Probabilistic Distance Clustering: Algorithm and Applications

The probabilistic distance clustering method of the authors [2, 8], assumes the cluster membership probabilities given in terms of the distances of the data points from the cluster centers, and the cluster sizes. A resulting extremal principle is then used to update the cluster centers (as convex combinations of the data points), and the cluster sizes (if not given.) Progress is monitored by the joint distance function (JDF), a weighted harmonic mean of the above distances, that approximates the data by capturing the data points in its lowest contours. The method is described, and applied to clustering, location problems, and mixtures of distributions, where it is a viable alternative to the Expectation–Maximization (EM) method. The JDF also helps to determine the “right” number of clusters for a given data set