A Convergence Study of the Possibilistic One Means Algorithm

The possibilistic one means (P1M) algorithm finds one single possibilistic cluster in a given data set. Several clusters can be found by sequential runs of P1M, which has been shown to outperform fuzzy clustering for data sets with large numbers of clusters. Several papers have theoretically proven the convergence of possibilistic clustering. Here, we do not prove convergence but analyze the convergence behavior of P1M. Artificial reference data sets containing possibilistic distributions (which for one-dimensional data correspond to Cauchy distributions) are generated. Experiments with such reference data sets indicate that (1) the number of P1M update steps linearly increases with the distance of the initial cluster center estimates, but for large distances converges to one single step, and (2) P1M will accurately find one of the cluster centers if the cluster centers are separate by at least five times the cluster radius. These findings are very useful to predict the performance of P1M clustering and whether for a given data set we can expect good estimates of the cluster centers.