JPH0836557A - Cluster classifying device - Google Patents

Abstract

PURPOSE:To properly classify clusters without any previous knowledge of the number, positions, distribution shape, etc., of the clusters and without depending upon processing procedures, to visually see the process and result of the processing to facilitate processing by computing and to obtain the hierarchical structure of the clusters. CONSTITUTION:The device consists of a map generation part 11 which generates a map consisting of a prototype group for input data by using linear self- structured feature mapping, a hierarchical structure generation part 12 which generates the hierarchical structure of the clusters from the map, and a labeling part 13 which classifies the input data according to the obtained map and hierarchical structure, and, the hierarchical structure generation part 12 consists of a map analysis part 121 which calculates a quantity showing the degree of integration of the clusters from the obtained map and generates a data sequence and a data sequence merging part 122 which generates the hierarchical structure of the clusters from the obtained data sequence.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a cluster classification device, and more particularly to a device for classifying a plurality of data into a plurality of clusters by grouping them into clusters according to their similarity.

[0002]

2. Description of the Related Art As a method for classifying a plurality of data into a plurality of clusters according to their similarity, there is a maximum likelihood estimation method. This method can be used when the number of clusters is known and the rough position of each cluster is known. First, assuming that the distribution of data in each cluster is, for example, a normal distribution, parameters such as mean and variance are approximately calculated. Next, the discriminant function is defined from the probability (certain distribution in this case) of certain data belonging to the cluster. Then, cluster classification is performed by assigning data to clusters according to the size of the discriminant function obtained from the parameters.

As a method in which the number of clusters is known and the shape of the distribution is not assumed, there are the K-means method and the LBG method.
This is to define an evaluation criterion for goodness of classification, optimize the evaluation criterion by sequentially repeating the operations of 1) selection of representative points of each cluster, 2) cluster classification based on the representative points, and cluster classification. Is called a non-hierarchical method.

When the number of clusters is unknown and the shape of the distribution cannot be assumed, that is, when there is no prior knowledge about the data, there is a hierarchical method. In this method, some distance is defined between data and clusters, and the data is sequentially integrated / divided based on the distance to perform cluster classification.

Further, a method has been proposed in which data is input to a self-organizing feature mapping neural network, data is assigned to elements on a two-dimensional map, and clustering is performed based on the number of data corresponding to the elements ( Xueg
ong Zhang, Yanda Li, "SELF-ORGANIZING MAP AS A NEW M
ETHOD FOR CLUSTERING AND DATA ANALYSIS ", Proceeding
s of the International Joint Conference on Neural
Networks, vol.3, pp. 2448-2451, 1993).

[0006]

As described above, most of the conventional methods for clustering data assume the number and position of clusters and the shape of distribution. However, in general, when performing cluster classification, the number of clusters and the shape of distribution are often unknown before classification. For example, when a feature vector is classified into clusters to divide an image into regions, the number of clusters and the shape of distribution are unknown before the classification.

The above-mentioned maximum likelihood estimation method and K-means method,
The LBG method is a method performed by assuming the number of clusters, positions, and the shape of distribution. In this case, the assumption may be wrong or
If the method of giving the initial value is inappropriate, the cluster is not classified even though it originally constitutes a cluster (over-integration), or what should be one cluster is classified into multiple clusters (over-division). ), The cluster is not originally classified (misclassification), and an appropriate result cannot be obtained. A method of sequentially changing the number of clusters and examining each case is disclosed in Japanese Patent Laid-Open No. 5-205058, but the classification process must be repeated for the number of clusters, which complicates the algorithm. And in that case, even if the number of clusters is correctly estimated, if the position and distribution assumptions are mistaken, misclassification will occur and proper classification cannot be performed.

The conventional hierarchical method which does not assume the number of clusters or the shape of distribution has the following problems. A-1) The result greatly changes depending on the procedure of the division / integration process and the setting of the initial state of the algorithm. A-2) Data that is not integrated (that is, not cluster-classified) may remain. A-3) It is difficult to represent the progress and results of the processing, and it is not possible to clearly determine when to end the processing, so that over-integration and over-division tend to occur.

In the method of inputting the above-mentioned data into the self-organizing feature mapping neural network, allocating the data to the elements on the two-dimensional map, and clustering from the number of data corresponding to the elements, The results can be displayed. However, although this method uses a two-dimensional map and can be displayed visually, the process of finding clusters computationally, not visually, is the result of large man-hours and complicated algorithms. Need.

