On convergence properties of the singlepass and online fuzzy c-means algorithm

Single pass fuzzy c-means and Online fuzzy c-means are two scalable versions of the widely used fuzzy c-means clustering algorithm. They both facilitate scaling to very large numbers of examples while providing partitions that very closely approximate those one would obtain using fuzzy c-means. They have been successfully applied to a number of data sets, most notably magnetic resonance image volumes of the human brain. In practice, the algorithms have converged on the data sets to which they been applied. Computers are of finite precision, which will allow real values to be converted to integers with minor loss of information. In this paper, we show that they will converge to local minima or saddle points of the modified objective function for any data set when weights are integers.