JPH1115832A - Cluster generation device and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate a cluster hierarchy permitting that one example belongs to plural clusters by means of shortening cluster generation time by considering the cluster whose number of appearing examples in common is large in a cluster set to be highly associated and generating the new cluster from the plural clusters. SOLUTION: An initial cluster generation means 2 generates the clusters for respective attribute values based on the given example, which is read from an example data base 5. A pair selection means 2 selects the pair of the clusters in the generated clusters. A cluster generation means 4 counts the number of the examples contained in common on the selected pair, generates the new cluster from the pertinent pair of plural clusters in the largest case and stores it in a cluster data base 6. The cluster whose number of the appearing examples in common is large in the cluster set is considered to be highly associated. The generation of the new cluster from the plural clusters is repeated and the cluster hierarchy is generated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a cluster generation device for generating a cluster based on a given case.

When a class for classifying a case is not given, an important problem is to classify the case. Clustering is a technique for generating a class that becomes a class itself or a subset in such a case. In general, a cluster is a set of similar cases. For example, it can be used to detect a group of similar people from questionnaire data. In the generation of clusters, the performance of the obtained cluster hierarchy changes depending on how similarities between clusters are measured and how clusters are generated. The present invention relates to how to measure and generate similarity between clusters.

[0003]

2. Description of the Related Art Conventionally, cluster generation methods include a sequential method and a collective method. In the sequential method, the instances to be clustered are given not by one time but by little time. When a new case is given, perform operations to make changes to the previously created cluster, instead of recreating it from scratch. Therefore, although the time required for cluster generation is short, the performance of the generated cluster hierarchy largely depends on the input order of cases.

In the collective method, since cases are given at once, there is no problem in the input order, but it takes time to generate clusters. For example, the Ward method is a typical method, but the amount of calculation is the cube of the total number of cases.

[0005]

As described above, when cluster generation is performed by a conventional sequential method, cluster generation can be performed quickly when a new case is given. There is a problem that it greatly depends on the input order of the cases.

Further, when the conventional batch method is used, there is no problem in the input order, but there is a problem that it takes time to generate clusters. Further, in many methods common to the sequential / collective methods, a cluster hierarchy in which one case belongs to only one class is generated. In order to solve a certain problem, a plurality of viewpoints are often required. In the conventional method of generating a hierarchy in which one case is included in only one class, a hierarchy is generated for each viewpoint. Necessity arises. Therefore, there is a demand for a cluster hierarchy generation method that can reduce the time required for hierarchy generation regardless of the input order of cases and further allows one case to belong to a plurality of clusters.

[0007] The present invention solves these problems,
For each value of each attribute, clusters are generated by collecting the cases with that value, and clusters with a large number of cases that appear in common in the cluster set are considered to be highly related, and a new cluster is created from multiple clusters. An object of the present invention is to generate a cluster hierarchy by repeatedly generating a cluster hierarchy, shortening the cluster generation time, and generating a cluster hierarchy that allows one case to belong to a plurality of clusters.

[0008]

Means for solving the problem will be described with reference to FIG. In FIG. 1, a processing device 1 loads a program from a recording medium (not shown) into a main storage and starts up to perform various processes. In this example, an initial cluster generating unit 2, a pair selecting unit 3, and a cluster It comprises a generating means 4 and the like.

The initial cluster generating means 2 generates a cluster. The pair selecting means 3 selects a cluster pair. The cluster generating means 4 counts the number of common occurrence cases for the selected pair and generates the largest number of pairs as a new cluster.

The case database 5 stores cases. The cluster database 6 stores generated clusters. The display device 7 displays a cluster or the like.

The input device 8 is for inputting various instructions and data. Next, the operation will be described. The initial cluster generating means 2 generates a cluster for each attribute value based on the given case read from the case database 5, and the pair selecting means 3 generates a pair of a plurality of clusters (for example, two) in the generated cluster. Is selected, and the cluster generation unit 4 counts the number of cases commonly included in the selected pair, and if the number is the largest, generates a new cluster from a plurality of clusters of the pair and stores the new cluster in the cluster database 6. I have to.

At this time, a new cluster is generated from the union of a plurality of clusters. In addition, a new cluster is generated from the intersection of a plurality of clusters.

