Abstract

This paper evaluates the performance of 5 previously presented in the literature cluster validity indices for the Fuzzy C-Means (FCM) clustering algorithm. The first two indices, the Fuzzy Partition Coefficient (<i>PC</i>), Fuzzy Partition Entropy Coefficient (<i>PEC</i>) select the number of clusters for which the fuzzy partition is more “crisp-like” or less fuzzy. The other three indices are the Fuzzy Davies-Bouldin Index (<i>FDB</i>), Xie-Beni Index (<i>XB</i>), and the <i>Index I (I)</i> choose the number of clusters which maximizes the inter-cluster separation and minimizes the within cluster scatter. A modification to these three indices is proposed based on the Bhattacharyya distance between clusters. The results show that this modification improves upon the performance of <i>Index I</i>. On the data sets presented on this paper the modifications of indices FDB and XB performed adequately.

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