Summarizing the above problems, the conditions required for the cluster classification device of the present invention are as follows. B-1) Appropriate cluster classification without over-integration or over-division can be performed without prior knowledge of the number, position, distribution shape, etc. of clusters. B-2) Cluster classification that does not depend on the processing procedure can be performed. B-3) You can visually see the progress and results of the processing,
Moreover, it is easy to process the result computationally.

Further, in the cluster classification, there is a case where the specific data should be further divided or integrated after the classification depending on its application purpose. At this time, if the hierarchical structure of the cluster is obtained, re-integration and re-division are easy. Therefore, the following B-4) is added to the above conditions B-1), B-2), and B-3). B-4) A hierarchical structure of clusters can be obtained.

The present invention has been made in view of such a situation, and its objects are the above-mentioned B-1), B-2),
The number of clusters satisfying the conditions of B-3) and B-4),
Appropriate cluster classification without over-integration or over-division can be performed without prior knowledge of position, distribution shape, etc., classification can be performed without depending on the processing procedure, and the progress and results of processing can be visually viewed. Moreover, it is easy to process the result computationally,
Another object of the present invention is to provide a cluster classification device that can obtain a hierarchical structure of clusters.

[0013]

A cluster classifying apparatus of the present invention which achieves the above object, uses a one-dimensional self-organizing feature mapping to create a map consisting of a group of prototypes for input data. , A hierarchical structure creating section for creating a hierarchical structure of the cluster from the map,
It is characterized by comprising the obtained map and a labeling section for classifying input data according to a hierarchical structure.

In this case, the hierarchical structure creating unit calculates a quantity representing the degree of cluster clustering from the obtained map and creates a data sequence, and a map analyzing unit that creates the cluster hierarchical structure from the obtained data sequence. And a data integration unit that calculates a cluster integration amount from the obtained map, and a prototype integration unit that creates a hierarchical structure of clusters. It is considered that it consists of only the prototype fusion part that creates the hierarchical structure of the cluster from the map.

[0015]

The function and operation of adopting the above configuration will be described below. First, the outline of the configuration of the present invention and its operation will be described with reference to the block diagram of FIG. 1 and FIGS. 2 to 6 which briefly show the process of cluster classification. First, the outline of the configuration of the present invention will be described. As shown in FIG. 1, a map creation unit 11 that inputs input data and creates a map, a hierarchical structure creation unit 12 that creates a hierarchical structure of clusters, It comprises a map labeled with a hierarchical structure and a labeling unit 13 that labels input data from input data.

The hierarchical structure creating section 12 is, for example, as follows.
The map analysis unit 121 calculates a quantity related to the cluster integration degree from a map and creates a data string, and the data string fusion unit 122 creates a cluster hierarchical structure based on the data string. Another example of the hierarchical structure creating unit 12 will be described later.

As an example showing the operation of the cluster classifying apparatus having this structure, consider classifying two-dimensional data into three clusters. One cluster in that is 2 more
It consists of two sub-clusters. Here, it is considered to obtain the hierarchical structure. Of course, before cluster classification, the number of clusters and the shape of the distribution are unknown.

First, the map creating section 11 will be described. The map creation unit 11 includes a data input unit 111 and a map unit 112. In the data input unit 111, the input data group 21 is input. Input data group 21
Is a two-dimensional vector as shown in FIG. 2, and is roughly divided into three clusters 21A, 21B, and 21C,
The one 21A includes two sub-clusters 21A1, 21
It consists of A2. However, until the explanation of the hierarchical structure creating unit 12, 21A has two sub-clusters 21A1 and 21A2.
It does not consider that it consists of A2.

Next, in the map section 112, the input data group 2
1 is used to create the map 31 of FIG. Map 31
Is constituted by a plurality (k pieces) of element groups 32. Each data of the input data group 21 corresponds to any element of the element group 32. A concrete correspondence method will be described. First, the prototype group 33 for the input data group 21 is created by the number of elements (k). Then, one of the prototype group 33 is assigned to each element. Then, each of the input data groups 21 may be associated with an element having a prototype most similar to the input data. At this time, in the input data group 21, the elements are prototyped so that the similar data correspond to the close elements on the map 31, and the dissimilar data respectively correspond to the distant elements on the map 31. assign. That is, the phase information of each data of the input data group 21 is reflected on the map 31.

In this way, from the input data group 21
A map 31 including element groups 32A to 32C corresponding to the vectors belonging to the clusters 21A to 21C is created.

