Nonnegative Matrix Factorization with Earth Mover's Distance Metric for Image Analysis.
Source: IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 33, Issue 8, p.1590-1602 (2011)
Abstract: 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 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 L2-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.