JPH0259980A - Treatment of clustering - Google Patents

Abstract

PURPOSE:To determine plural templates to high accurately recognize a test sample different from a learning sample by executing clustering based on a forecasting error. CONSTITUTION:Each sample is made into one cluster, the distances between all the clusters are obtained, all the cluster pairs are ranked starting from a cluster pair having the shortest distance between them, the cluster pair having the shortest distance are made into C1, C2, respective forecasting errors are obtained for a case when the cluster pair C1 and C2 are united and for another case when the cluster pair C1 and C2 are not united, and when the forecasting error in the former case is smaller, the C1 and C2 are united and made into one cluster, and current processing returns to the first processing. On the other hand, when the forecasting error in the latter case is smaller, if the next rank cluster pair exists and the distance between the second rank cluster pair is shorter than a certain fixed value, the cluster pair C1 and C2 are held as they are, and the current processing returns to the second processing. In the other cases, a protruding polyhedron composed of each sample for each cluster is obtained, the average value of respective samples to be endpoints is obtained, and the average value is made into the template. Thus, clustering can be stably executed.

Description

DETAILED DESCRIPTION OF THE INVENTION (1) Technical field to which the invention pertains The present invention relates to, for example, (i) a method for unsupervised classification, (ii) a method for determining subclasses in character/figure recognition systems, etc.; ji) It relates to a clustering processing method used in a method of creating a plurality of templates when constructing an L'ffl knowledge dictionary.

(2) Conventional technology In the past, clustering methods performed clustering based only on the distance between samples and the distance between clusters on the assumption that the training samples accurately reflected the characteristics of the population. However, when the number of training samples was small, the clustering results were greatly affected by biased samples in the training samples. For example, when determining multiple templates using a clustering method during recognition static configuration, the determination of multiple templates was greatly influenced by the bias of the training sample and was not effective when recognizing the test sample.

(3) Object of the Invention An object of the present invention is to provide a clustering processing method that reduces the influence of bias in learning samples and performs stable clustering even when the number of learning samples is small.

(4) Structure of the Invention The following is a description of an example in which a plurality of templates are used when constructing a recognition dictionary for a five character/figure recognition method.

(4-1') Differences between the characteristics of the invention and the prior art Figure 3 shows the following:
1 is an example of a processing block diagram of a multiple template determination method using a conventional clustering method; FIG.

Training samples are represented by feature vectors.

Before starting processing, determine the number of templates (let it be K). Also, let N be the number of samples. Each cluster is T=N/
It consists of 2 samples.

In process 11, one arbitrary sample Si is selected from the learning samples.

In process 12, T-1 samples are selected in descending order of distance from the learning sample to St.

In process 13, the sample selected in process 12 and Si
A total of T samples are removed from the learning samples.

In process 14, the average of the T samples is used as a template.

In process 15, if there are any samples left, the process returns to process 11, and if there are no samples left, the process ends.

For the alleys used in the process 12, Euclint distance, City-Bronck distance, etc. may be used.

As described above, the conventional processing method does not take into account the influence of bias in the learning sample, so if a different learning sample is used, there is a high possibility that the template to be determined will change significantly.

This means that when recognizing a test sample that is different from the training sample, multiple templates determined using the training sample are less effective. The present invention provides a method for reducing bias in learning samples when determining templates.9. It is possible to determine multiple templates that recognize test samples with high accuracy.

(1-2) Examples FIG. 1 is an example of a processing block diagram of the present invention.

It is assumed that the training samples are represented by feature vectors.

In process 2I, each sample is treated as one cluster.

In process 22, the distances between all clusters are determined and the clusters are ranked in descending order of distance. Let the cluster pair with the minimum distance be C1 and C2.

In process 23, prediction errors, which will be described later, are obtained for cases in which C1 and 02 are combined and cases in which they are not combined.

In process 24, if the prediction error is smaller when C1 and 02 are combined, CI and C2 are combined to form one cluster and the process returns to process 22. If the prediction error is smaller if C1 and C2 are not fused, the process proceeds to step 25.

In process 25, if a cluster pair of the first order exists and the distance between them is smaller than a certain value, the cluster pair of the next order is set as CI and C2 and the process returns to process 23. In other cases, the process advances to step 26.

In process 26, a convex stripe made up of individual samples is obtained for each cluster, the average of the samples serving as the end points of the convex stripe is taken, and the process is completed using the average value as a template.

The distance between clusters is defined as follows.

Let the distance from C1 to 02 be the largest among the distances from 01 to the samples belonging to 02.

Similarly, the distance from C2 to 01 is assumed to be the maximum among the distances from 02 to the samples belonging to CI. Then, the larger of the distance from CI to 02 and the distance from C2 to C1 is set as the distance between clusters C1 and 02.

The distance between cluster C1 and sample X is defined as follows. FIG. 2 is an explanatory diagram illustrating this definition. The end points of the convex striped surface T of the sample Wi in the cluster are found, and the average of the end points is set as Y. Let Z be the projection point from sample X onto hyperplane 1 containing samples of cluster C1. The distance from X to Z is DI, and the distance from Y to Z is D2. If the distance between Y and the point where the straight line connecting Y and Z intersects the boundary surface of the convex stripe is D3, then the distance between cluster C1 and sample X is defined as DI+D2/D3. DI, D2. D
3 is not particularly limited as long as it satisfies distance axioms such as Euclidean distance and City-Brock distance.

The prediction error is defined as follows. The samples belonging to cluster C are Xi (i=l,...n), and the test samples generated using random numbers are Zj (j=1...n).
...m). The distance from cluster C to Zj is Dj, and the distance from the sample of cluster C to Xk (1<=k<
−n) from the cluster consisting of samples excluding Z
Let the distance to j be Dj(-k). The prediction error of cluster C is calculated by calculating the difference between Dj and Dj(-k) for all test samples when all samples of cluster C are removed one by one, and is defined as follows.

ΣΣ(Dj-Dj (-k))" The prediction error when clusters C1 and C2 are combined is calculated by considering clusters C1 and C2 as one cluster, and the prediction error is calculated by considering clusters C1 and C2 as one cluster. The prediction error when not merging is:

The distance to the test sample is calculated as the distance from the closer cluster of clusters C1 and C2. As explained above, the prediction error becomes smaller if the clustering result does not change even if the number of samples decreases by one.

(5) As described in detail of the invention, according to the present invention, clustering is performed based on prediction errors, so even if the training samples are slightly changed, the obtained Tenbrei will hardly change, that is, a small number of biased training samples It becomes possible to determine multiple templates that can recognize test samples different from training samples with high accuracy without being affected by

[Brief explanation of the drawing]

FIG. 1 is a processing block diagram of the present invention, FIG. 2 is an explanatory diagram explaining the definition of the distance from a cluster to a sample point, and FIG.
The figure shows an example of a processing block diagram of a multiple template determination method using a conventional clustering method. Patent applicant Nippon Telegraph and Telephone Corporation

Claims (1)

[Claims] In a processing method for clustering a plurality of samples represented by N-dimensional vectors, in the process of merging clusters starting from an initial state in which each sample forms one cluster, N-dimensional It includes a process of calculating the distance from a cluster to any point in the vector space, a process of calculating the distance between clusters, and a change in the distance to the test sample when some of the samples that make up the cluster are removed. a step of calculating as a prediction error, a step of determining whether to fuse cluster pairs based on the prediction error in the order of the cluster pairs having the smallest inter-cluster distance calculated in the step of calculating the distance between the clusters,
A clustering processing method comprising a step of determining the end of processing based on an inter-cluster distance and a prediction error.