Convergence of the Single-Pass and Online Fuzzy C-Means Algorithms

Scalable versions of the widely used fuzzy c-means clustering algorithm called single-pass fuzzy c-means and online fuzzy c-means have been recently introduced. Both algorithms facilitate scaling to very large numbers of examples while providing partitions that very closely approximate those one would obtain using fuzzy c-means. Both algorithms have been successfully applied to a number of datasets, most notably, magnetic resonance image volumes of the human brain. In this letter, we show that weighting examples in the fuzzy c-means algorithm does not cause a violation in its convergence proof, and we provide a separate proof of convergence that holds for any dataset.