Modified fuzzy gap statistic for estimating preferable number of clusters in fuzzy k-means clustering

In clustering methods, the estimation of the optimal number of clusters is significant for subsequent analysis. Without detailed biological information on the genes involved, the evaluation of the number of clusters becomes difficult, and we have to rely on an internal measure that is based on the distribution of the data of the clustering result. The Gap statistic has been proposed as a superior method for estimating the number of clusters in crisp clustering. In this study, we proposed a modified Fuzzy Gap statistic (MFGS) and applied it to fuzzy k-means clustering. For estimating the number of clusters, fuzzy k-means clustering with the MFGS was applied to two artificial data sets with noise and to two experimentally observed gene expression data sets. For the artificial data sets, compared with other internal measures, the MFGS showed a higher performance in terms of robustness against noise for estimating the optimal number of clusters. Moreover, it could be used to estimate the optimal number of clusters in experimental data sets. It was confirmed that the proposed MFGS is a useful method for estimating the number of clusters for microarray data sets.