Evaluation of Fuzzy Clustering

Abstract

What is natural classification? The search for an answer to this question is the basis of fuzzy clustering. The essence of fuzzy clustering is to consider not only the belonging status of an object to the assumed clusters, but also to consider how much each of the objects belong to the clusters. Fuzzy clustering is a method to obtain “natural groups“ in the given observations by using an assumption of a fuzzy subset on clusters. By this method, we can get the degree of belongingness of an object to a cluster. That is, each object can belong to several clusters with several degrees, and the boundaries of the clusters become uncertain. Fuzzy clustering is a natural classification when considering real data. There is no doubt concerning the usefulness of this clustering seeing its wide application to many fields. However, these methods all suffer in that it is difficult to interpret the clusters obtained. Such clustering sometimes causes confusion when trying to understand clustering behavior because each cluster is not exclusive. Each cluster has its own degree of mixing with other clusters. Sometimes, a very mixed cluster is created which makes it difficult to interpret the result. In this case, we need to evaluate the cluster homogeneity in the sense of the degree of belongingness. In this chapter, we describe evaluation techniques [40], [42] for the result of fuzzy clustering using homogeneity analysis [16].