A LEAST BIASED FUZZY CLUSTERING METHOD

A new operational definition of cluster is proposed, and a fuzzy clustering algorithm with minimal biases is formulated by making use of the Maximum Entropy Principle to maximize the entropy of the centroids with respect to the data points (clustering entropy). We make no assumptions on the number of clusters or their initial positions. For each value of an adimensional scale parameter beta', the clustering algorithm makes each data point iterate towards one of the cluster's centroids, so that both hard and fuzzy partitions are obtained. Since the clustering algorithm can make a multiscale analysis of the given data set we can obtain both hierarchy and partitioning type clustering. The relative stability with respect to beta' of each cluster structure is defined as the measurement of cluster validity. We determine the specific value of beta' which corresponds to the optimal positions of cluster centroids by minimizing the entropy of the data points with respect to the centroids (clustered entropy). Examples are given to show how this least-biased method succeeds in getting perceptually correct clustering results.