Classification Rules in Methods of Clustering

While classification rules are essential in supervised classification methods, they are not noticed well in methods of clustering. Nevertheless, some clustering techniques have clear rules of classification, while they are not obvious in other methods. This paper discusses classification rules or classification functions in the former class including K-means, fuzzy c-means, and the mixture of distributions, and shows theoretical properties that exhibit the nature of a method in this class. In contrast, linkage methods of agglomerative hierarchical clustering do not appear to have classification rules. We show, however, the single linkage method has the rule of nearest neighbor classification, while other linkage methods not. An advanced method using positive-definite kernels is also discussed.