Clustering Based on Enhanced (α)-Expansion Move

The exemplar-based data clustering problem can be formulated as minimizing an energy function defined on a Markov random field (MRF). However, most algorithms for optimizing MRF energy function can’t be directly applied to the task of clustering, as the problem has a high-order energy function. In this paper, we first show that the high order energy function for the clustering problem can be simplified as a pairwise energy function with the metric property, and consequently it can be optimized by the α-expansion move algorithm based on graph cut. Then, the original expansion move algorithm is improved in the following two aspects: (I) Instead of solving a minimal s-t graph cut problem, we show that there is an explicit and interpretable solution for minimizing the energy function in the clustering problem. Based on this interpretation, a fast α-expansion move algorithm is proposed, which is much more efficient than the graph cut based algorithm. (II) The fast α-expansion move algorithm is further improved by extending its move space so that a larger energy value reduction can be achieved in each iteration. Experiments on benchmark datasets show the enhanced expansion move algorithm has a better performance, compared to other state-of-the-art exemplar-based clustering algorithms.