Therefore, clusters are generated by collecting cases having the values of the respective attributes, and clusters having a large number of cases appearing in common in the cluster set are regarded as having a high association, and a plurality of clusters are considered. By repeatedly generating a new cluster from, a cluster hierarchy can be generated by reducing the cluster generation time and allowing one case to belong to a plurality of clusters.

[0014]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, an embodiment and operation of the present invention will be described in detail with reference to FIGS.

FIG. 2 is a flowchart illustrating the operation of the present invention. This is a flowchart for explaining the detailed operation of the configuration in FIG. In FIG. 2, S1 inputs a case set.

In step S2, a parameter K and a cluster limit number L are determined. This is, as described on the right, the parameter K
And the cluster control number L, and based on this, as described on the right side, K × standard deviation = determination of a positive real multiple of the standard deviation, and the maximum number of the total of the class or its subset (cluster) Is determined as L.

In step S3, an initial cluster hierarchy is generated. In this case, an initial cluster hierarchy is generated for the case set input in S1 as shown in FIG. 3 to be described later, that is, as shown in FIG. Each cluster has a value of attribute am of v
An initial cluster hierarchy composed of a cluster of mv cases collected is generated.

In step S4, it is determined whether or not the processing is completed. It is determined whether the process from S5 onward is repeated until the number of clusters becomes L or until there are no clusters to be selected as a pair. If YES, the process ends. NO
In the case of, the process proceeds to S5.

In step S5, a cluster pair is selected. S6
Counts the number of common occurrences. This counts the number of commonly occurring cases for the selected pair of clusters.

In step S7, the number of estimated common cases is calculated (described later). In S8, it is determined whether or not the number of common occurrence cases counted in S6 is sufficiently larger than the estimated number of common cases calculated in S7. In the case of YES, the process proceeds to S9. In the case of NO,
Return to S4 and repeat.

In step S9, the ratio of the number of cases is calculated. S10
Stores the largest ratio. In S11, it is determined whether all pairs have been tried. In the case of YES, the pair having the largest ratio is selected in S12, a new cluster is generated in S13, and the process returns to S4 and repeats. On the other hand, if NO in S11, the process returns to S4 and repeats.

Here, S3 to S13 will be described in detail below. As shown in FIG. 3 described later, a cluster including all cases is generated as Croot, and a set of cases in which the value of the attribute am is vmv is generated as a leaf cluster (S3). Then, the degree of relevance of the cluster pairs of the number of cases that appear in common is evaluated. If the number is sufficiently larger than the estimated number of common cases (YES in S8), it is considered that the association is high. The estimated number of common cases is calculated by the following equation.

E _ij = (| C _i | × | C _j |) / N (1) where | C _i | and | C _j | represent the number of cases included in clusters i and j, respectively. Represents the total number of cases. The standard deviation at this time is d _ij = ｛| C _i | × | C _j | × (N− | C _i |) × (N− | C _j |)} ^1/2 / ｛N ² × (N− 1)｝ ^1/2 (2). Here, when the following equation (3) including the parameter K is satisfied, the relationship between the two clusters is considered to be high, and the two clusters are selected as candidates (S8).

| C _i ∩C _j |> e _ij + K · d _ij (3) Here, the left side represents the intersection of (e) in FIG. 4 described later.
Next, the following equation (4) is calculated (S9).

| C _i ∩C _j | / (| C _i | × | C _j |) (4) Here, the left expression represents the intersection of (e) in FIG. This represents the union of FIG. 4D described later.

From the calculated results, by selecting a cluster pair that satisfies Expression (3) and maximizes Expression (4), the tendency of selecting clusters with a large number of cases can be reduced (S9, S10). ).

Then, the union of the selected cluster pair is generated as a new cluster, and linked to the higher rank of the selected pair, to obtain FIG. 4B described later. In addition, by generating a product set of the selected cluster pair as a new cluster and linking it to the lower order of the selected pair, the result becomes FIG.

As described above, by generating a cluster for each attribute value and repeatedly generating a new cluster from a cluster pair having a large relation, a cluster hierarchy is generated. It is possible to generate a cluster hierarchy that allows to belong to a plurality of classes. The details will be sequentially described below.

