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Issue No. 08 - August (2011 vol. 33)
ISSN: 0162-8828
pp: 1590-1602
Roman Sandler , Yahoo! Research, Haifa
Michael Lindenbaum , Technion, Israel Institute of Technology, Haifa,
Nonnegative matrix factorization (NMF) approximates a given data matrix as a product of two low-rank nonnegative matrices, usually by minimizing the L_2 or the KL distance between the data matrix and the matrix product. This factorization was shown to be useful for several important computer vision applications. We propose here two new NMF algorithms that minimize the Earth mover's distance (EMD) error between the data and the matrix product. The algorithms (EMD NMF and bilateral EMD NMF) are iterative and based on linear programming methods. We prove their convergence, discuss their numerical difficulties, and propose efficient approximations. Naturally, the matrices obtained with EMD NMF are different from those obtained with L_2-NMF. We discuss these differences in the context of two challenging computer vision tasks, texture classification and face recognition, perform actual NMF-based image segmentation for the first time, and demonstrate the advantages of the new methods with common benchmarks.
Nonnegative matrix factorization, earth mover's distance, image segmentation.

R. Sandler and M. Lindenbaum, "Nonnegative Matrix Factorization with Earth Mover's Distance Metric for Image Analysis," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 33, no. , pp. 1590-1602, 2011.
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