Abstract: As a generalization of the conventional possibilistic and kernel based possibilistic clustering model, a new kernel based possibilistic clustering model was proposed. The new approach performs the clustering by optimizing the proposed kernel possibilistic Xie-Beni index using the RJMCMC (Reversible Jump Markov Chain Monte Carlo) based simulated annealing algorithm (SA), which makes the number of clusters change in a given range and the optimal number of clusters and partitioning obtained automatically. In contrast to the conventional SA based possibilistic or kernel based possibilistic clustering, it has a higher efficiency and avoids the problem of generating coincident clusters. The contrast experiments on real and artificial data show the effectiveness of the proposed algorithm.

Key words: possibilistic clustering, simulated annealing, reversible jump Markov chain Monte Carlo (RJMCMC), kernel function, cluster validity