It should be noted that the symbols of the clusters 21A to 21C are added for convenience of explanation, and the input data group 21 is not labeled at all before cluster classification. If some input data is labeled before cluster classification,
You can easily classify unlabeled data after creating a map. This method will be described. 1) An element on the map 31 corresponding to data belonging to the cluster 21A having a certain label (for example, A) is selected, and the label A is given to the element. 2) Perform operation 1) with 21B, 2
This is also performed for data belonging to the 1C cluster, and each of the element groups on the map 31 is given one of the labels A to C. 3) Find the element on the map corresponding to the unlabeled input data group 21 and use the label of the element as the label of the data. By performing the operations 1) to 3), all the input data can be labeled and the cluster classification is completed. Looking at the map 31, it seems that the above operation 2) has been completed, but since the input data group 21 is not labeled at all, it is still unknown where in the map 31 the cluster exists. Is. Therefore, the map must be analyzed to find where on the map 31 the clusters reside.

Then, in order to find where on the map the cluster exists, the map analysis unit 121 analyzes the map 31 created by the map creation unit 11. Less than,
The map analysis unit 121 will be described. Map analysis unit 1
Reference numeral 21 includes an integration degree calculation unit 121A that calculates an amount related to the integration degree of the cluster for each element, and a data string creation unit 121B that creates a data string according to the result. Examples of the quantity indicating the cluster integration degree include the following quantities.

C-1) The number of input data groups corresponding to each element of the element group 32 on the map 31.

C-2) A prototype assigned to an element on the map 31, the element and the map 31
Similarity to the prototype assigned to the adjacent element above. A cluster is a collection of similar data in the space of the data group. Using this property, the reason why the amounts of C-1) and C-2) described above indicate the degree of cluster integration will be described.

Since the amount of data in the cluster is larger than that in the outside of the cluster, if the numbers of input data corresponding to the elements are compared, if the elements corresponding to the data near the center of the cluster have the corresponding number of data, The number of corresponding data should be small in the case of an element corresponding to data deviated from the center of the cluster. Therefore, if the amount of C-1) is used, as shown in FIG. 4A, a histogram in which a mountain portion represents a cluster is created. Hereinafter, this amount is also referred to as the number of wins V.

Next, the amount of C-2) will be described. As mentioned above, the prototypes of each of the adjacent elements on the map are similar in the input data space. Also,
From the similarity that the data in the clusters are similar,
It can be said that the similarity of the prototype is high inside the cluster and low outside the cluster. From these two facts, by comparing the prototypes of the adjacent elements on the map, it is possible to distinguish whether the corresponding input data of the element is the cluster center or the outside of the cluster from the similarity. Specifically, if the prototypes of adjacent elements on the map have high similarity, the element is the element corresponding to the data near the center of the cluster, and conversely, the adjacent elements on the map If the prototypes have a low degree of similarity, the element is an element corresponding to data deviated from the cluster center. For example, in the case of two-dimensional vector data, if the Euclidean distance is selected as the similarity, the similarity is low when the distance is large, and the similarity is high when the distance is small. At this time, C
If a human sgram is created using the amount of -2), the result of FIG.
As shown in (b), the mountains are represented as clusters. Hereinafter, this amount is also referred to as a similarity dM between adjacent elements.

The number of wins V and the similarity dM between adjacent elements
From the definition of, it can be seen that the amount of V / dM also represents the cluster integration degree. At this time, the mountains from valleys to valleys represent clusters.

From the nature of such a histogram, FIG.
Dividing a mountain in the case of (a) and a valley in the case of FIG. 4B corresponds to dividing the map into clusters. Therefore, the number of peaks or valleys in this histogram corresponds to the number of clusters. Since the elements on the map corresponding to each peak or valley correspond to the prototype of the cluster, it means that an appropriate number of clusters could be classified at this point (three in this case). Then, do the following:

First, the data string creating unit 121B creates a data string from various amounts of the histogram. This data string will be described. The number of wins corresponding to the element i and the similarity between adjacent elements are V _i and dM _i , respectively. Then, a data string {X _k } like the formula (1) is created.

[0030] In the case of the histogram as shown in FIG. 4, FIG. 5 shows the data string {X _k } plotted on the number line. in this way,
It can be seen that the data string {X _k } forms clusters on the number line in the portions corresponding to the peaks in FIG. 4A and the valleys in FIG. 4B. Qualitatively describe {X _k }. First, the coordinates of the weight vector of the element k are connected by a polygonal line in the n-dimensional space. It can be said that X _k is the coordinate of the element k on the line when the broken line is straightened. At this time, the i-th point of the data string {X _k } is the i-th point of the map 31.
It corresponds to the second element. That is, it can be considered that n-dimensional vector input data composed of a plurality of clusters is converted into a one-dimensional data set so that the clusters can be easily extracted.

