A cluster validation index for GK cluster analysis based on relative degree of sharing

In this paper, the problem of traditional validity indices when applied to the Gustafson-Kessel (GK) clustering are reviewed. A new cluster validity index for the GK algorithm is proposed. This validity index is defined as the average value of the relative degrees of sharing of all possible pairs of fuzzy clusters in the system. It computes the overlap of each pair of fuzzy clusters by considering the degree of sharing of each data point in the overlap. The optimal number of clusters is obtained by minimizing the validity index. Experiments in which the proposed validity index and several traditional validity indices were applied to 6 data sets highlight the superior qualities of the proposed index. The results indicate that the proposed validity index is very reliable.