Extension of the gap statistics index to fuzzy clustering

The well-known gap statistic index proposed by Tibshirani et al. has successfully applied in many clustering evaluations. However, the gap statistic index cannot evaluate the clustering partitions from any fuzzy clustering algorithm. This is because fuzzy clustering cannot provide the within-cluster similarity measure that is used in the gas statistic index. Thus, the applicable range of the gap statistic index is very limited. In this paper, we present a new method that extends the gap statistic index to fuzzy clustering by using fuzzy membership notations. Our proposed method can extend the applicability of the gap statistic index, and outperform other existing fuzzy indices in several aspects. Experiments on eight sets of synthetic and real datasets are used to verify the applicability and efficiency of the proposed method.