Since V _i is the number of input data groups corresponding to i elements on the map 31, information that the number of each point is V _k in the data string {X _k } of FIG. If added, clusters can be more easily extracted.

Next, the data string merging unit 122 creates a hierarchical structure using the data string {X _k } created by the data string creating unit 121B. This hierarchical structure has a data string {X _k }
The values close to each other are sequentially merged until they finally become one, and are displayed by displaying the process. For example, in this case, the hierarchical structure is as shown in FIG.
The fusion process will be described later in detail.

As described above, it was found that the number of clusters was roughly divided into three by dividing the histogram, but it can be seen that the hierarchical structure is as shown in FIG.

The labeling unit 13 labels the input data based on the hierarchical structure created by the data string merging unit 122 described above. The labeling unit 13 includes a map label unit 131 that labels a map based on a hierarchical structure,
Data input unit 132 for inputting data to be labeled
And the data label part 1 that labels the input data
33.

The map label section 131 labels the map based on the hierarchical structure. Based on the hierarchical structure, for example, as shown in FIG. 6, the maps are labeled as A, B, and C to form a map 61. Next, the input data group 21 is input again by the data input unit 132, and the input data group 21 is labeled. The input data group 21 and the labeled map 61 are used for labeling. Specifically, the element on the map 61 corresponding to the input data group 21 may be found and the label of the element may be used as the label of the data. When labeling of all data groups 21 is completed, the input data group 21 is classified into three clusters A, B, and C, as shown in FIG. In FIG. 6, the data belonging to each of the clusters A, B, and C is circled. Here, for convenience of explanation, this circle is added to enclose a portion of the data, and does not indicate a strict separation boundary line. Note that, as described above, the input data in FIG. 2 is not labeled in advance. Note that labeling is done for the first time by the labeling unit 13. Here, for convenience, the label of FIG. 2 and the label of FIG. 6 are matched.

In addition, in the case of subdividing and integrating only a specific part, it may be performed based on a hierarchical structure. From the hierarchical structure of FIG. 5, it can be seen that A and B may be reintegrated as one cluster as shown in map 61a), and to reclassify A, as shown in map 61b),
It can be classified as A1 and A2. This will be shown in a later example.

The above is the outline of the operation of the cluster classification device of the present invention. The data group 21 of FIG. 2 is roughly divided into three clusters A, B and C as shown in FIG. This is what was calculated as shown in FIG. This action is
It is clear that no prior knowledge of the number of clusters, position, shape of distribution, etc. is required, and the condition B-1) required for the cluster classification device of the present invention is satisfied.

Next, B-2) ... cluster classification independent of the processing procedure can be performed, and B-3) ... progress and results of the processing can be visually viewed, and the results can be calculated. It is shown that the present invention satisfies the condition that it is easy to process ... Therefore, the map creation unit 11
Will be described in more detail.

As described above, the map creating section 11 creates a prototype of the data group and assigns the prototype to the elements of the map so as to reflect the phase of the input data. Prototypes can be created using the vector quantization method, but the prototypes cannot be assigned to map elements so as to reflect the phase of the input data. As a method of simultaneously creating a prototype and assigning a prototype for reflecting the phase of input data, there is a self-organizing feature mapping (hereinafter referred to as SOM) algorithm by Kohonen (T. Kohonen, "Self- Organization and Associative Mem
ory ", Third Edition, Springer-Verlag, Berlin, 1989).
The SOM will be described below.

The SOM, as shown schematically in FIG.
It is composed of a layer ML of element groups arranged in a dimension (hereinafter referred to as a map layer ML) and an input layer IP for inputting data. This map layer ML shows elements arranged in two dimensions in FIG. 7, but elements arranged in one dimension may be used. Input layer I
P is coupled to all the elements of the map layer ML and can input data to all the elements of the map layer ML. The input data may be either a scalar or a vector, but here, in general, a vector x (n-dimensional) is used. The element i of the map layer ML (i is the order on the map,
The total number of elements is k. ) Are all weight vectors m _i
(n-dimensional). The SOM algorithm determines the weight vector to be updated from the similarity between the input vector x and the weight vector m _{i of} each element <similarity matching>, and sets the weight vector m _i to the input vector x.
It is divided into <update> which is closer to. Then, by repeating the actions of both, a weight vector m _i (1 ≦ i ≦ k) that reflects the distribution of the input vector x is generated.
The specific expressions of <similarity matching> and <update> are shown below.

