Entropy-Rate Clustering: Cluster Analysis via Maximizing a Submodular Function Subject to a Matroid Constraint

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 simi...

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Vydáno v:	IEEE transactions on pattern analysis and machine intelligence Ročník 36; číslo 1; s. 99 - 112
Hlavní autoři:	Ming-Yu Liu, Tuzel, Oncel, Ramalingam, Srikumar, Chellappa, Rama
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Los Alamitos, CA IEEE 01.01.2014 IEEE Computer Society The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithm design and analysis Algorithms Applied sciences Artificial intelligence Clustering Clustering algorithms Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Data processing. List processing. Character string processing discrete optimization Entropy Exact sciences and technology Graph theory Heuristic Image segmentation Information retrieval. Graph information theory Linear programming Mathematics Memory organisation. Data processing Pattern recognition. Digital image processing. Computational geometry Sciences and techniques of general use Software submodular function superpixel segmentation Theoretical computing Topology Uncertainty Cluster analysis Data analysis Graph construction Combinatorial problem Random walk Matroid Group size Cluster Entropy Graph theory Topology Clustering Random graph superpixel segmentation Submodular function Image segmentation Vector space Greedy algorithm discrete optimization Discrete programming Metric Objective function Linear space Information theory
ISSN:	0162-8828, 1939-3539, 2160-9292, 1939-3539
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 ObjectType-Article-2 ObjectType-Feature-1
ISSN:	0162-8828 1939-3539 2160-9292 1939-3539
DOI:	10.1109/TPAMI.2013.107