A Fuzzy Gap Statistic for Fuzzy C-Means

C. Sentelle, S.L. Hong, M. Georgiopoulos, and G.C. Anagnostopoulos (USA)


Fuzzy C-Means, gap statistic, cluster validity.


The gap statistic is a statistical method for determining the number of optimal clusters for an unsupervised clustering algorithm and has been shown to outperform other cluster validity indices for the K-means clustering algorithm. In this paper, we assess the performance of the gap statistic when applied to the Fuzzy C-Means (FCM) algorithm and introduce a fuzzy gap statistic. We compare the gap statistic performance versus the partition coefficient and entropy indices introduced by Bezdek, the Xie-Beni and extended Xie-Beni indices, and the Fukuyama-Sugeno index. We show that the fuzzy gap statistic is more robust than the ordinary gap statistic for the IRIS data set, and we show promising results when comparing the gap statistic to the traditional fuzzy clustering indices.

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