<Similarity Matching> _{<Update> m i (t + 1)} = m i (t) + α (t) {x (t) -m i (t)} i∈N c m i (t + 1) = m i (t) Others ... ( 3) where | x−m _i | is the Euclidean distance between x and m _i ,
C is the element with the smallest distance (victory element), N _c
Is the neighborhood of the winning element C in the map layer ML, α (t) is a positive constant, and t is the time. While repeating the update, N
The magnitudes of _c and α (t) are gradually reduced. Also, α
(T) can be selected so as to become smaller as the distance from the victory element C increases.

[0042] Type sequentially choose x at random from the set of input vectors x, by repeating the update of the weight vector m _i, the weight vector m _i which reflects the distribution of the input vector x (1 ≦ i ≦ k) is To generate. That is, the weight vector m _i (1 ≦ i ≦ k) is a prototype of the distribution of the input vector x. Then, when the weight vector of a certain element is updated so as to approach the input vector, the elements in the vicinity of that element on the map are also updated,
The elements adjacent to each other on the map correspond to vectors close to each other in the space of the input vector. Therefore, the SOM algorithm can create a set of prototypes that reflect the topology of the input data space.
The SOM algorithm has the following features.

D-1) Weight vector m _i (1≤i≤k)
A proper map can be created regardless of the initial state of. D-2) An appropriate map can be created regardless of the input order of the input vector x. D-3) Since the map is one-dimensional or two-dimensional, the phase of the input data can be visually seen. D-4) Since the simple operations of <similarity matching> and <update> are repeated, the algorithm is simple.

Here, an appropriate map means that the set of prototypes well reflects the phase of input data. The features of D-1) and D-2) satisfy the condition that the cluster classification device of the present invention requires, that is, B-2) ... Cluster classification independent of the processing procedure can be performed. The feature of D-3) is that it contributes to the condition that B-3) ... The progress of processing and the result can be visually viewed, and that the result can be processed easily.

However, when the map is two-dimensional, it can be visually viewed, but it is not easy to process the result computationally. When the map is made one-dimensional, the one-dimensional histogram is considerably easier to calculate than the two-dimensional or more histogram. Therefore, the condition of B-3) can be satisfied.

Because of the effectiveness of the SOM algorithm, the map generator 11 adopts this one-dimensional SOM algorithm. That is, the data input unit 111 of the map creating unit 11 is used as the SOM input layer IP and the map unit 112.
Is a map layer ML of SOM. With this configuration, create a set of prototypes that reflect the phase of the input data,
Create a one-dimensional map consisting of elements with the prototype. As described above, the cluster classification device of the present invention including this map creation unit 11 can satisfy the conditions of B-2) and B-3).

In the SOM algorithm performed by the map creating section 11, the creation of the map 31 ends when the peaks and valleys of the histogram become clear. At this time,
The creation may be completed without inputting all the data of the input data group 21. If the peaks and valleys of the histogram are not clear at the time when all the data in the input data group 21 are input, input the input data group 21 again and finish the map creation when the peaks and valleys are clear. do it. Although it is easy to visually judge whether the peaks and valleys of the histogram are clear, it is an evaluation criterion (smoothness of the graph, relative ratio of the maximum value and the minimum value) that indicates whether the peaks and valleys of the histogram are clear. Etc.),
It is also possible to judge automatically. Also in this case, the one-dimensional histogram is obviously easier to process than the two-dimensional histogram. It should be noted that even if the histogram is not used, the fact that the difference between the input data group 21 and the prototypes corresponding thereto becomes gradually smaller as the SOM algorithm progresses is utilized, and when the value or the change rate becomes smaller than a certain threshold value. The creation of the map 31 may be finished.

Next, it is shown that the present invention satisfies the condition B-4) ... A cluster hierarchical structure can be obtained. Therefore, the hierarchical structure creating unit 12 will be described in more detail. As described above, the hierarchical structure creating unit 12 converts the n-dimensional vector input data composed of a plurality of clusters into a one-dimensional data set as shown in FIG. Get the structure.

As a method for obtaining such a hierarchical structure, there is a melting algorithm (Kenneth Rose et a
l., "Statistical Mechanics and Phase Transition in
Clustering ", Phys. Rev. Lett. 65, pp. 945-948 (1990)).
This algorithm defines that an energy function is defined from a certain vector data and a set of prototypes for the vector data, and that the local minimum solution of the energy (here, the set of prototypes is a solution) represents a cluster. The shape of the energy function is modified by the temperature parameter and generally becomes smoother as the temperature rises,
Moreover, the number of local solutions is reduced. That is, as the temperature increases, the number of prototypes decreases. Since the prototype may be considered to represent a cluster, the hierarchical structure can be understood by displaying the relationship between the prototype coordinates and the temperature.

