Fuzzy Cluster Analysis and its Evaluation Method(<Special Issue>Contribution to 21 Century Intelligent Technologies and Bioinformatics)

Abstract

Conducting the hierarchical cluster analysis, in fuzzy theory, we often use transitive closure (by Zadeh) to make a matrix follow the transitive law. However, it tends to make the entries in the matrix greatly different from the entries in the original data. With this tendency, various methods have been proposed in the fields of statistical analysis and multivariate analysis, etc. Here, we will not only introduce some typical methods, but also illustrate an evaluation method of their clustering results. On the other hand, the number of clusters may have to be decided in the actual cluster analysis. That is, this is a problem of which cutting level is optimal for a partition tree. Concerning this problem, while the steepest decent method in multivariate analysis and the AIC method in statistical analysis have been designed, we will propose a fuzzy decision method which is based on the evaluation function paying attention to the size and number of clusters at each level. In this paper, we further detail the practical effectiveness of our method through an application to sociometry analysis.