, IC (Integrated Circuit) cards (including memory cards) / optical cards and other card recording media, or masks ROM / EPROM (Erasable Programmable Read Only Memory) / EEPROM (Electrically Erasable Programmable Read Only)
Memory) / a recording medium that carries a fixed program including a semiconductor memory such as a flash ROM. Therefore, the present invention can be provided as a computer-readable recording medium recording a program for causing a computer to execute each step of the clustering method.

It is a block diagram which shows the structure of the function of the clustering automation apparatus 1 which is one Embodiment of this invention. It is a figure which shows an example of the XY coordinate system 21 which shows the position of the two-dimensional vector converted by the dimension reduction means 11. FIG. It is a figure which shows an example of the image 22 converted by the imaging means. It is a figure which shows an example of the data structure 31 of the pixel converted by the imaging means. It is a figure which shows an example of the image 23 in which the initial area | region extracted by the area | region extraction means 13 was shown. It is a figure which shows an example of the data structure 32 of the pixel after the area | region extraction process by the area | region extraction means 13. FIG. It is a figure which shows an example of the two-dimensional normal distribution 24 extracted by the cluster range determination means. It is a figure which shows an example of the two-dimensional normal distribution 25 extracted by the cluster range determination means. It is a figure which shows an example of the data structure 33 of the pixel after the cluster range determination process by the cluster range determination means. It is a figure which shows an example of the image 26 by which the cluster determination means 15 classified the pixel into the cluster. It is a flowchart which shows the process sequence of the imaging process which the imaging means 12 performs. It is a flowchart which shows the process sequence of the area | region extraction process which the area | region extraction means 13 performs. It is a flowchart which shows the process sequence of the cluster range determination process which the cluster range determination means 14 performs. It is a flowchart which shows the process sequence of the cluster determination process which the cluster determination means 15 performs.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Clustering automation apparatus 10 Multidimensional vector data input means 11 Dimension reduction means 12 Imaging means 13 Area extraction means 14 Cluster range determination means 15 Cluster determination means 16 Multidimensional vector data storage means

Claims (5)

Input means for inputting multidimensional vector data representing a multidimensional vector;
Dimension conversion means for converting the multidimensional vector data input by the input means into two-dimensional vector data representing a two-dimensional vector by a predetermined dimension conversion method;
Image data representing an image composed of pixels to which the two-dimensional vector data converted by the dimension conversion means is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and to which a frequency indicating the number of the corresponding two-dimensional vector is given. Imaging means for converting to
A region extracting unit that extracts a region constituted by adjacent pixels from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels represented by the image data converted by the imaging unit; ,
From the frequency distribution given to the pixels included in each region extracted by the region extraction means, a normal distribution constituting the distribution is extracted, and for each extracted normal distribution, the average of each normal distribution is centered, and Cluster range determining means for determining a range determined based on the standard deviation as a cluster range;
A clustering apparatus comprising: a cluster whose range is determined by a cluster range determination unit according to a predetermined classification condition for equalizing the number of pixels classified into clusters; and a pixel classification unit that classifies each pixel. . The predetermined classification conditions are:
If the frequency given to a pixel is a frequency that constitutes only one normal distribution, classify the pixel to which the frequency is given into a cluster corresponding to the normal distribution that the frequency constitutes,
When a part of the frequency assigned to a pixel is a frequency that forms a plurality of normal distributions, the pixel to which the frequency is assigned is selected from the normal distributions that are part of the frequency. Classify the cluster into the cluster corresponding to the normal distribution with the largest evaluation value divided by the mean,
When the frequency given to a pixel is a frequency that does not constitute any normal distribution, the evaluation value is the highest among the clusters in the range closest to the pixel to which the frequency is assigned. The clustering apparatus according to claim 1, wherein the clustering apparatus is classified into large clusters. An input step for inputting multidimensional vector data representing the multidimensional vector;
A dimension conversion step of converting the multidimensional vector data input in the input step into two-dimensional vector data representing a two-dimensional vector according to a predetermined dimension conversion condition;
Image data representing an image made up of pixels to which the two-dimensional vector data converted in the dimension conversion step is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and to which a frequency representing the number of the corresponding two-dimensional vector is given. An imaging step to convert to
An area extraction step for extracting an area constituted by adjacent pixels from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted in the imaging step; ,
From the frequency distribution given to the pixels included in each region extracted in the region extraction step, a normal distribution that constitutes the distribution is extracted, and for each extracted normal distribution, the average of each normal distribution is centered, and A cluster range determining step for determining a range determined based on the standard deviation as a cluster range;
A clustering method comprising: a pixel classification step for classifying each pixel into a cluster whose range is determined in the cluster range determination step according to a predetermined classification condition for equalizing the number of pixels classified into clusters. . An input step for inputting multidimensional vector data representing the multidimensional vector;
A dimension conversion step of converting the multidimensional vector data input in the input step into two-dimensional vector data representing a two-dimensional vector according to a predetermined dimension conversion condition;
Image data representing an image made up of pixels to which the two-dimensional vector data converted in the dimension conversion step is represented by a value indicating the presence or absence of the corresponding two-dimensional vector and to which a frequency representing the number of the corresponding two-dimensional vector is given. An imaging step to convert to
An area extraction step for extracting an area constituted by adjacent pixels from pixels represented by values indicating that there is a corresponding two-dimensional vector among the pixels indicated by the image data converted in the imaging step; ,
From the frequency distribution given to the pixels included in each region extracted in the region extraction step, a normal distribution that constitutes the distribution is extracted, and for each extracted normal distribution, the average of each normal distribution is centered, and A cluster range determining step for determining a range determined based on the standard deviation as a cluster range;
In order to cause a computer to execute a pixel classification step for classifying each pixel in a cluster whose range is determined in a cluster range determination step according to a predetermined classification condition for equalizing the number of pixels classified into clusters. program.   The computer-readable recording medium which recorded the program of Claim 4.

Images