The updating rule of the melting algorithm will be described using equations. The data is x, the prototype is y, and the partition function Z and the free energy F are represented by the following equations. Here, the subscripts under Σ and Π indicate the sum and product of the symbols, respectively. Substituting Z for F and obtaining the minimum value of F, ∂F / ∂
Solve y = 0. As a result, the prototype y becomes as follows.

[0051] This expression is the update rule for the prototype y of the melting algorithm. At a certain temperature T, this updating rule is performed to find y. Then, the temperature T is increased, this updating rule is performed again, and y is obtained. As the temperature T rises, the number of local minima in F gradually decreases, eventually reaching 1
Become one The local minimum of F corresponds to the prototype of the cluster. As the temperature T is increased from cold to hot, the prototypes of the clusters fuse close together. Therefore, by expressing the relationship between the temperature T and the prototype y of the cluster in a graph, the hierarchical structure of the cluster can be obtained. When displaying the prototype, the y-coordinate may be displayed as it is, or may be displayed in association with the one-dimensionally arranged SOM prototypes.

The melting algorithm has drawbacks such that when the data x is two-dimensional or more, it is difficult to display a prototype and it is difficult to fuse isolated points. However, since the data set created by the map analysis unit 121 is one-dimensional and is created from the prototype group of n-dimensional vector data created by the map creation unit 11, isolated points are difficult to create. In addition, the melting algorithm increases the calculation amount as the dimension of the input data increases,
Since the data string in this case is one-dimensional regardless of the dimension of the input data to be classified by the cluster classification device, the calculation amount is constant. From the above, the drawbacks of the melting algorithm can be solved.

Therefore, the hierarchical structure creating section 12 uses this melting algorithm to obtain the hierarchical structure of the data from the one-dimensional data set. The present invention using this melting algorithm in the hierarchical structure creating unit 12 is B-
4) The condition that a hierarchical structure of clusters can be obtained is satisfied.

The appropriate number of clusters can be found by analyzing the histogram in the integration degree calculating unit 121A, but can also be found in the data string merging unit 122. It can be said that a suitable cluster has a longer temperature range in which the prototype occurs in the melting algorithm. Therefore, the number of clusters when the prototypes are not fused and the remaining temperature range is long may be set as an appropriate number of clusters. If the peaks and valleys of the histogram are subtle due to noise or the like and analysis is difficult, the number of clusters may be calculated by the data string fusion unit 122.

The configuration and operation of the cluster classification device of the present invention have been described above. The cluster classification device of the present invention is
The following cluster classification device satisfies the conditions of -1), B-2), B-3), and B-4).

That is, using a one-dimensional self-organizing feature mapping, a map creating section for creating a map consisting of prototypes for input data, and a hierarchical structure creating section for creating a hierarchical structure of clusters from the map are obtained. A cluster classification device, comprising: the created map and a labeling unit that classifies input data according to a hierarchical structure.

In this case, as shown in FIG. 1, the hierarchical structure creating unit calculates a quantity representing the cluster integration degree from the obtained map and creates a data string, and the obtained data string from the map analyzing unit. In the case where it is composed of a data string fusion unit that creates a hierarchical structure of clusters, and as shown in FIG.
FIG. 11A, which shows a case including an integration degree calculation unit that calculates an amount indicating the integration degree of the cluster from the obtained map and a prototype fusion unit that creates a hierarchical structure of the cluster.
It is conceivable that the prototype fusion unit only creates a hierarchical structure of clusters from the obtained map.

B-1) Appropriate cluster classification without over-integration or over-division can be performed without prior knowledge of the number of clusters, positions, distribution shapes, etc. B-2) Cluster classification that does not depend on the processing procedure can be performed. B-3) You can visually see the progress and results of the processing,
Moreover, it is easy to process the result computationally.

B-4) A hierarchical structure of clusters can be obtained.

[0060]

Embodiments of the cluster classification device of the present invention will be described below. In order to simplify the display of the cluster classification, an example of dividing the two-dimensional vector data as shown in FIG. 2 into clusters and obtaining the hierarchical structure will be shown again. First, as a first embodiment of the present invention, a case where the same two-dimensional vector data as in FIG. 2 is input will be described. In this embodiment,
The number of elements of the map 31 of the map unit 112 is 30.

