CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2014 vol.36 Issue No.01 - Jan.
Entropy-Rate Clustering: Cluster Analysis via Maximizing a Submodular Function Subject to a Matroid Constraint
Issue No.01 - Jan. (2014 vol.36)
Ming-Yu Liu , Mitsubishi Electr. Res. Labs. (MERL), Mitsubishi Electr. Corp., Cambridge, MA, USA
Oncel Tuzel , Mitsubishi Electr. Res. Labs. (MERL), Mitsubishi Electr. Corp., Cambridge, MA, USA
Srikumar Ramalingam , Mitsubishi Electr. Res. Labs. (MERL), Mitsubishi Electr. Corp., Cambridge, MA, USA
Rama Chellappa , Univ. of Maryland, College Park, MD, USA
We propose a new objective function for clustering. This objective function consists of two components: the entropy rate of a random walk on a graph and a balancing term. The entropy rate favors formation of compact and homogeneous clusters, while the balancing function encourages clusters with similar sizes and penalizes larger clusters that aggressively group samples. We present a novel graph construction for the graph associated with the data and show that this construction induces a matroid--a combinatorial structure that generalizes the concept of linear independence in vector spaces. The clustering result is given by the graph topology that maximizes the objective function under the matroid constraint. By exploiting the submodular and monotonic properties of the objective function, we develop an efficient greedy algorithm. Furthermore, we prove an approximation bound of 1/2 for the optimality of the greedy solution. We validate the proposed algorithm on various benchmarks and show its competitive performances with respect to popular clustering algorithms. We further apply it for the task of superpixel segmentation. Experiments on the Berkeley segmentation data set reveal its superior performances over the state-of-the-art superpixel segmentation algorithms in all the standard evaluation metrics.
discrete optimization, Clustering, superpixel segmentation, graph theory, information theory, submodular function,
Ming-Yu Liu, Oncel Tuzel, Srikumar Ramalingam, Rama Chellappa, "Entropy-Rate Clustering: Cluster Analysis via Maximizing a Submodular Function Subject to a Matroid Constraint", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.36, no. 1, pp. 99-112, Jan. 2014, doi:10.1109/TPAMI.2013.107