An error convergence simulation study of hard vs. fuzzy c-means clustering

We have previously demonstrated that the fuzzy c-means (FCM) algorithm is effective for separating cerebrospinal fluid (CSF), white and gray matter tissue clusters in brain magnetic resonance images of children with and without hydrocephalus. In this paper we report results of some simulation studies comparing the hard c-means (HCM) algorithm, FCM and a variant of FCM referred to as SFCM. We show that under certain conditions of cluster shape, size and overlap, the two fuzzy algorithms are more stable than HCM in the sense that the error decreases more monotonically as a function of iteration number. We also demonstrate that the second error difference should be used as a stopping criterion for FCM. Finally, we show that maximizing the sum of squared memberships is a better indicator of the number of clusters present in the data than a criterion based on both minimizing the intracluster distance and maximizing the intercluster distance