FIG. 3 is an explanatory diagram (part 1) of the present invention. This is a diagram for explaining the concept of the initial cluster.
FIG. 3A is a conceptual diagram of an initial cluster. Here, a cluster including all cases is generated as Croot. Next, a set of cases in which the value of the attribute am is vmv is generated as a leaf cluster as illustrated.

FIG. 3B shows a specific example of the initial cluster. Here, a cluster “furniture” is generated as a cluster Croot including all cases. Next, as the leaf cluster, those having the attribute “number of legs” having the values “0” and “3” are generated as clusters “number of legs = 0” and “number of legs = 3” as shown in the figure. . Similarly, as a leaf cluster, a cluster having a value of attribute “material” having “tree” is generated as a cluster “material = tree” as illustrated.

As described above, the cluster C including all cases
By generating a root and generating a set of cases for each attribute value as a leaf cluster, it is possible to generate an initial cluster from the case set.

FIG. 4 is an explanatory diagram (part 2) of the present invention. This is a diagram for explaining the concept when one new cluster is generated from a plurality of clusters having a strong relationship from the initial cluster.

FIG. 4A shows two clusters C _i and C _j of a pair selected from the cluster hierarchy. FIG. 4B shows an example of a method of using the union as a new cluster.
Link The two clusters C _i, the union of C _j when a new cluster Cm is the two clusters C _i, the upper pair, as shown a new cluster Cm union of C _j Attach.

FIG. 4C shows an example of a method of using the intersection set as a new cluster. Link The two clusters C _i, the product set of C _j when a new cluster Cm is the two clusters C _i, the lower pair, as shown a new cluster Cm set intersection of C _j Attach.

FIG. 4D is a diagram schematically showing the union. The union set (in the case of (b) in FIG. 4) is represented by | C _i | + | C _j |, and is the sum of the portions of the cluster C _i and the cluster C _j indicated by oblique lines.

FIG. 4E is a diagram schematically showing the intersection. The intersection (in the case of (c) in FIG. 4) is represented by | C _i ｜ C _j |, and is an overlapping portion of each of the cluster C _i and the cluster C _j indicated by oblique lines.

FIG. 5 shows an example of a cluster hierarchy according to the present invention.
This is an example of a cluster hierarchy after a new cluster in the case of the union set and a new cluster in the case of the intersection set described above are generated for the initial cluster in FIG. 3B.

For example, the cluster of the union on the left side is a new cluster “the number of legs = 3 o” as the union of two pairs of the cluster “number of legs = 3” and the cluster “material = tree”.
r material = tree ”is generated and linked to a higher order.

Similarly, for example, the cluster of the product set on the right side is a new cluster “material = plastic and shape = square” as a product set of two pairs of the cluster “material = plastic” and the cluster “shape = square”. Generated and linked below.

As described above, a new cluster can be generated from a cluster pair having a large relation by finding a relevant pair from the cluster set and linking the union / intersection to the upper / lower levels. Becomes

FIGS. 6 and 7 show flowcharts for explaining the operation of the system according to the present invention. This is a flowchart for explaining the detailed system operation of FIG.
Portions corresponding to S1 to S13 in FIG. 2 are described at the left end.

In FIG. 6, S21 inputs a case set (S1). In S22, the parameter k and the cluster limit number L are determined. In step S23, m = 0 is initially set. This initializes the value of the variable m when generating a new cluster Cm.

In step S24, i = 0 is initialized. S25
Is initially set to j = 0. In step S26, the attribute ai has the value v
A cluster Cm consisting of all cases ij is created.

In S27, m = m + 1. S28 is j
= (The number of values taken by ai-1). In the case of YES, the process proceeds to S30. On the other hand, in the case of NO, j = j + 1 in S29, the process returns to S26, and the process of creating the next cluster Cm is repeated.

In step S30, it is determined whether i = (the number of all attributes-1). In the case of YES, the process proceeds to S32. On the other hand, if NO, i = i + 1 is set in S31, and the process returns to S25 and repeats. In S32, Pmax = 0 and Cmax = 0 are initially set.

In step S33, i = 0 is initialized. S34
Is j = i + 1. In step S35, the number of cases | C _i ∩C _j | included in the clusters C _i and C _j is counted.