First, FIG. 8 shows a histogram corresponding to FIG. According to FIG. 8, three peaks are formed, and it is visually clear that the input data group 21 is composed of three clusters. Next, FIG. 9 shows the hierarchical structure obtained by the hierarchical structure creating unit 12. From this figure, classification (a),
FIG. 10 shows the result of dividing the input data group 21 by the maps 61a), 61, 61b) by dividing the prototype into three types of (b) and (c).

The one-dimensional map of the map unit 112 is
The elements of the map may be in a ring shape in which they are connected on both sides, or may be in a string shape separated from each other. The two differ in the concept of the neighborhood when updating the element weight. The ring shape corresponds to connecting both sides of the map as neighborhoods, and the string shape corresponds to not connecting both sides of the map. In the case of the ring shape, the reflection of the phase relationship of the input data is distorted on both sides of the map <BorderEffects> (T.Kohonen, "Th
ings You Haven't Heard about the Self-Organizing M
ap ", Proc. IEEE Int. Conf. on Neural Network, vol.3,
pp.1147-1156,1993) can be excluded. In the case of a string shape, both sides are always cut off, which is convenient when displaying in a histogram or a hierarchical structure. In this case, in order to remove the boundary effect, the elements on both sides may be excluded from the input data of the melting algorithm, removed from the horizontal axis of the histogram, or the like.

In the melting algorithm, y was obtained by substituting the data {X _k } for x in the equation (6). Here, additional information that the number of k-th data is V _k can be included in the update formula. At this time, the update formula is as shown in formula (7).

[0064] When the updating formula is set to the formula (7) instead of the formula (6), the magnitude of the peaks and valleys of the histogram of V contributes to the determination of the hierarchical structure of the cluster. Therefore, an isolated point having a small V is hard to be a prototype, and it is possible to solve the above-described drawback of the melting algorithm, that is, the problem that an isolated point is likely to be a cluster. However, since an isolated point is less likely to occur in the data string during the process of creating the data string, in particular, when the distribution of the input data is smooth with little noise, either equation (6) or equation (7) is used. However, if the distribution of input data has a lot of noise and isolated points are likely to occur in the data string, it is effective to use the equation (7). In this embodiment, the expression (7) is used.

In equation (6), substituting P (xεy) for y, ignoring the dependency of x, and deriving the denominator of P (xεy) yields equation (8). Become (Yui-fai Wong, "
Clustering Data by Melting ", Nural Computation, 5,89
-104 (1993)).

[0066] Since the formula (8) has a smaller number of sums of exponential functions than the formula (6), the amount of calculation is small and the algorithm can be speeded up. Therefore, in the hierarchical structure creating unit 12,
You may use the melting algorithm of Formula (8).
Further, the term V may be added to the equation (8) as in the equation (7). As shown in FIG. 1, the hierarchical structure creating unit 12 of the above-described embodiment first creates a data string and then creates a hierarchical structure by fusing the data.

In addition to the above, the hierarchical structure creating section 12 also includes
As shown in 1 (a), by utilizing the fact that the prototypes of SOMs created by the map unit 112 are arranged one-dimensionally,
A hierarchical structure may be created directly from the prototype of the n-dimensional vector. In this case, the vector of the n-dimensional prototype of the map layer is directly converted into the prototype fusion unit 15
The prototype obtained by the fusion may be displayed as the input of the melting algorithm of 1. The display of the prototype will correspond to the prototypes of the SOMs arranged in one dimension. FIG. 11A shows the case where the equation (6) or (8) is used for updating the melting algorithm, and when the equation (7) using V is used, FIG.
As shown in (b), the hierarchical structure creating unit 12 may be provided with the integration degree calculating unit 152 before the prototype merging unit 151.

It should be noted that the configurations of FIG. 1 and FIGS. 11A and 11B have different dimensions of the melting algorithm, but the essence of the algorithm is the same, so that the fusion process produces the same result. Can be obtained. Therefore, the result of the present example shows only the case of the configuration of FIG. In the case of FIG. 1, the number of dimensions of the melting algorithm can be set to one dimension regardless of the dimension of the input data to be classified by the cluster classification device, and FIG.
In (b), since the prototypes are combined as they are, the data string creation unit 121B can be omitted.

Although the input data of the above-mentioned embodiment are all two-dimensional vectors, by changing the number of dimensions of the prototype 33 of the data input sections 111 and 132 and the map section 112, a multidimensional vector can be converted into a scalar. You can also

As an example when the dimensions are changed, FIG.
The histogram and the obtained hierarchical structure in the case of five-dimensional vector clusters are shown. 13 shows an example of a histogram of V, dM, and V / dM in the case of four-dimensional four clusters and the obtained hierarchical structure when the dimension and the amount of the histogram are changed. According to the histogram of FIG. 13, when finding an appropriate number of clusters, it is easy to analyze by using dM or V / dM. This is due to the aforementioned boundary effect and another property of SOM, which is equal probability that the number of wins becomes equal as the algorithm progresses.

