Enhanced cluster validity index for the evaluation of optimal number of clusters for Fuzzy C-Means algorithm

Abstract

Cluster validity index is a measure to determine the optimal number of clusters denoted by (C) and an optimal fuzzy partition for clustering algorithms. In this paper, we proposed a new cluster validity index to determine an optimal number of hyper-ellipsoid or hyper-spherical shape clusters generated by Fuzzy C-Means (FCM) algorithm called as VI DSO index. The proposed validity index jointly exploits all the three measures named as intra-cluster compactness, an inter-cluster separation and overlap between the clusters. The proposed intra-cluster compactness is based on relative variability concept which is a statistical measure of relative dispersion or scattering of data in various dimensions within the clusters. The proposed inter-cluster separation measure indicates the isolation or distance between the fuzzy clusters. The proposed inter-cluster overlap measure determines the degree of overlap between the fuzzy clusters. The best fuzzy partition produced by the VI DSO index is expected to have low degree of intra-cluster compactness, higher degree of inter-cluster separation and low degree of inter-cluster overlap. The efficacy of VI DSO index is evaluated on six benchmark data sets and compared with a number of known validity indices. The experimental results and the comparative study demonstrate that, the proposed index is highly effective and reliable in estimating the optimal value of C and an optimal fuzzy partition for each data set because, it is insensitive with change in values of fuzzification parameter denoted by m. In contrast, the other indices [2], [3], [6], [7] fails to achieve the optimal value of C due to it is susceptibility with change in m.