Black Hole Entropic Fuzzy Clustering

Abstract

Clustering is a common approach for finding the intrinsic pattern structure embedded in unlabeled data. In this paper, a new clustering algorithm, called black hole entropic fuzzy clustering (BHEFC), is presented to absorb the merits of three aspects: 1) black hole entropy (BHE)-based information theory; 2) fuzzy clustering; and 3) Bayesian inference model. First, through the link between clustering and the black hole phenomenon in astrophysics, the minimum BHE criterion for fuzzy clustering is proposed. Then, it is revealed that BHE-based fuzzy clustering can be realized by using a maximum-a-posteriori (MAP) framework, which in fact indicates that fuzziness and probability can co-jointly work in a collaborative rather than repulsive way. According to the proposed MAP framework for BHEFC, the fuzzifier ${m}$ , which is limited to be less than 1 rather than bigger than 1 in fuzzy ${c}$ -means, can be explained as the partition accuracy in the form of (1− ${m}$ ) for a dataset, and the fuzzy memberships and clustering centers can be determined in a probabilistic inference way, by means of iterative sampling with the assumption of the Dirichlet distribution of the fuzzy memberships. The incremental version of the proposed fuzzy clustering model is also developed here. Experimental results on synthetic and real datasets and images for segmentation demonstrate the improved clustering results of the proposed algorithms over the comparison algorithms.