In step S36, the estimated number of common cases e _ij and its standard deviation d _ij when C _i and C _j are independent are calculated. S in FIG.
37 determines whether | C _i ∩C _j |> e _ij + K · d _ij . Y
In the case of ES, the process proceeds to S38. If NO, S4
Go to 0.

In S38, P _max <(| C _i ∩C _j |) /
(| C _i | + | C _j |). If yes,
Proceed to S39. In the case of NO, the process proceeds to S40. S39
Performs P _max = (| C _i ∩C _j |) / (| C _i | + | C _j |) C _max ← (C _i , C _j ).

In step S40, it is determined whether j = m-1. YES
In the case of, the process proceeds to S42. In the case of NO, j = j + 1 is performed in S41, and the process returns to S35 and repeats. In S42, i =
m-2. In the case of YES, the process proceeds to S44.
In the case of NO, i = i + 1 is set in S43, and the process returns to S34 and is repeated.

A step S44 decides whether C _max max0. YES
In the case of, the process proceeds to S45. If NO, the process ends. In step S45, Cm is created from _Cmax by the operator.

At S46, m = m + 1. S47 is m
= L. If YES, the process ends. If NO, the process returns to S32 and is repeated.

[0052]

As described above, according to the present invention,
For each value of each attribute, clusters are generated by collecting the cases with that value, and clusters with a large number of cases that appear in common in the cluster set are considered to be highly related, and a new cluster is created from multiple clusters. Since the configuration of generating a cluster hierarchy by repeating generation is adopted, it is possible to generate a cluster hierarchy that allows one case to belong to a plurality of classes by shortening the cluster generation time. Thus, (1) one cluster is generated for each attribute value, a new cluster is generated from clusters having a large number of commonly appearing cases, and one case belongs to a plurality of classes. It is possible to cope with the case.

(2) The processing time required to generate a cluster hierarchy is proportional to the cube of the number of clusters in the hierarchy and the total number of cases. Usually, a class set that is too complex is not needed because it is difficult to use as knowledge. Therefore, the number of clusters in the hierarchy set as a parameter can be made smaller than the number of cases. As a result, a cluster can be generated in a relatively short time.

(3) According to the above (1) and (2),
For a large-scale case set in which one case belongs to a plurality of concepts, it is possible to effectively learn clusters constituting a class.

[Brief description of the drawings]

FIG. 1 is a system configuration diagram of the present invention.

FIG. 2 is a flowchart illustrating the operation of the present invention.

FIG. 3 is an explanatory diagram (No. 1) of the present invention.

FIG. 4 is an explanatory diagram (No. 2) of the present invention.

FIG. 5 is an example of a cluster hierarchy according to the present invention.

FIG. 6 is a flowchart (part 1) for explaining the system operation of the present invention.

FIG. 7 is a flowchart (part 2) for explaining the system operation of the present invention.

[Explanation of symbols]

 1: Processing unit 2: Initial cluster generation unit 3: Pair selection unit 4: Cluster generation unit 5: Case database 6: Cluster database 7: Display unit 8: Input unit

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Seishi Okamoto 4-1-1 Kamikadanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Inside Fujitsu Limited (72) Inventor Osamu Sato 4-chome, Kamiodanaka Nakahara-ku, Kawasaki City, Kanagawa Prefecture No. 1 Inside Fujitsu Limited

Claims (4)

[Claims] 1. A cluster generating apparatus for generating a cluster based on a given case, comprising: means for generating a cluster for each attribute value based on the given case; Means for generating a new cluster from the plurality of clusters when the number of cases commonly included in the cluster is large. 2. The cluster generating apparatus according to claim 1, wherein a new cluster is generated from the plurality of clusters, and a union of the plurality of clusters is set as a new cluster. 3. The cluster generation apparatus according to claim 1, wherein a new cluster is generated from the plurality of clusters, and an intersection of the plurality of clusters is set as a new cluster. 4. A means for generating a cluster for each attribute value based on a given case, and, when the number of cases commonly included in a plurality of clusters among the generated clusters is large, said plurality of clusters A recording medium storing a program functioning as a means for generating a new cluster from a cluster.