ON CLUSTER VALIDITY FOR THE FUZZY C-MEANS MODEL

Many functionals have been proposed for validation of partitions of object data produced by the fuzzy c-means (FCM) clustering algorithm. We examine the role a subtle but important parameter-the weighting exponent m of the FCM model-plays in determining the validity of FCM partitions, The functionals considered are the partition coefficient and entropy indexes of Bezdek, the Xie-Beni, and extended Xie-Beni indexes, and the Fukuyama-Sugeno index. Limit analysis indicates, and numerical experiments confirm, that the Fukuyama-Sugeno index is sensitive to both high and low values of m and may be unreliable because of this. Of the indexes tested, the Xie-Beni index provided the best response over a wide range of choices for the number of clusters, (2-10), and for m from 1.01-7, Finally, our calculations suggest that the best choice for rn is probably in the interval [1.5, 2.5], whose mean and midpoint, m = 2, have often been the preferred choice for many users of FCM.