On evaluation of clustering using homogeneity analysis

Proposes a new technique to evaluate the results of fuzzy clustering. Fuzzy clustering is a method to obtain “natural groups” from given observations by using the assumption of a fuzzy subset on clusters. By this method, we can obtain the “degree of belongingness” of an object to a cluster, i.e. each object can belong to several clusters with several degrees, and the boundaries of the clusters become uncertain. However, such clustering sometimes causes confusion when trying to understand the clustering behavior, because the clusters are not exclusive, so each cluster has its own property of mixing with other clusters. Sometimes, a very mixed cluster is created, which makes it difficult to interpret the results. In this case, we need to evaluate the cluster homogeneity in the sense of the degree of belongingness. So, in this paper, I propose an evaluation technique for the results of fuzzy clustering using homogeneity analysis. Several numerical examples demonstrate the validity of this method