Simulated annealing using a reversible jump Markov chain Monte Carlo algorithm for fuzzy clustering

In this paper, an approach for automatically clustering a data set into a number of fuzzy partitions with a simulated annealing using a reversible jump Markov chain Monte Carlo algorithm is proposed. This is in contrast to the widely used fuzzy clustering scheme, the fuzzy c-means (FCM) algorithm, which requires the a priori knowledge of the number of clusters. The said approach performs the clustering by optimizing a cluster validity index, the Xie-Beni index. It makes use of the homogeneous reversible jump Markov chain Monte Carlo (RJMCMC) kernel as the proposal so that the algorithm is able to jump between different dimensions, i.e., number of clusters, until the correct value is obtained. Different moves, like birth, death, split, merge, and update, are used for sampling a candidate state given the current state. The effectiveness of the proposed technique in optimizing the Xie-Beni index and thereby determining the appropriate clustering is demonstrated for both artificial and real-life data sets. In a part of the investigation, the utility of the fuzzy clustering scheme for classifying pixels in an IRS satellite image of Kolkata is studied. A technique for reducing the computation efforts in the case of satellite image data is incorporated.