An integrity-based fuzzy c-means method resolving cluster size sensitivity problem

Cluster size insensitive FCM (csiFCM) dynamically adjusts the membership value of each object based on the size of the cluster to which it is assigned after defuzzification to resolve the size sensitivity problem. Our investigation indicates that csiFCM cannot correctly partition datasets containing clusters with dispersive data distribution or insignificant distinction from others, if initial cluster centers are not properly selected. In this paper, we present a concept of cluster integrity and propose an enhanced conditional FCM, itgFCM, based on both cluster integrity and cluster size. For objects classified to a cluster of high integrity after defuzzification, itgFCM assigns their condition values predominantly depending on the size of that cluster. If an object is assigned to a cluster of low integrity, itgFCM adjusts the size-dependent condition value with a multiplicative weight that grows with both the complement of cluster integrity and the object´s purity. Experimental results demonstrate that itgFCM can partition numerical datasets as well as synthetic and real images of various number of classes to clusters that are more conforming to human perception than csiFCM can, regardless of both initial cluster centers and data distribution of the datasets.