In the case of a multidimensional vector, it is difficult to represent the data on the coordinate axes as they are, so it is effective to visually discover the clusters and to know the hierarchical structure as in the present invention.

As the input data of the present invention, a scalar or vector of any size may be selected. That is, SO
The M algorithm is D-1) ... Weight vector m _i (1 ≦
Since there is a feature that an appropriate map can be created regardless of the initial state of i ≦ k), it is not necessary to standardize the data in advance or to know the features of the data (the number of clusters, cluster positions, etc.). Therefore, cluster classification is possible for all input data such as image information, voice information, communication symbols, time series data, and the like.

[0073]

As described above, according to the present invention, it is possible to provide a cluster classification device that satisfies the following conditions.

B-1) Appropriate cluster classification without over-integration or over-division can be performed without any prior knowledge of the number, position, distribution shape, etc. of clusters. B-2) Cluster classification that does not depend on the processing procedure can be performed. B-3) You can visually see the progress and results of the processing,
Moreover, it is easy to process the result computationally.

B-4) A hierarchical structure of clusters can be obtained.

[Brief description of drawings]

FIG. 1 is a diagram showing an outline of a basic configuration of the present invention.

FIG. 2 is a diagram showing an example of data for cluster classification according to the present invention.

FIG. 3 is a diagram showing a map created by a map creating unit in FIG.

FIG. 4 is a distribution diagram of the number of wins calculated by the integration degree calculation unit of FIG. 1 and the similarity between adjacent elements.

5 is a diagram showing a hierarchical structure of a data string created by the data string creating unit and a cluster created by the data string merging unit of FIG. 1;

FIG. 6 is a diagram showing maps and data labeled by a labeling unit.

FIG. 7 is a diagram showing a structure of self-organizing feature mapping.

FIG. 8 is a diagram showing a histogram of the number of wins according to one embodiment of the present invention.

FIG. 9 is a diagram showing a hierarchical structure of clusters according to an embodiment of the present invention.

FIG. 10 is a diagram showing labeled data in one example of the present invention.

FIG. 11 is a diagram showing another configuration example of the hierarchical structure creation unit of the present invention.

FIG. 12 is a diagram showing a histogram of winning numbers and a hierarchical structure of clusters in the case of a three-dimensional vector of five clusters.

FIG. 13 is a diagram showing a histogram of the number of wins, the degree of similarity between adjacent elements and their ratio, and a hierarchical structure of clusters in the case of four-dimensional vector four clusters.

[Explanation of symbols]

 11 ... Map creation unit 12 ... Hierarchical structure creation unit 13 ... Labeling unit 21 ... Input data group 21A, 21B, 21C ... Cluster 21A1, 21A2 ... Sub-cluster 31 ... Map 32 ... Element group 32A, 32B, 32C ... Element group 33 Prototype group 61, 61a), 61b) ... Map 111 ... Data input unit 112 ... Map unit 121 ... Map analysis unit 122 ... Data string fusion unit 121A ... Integration degree calculation unit 121B ... Data sequence creation unit 122 ... Data sequence fusion unit 131 ... Map label part 132 ... Data input part 133 ... Data label part 151 ... Prototype fusion part 152 ... Integration degree calculation part V ... Number of wins dM ... Similarity between adjacent elements ML ... Map layer IP ... Input layer

Claims (4)

[Claims] 1. A map creating unit for creating a map of prototypes for input data using one-dimensional self-organizing feature mapping, and a hierarchical structure creating unit for creating a hierarchical structure of clusters from the map. A cluster classification device, comprising: a labeled map and a labeling unit that classifies input data according to a hierarchical structure. 2. The hierarchical structure creating unit according to claim 1,
It is characterized by comprising a map analysis unit that calculates a quantity representing the cluster integration degree from the obtained map and creates a data sequence, and a data sequence fusion unit that creates a cluster hierarchical structure from the obtained data sequence. Cluster classifier. 3. The hierarchical structure creating section according to claim 1,
A cluster classification device comprising: an integration degree calculation unit that calculates an amount representing the integration degree of a cluster from the obtained map; and a prototype fusion unit that creates a hierarchical structure of the cluster. 4. The hierarchical structure creating unit according to claim 1,
A cluster classification device characterized by comprising only a prototype fusion unit for creating a hierarchical structure of clusters from the obtained map.