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CVPR
2009
IEEE

Nonnegative Matrix Factorization with Earth Mover's Distance metric

9 years 7 months ago
Nonnegative Matrix Factorization with Earth Mover's Distance metric
Nonnegative Matrix Factorization (NMF) approximates a given data matrix as a product of two low rank nonnegative matrices, usually by minimizing the L2 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 a new NMF algorithm that minimizes the Earth Mover's Distance (EMD) error between the data and the matrix product. We propose an iterative NMF algorithm (EMD NMF) and prove its convergence. The algorithm is based on linear programming. We discuss the numerical difficulties of the EMD NMF and propose an efficient approximation. Naturally, the matrices obtained with EMD NMF are different from those obtained with L2 NMF. We discuss these differences in the context of two challenging computer vision tasks
Roman Sandler, Michael Lindenbaum
Added 16 Aug 2010
Updated 16 Aug 2010
Type Conference
Year 2009
Where CVPR
Authors Roman Sandler, Michael Lindenbaum
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