A Fuzzy Clustering and Fuzzy Merging Algorithm

Some major problems in clustering are: i) find the optimal number K of clusters; ii) assess the validity of a given clustering; iii) permit the classes to form natural shapes rather than forcing them into normed balls of the distance function; iv) prevent the order in which the feature vectors are read in from affecting the clustering; and v) prevent the order of merging from affecting the clustering. The k-means algorithm is the most efficient, easiest to implement and has known convergence, but it suffers from all of the above deficiencies. We employ a relatively large number K of uniformly randomly distributed initial prototypes and then thin by deleting any prototypes that are too close to another in a manner to leave fewer uniformly distributed prototypes. We then employ the k-means algorithm, eliminate empty and very small clusters and iterate a process of computing a new type of fuzzy prototypes and reassigning the feature vectors until the prototypes become fixed. At that point we merge the K small clusters into a smaller number K of larger classes. The algorithm is tested on both simple and difficult data sets. We modify the Xie-Bene validity measure to determine the goodness of the clustering for multiple values of K.