DocumentCode :
1436887
Title :
Nonnegative Matrix Factorization with Earth Mover´s Distance Metric for Image Analysis
Author :
Sandler, Roman ; Lindenbaum, Michael
Author_Institution :
Yahoo! Res., Haifa, Haifa, Israel
Volume :
33
Issue :
8
fYear :
2011
Firstpage :
1590
Lastpage :
1602
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.
Keywords :
image classification; image segmentation; image texture; linear programming; matrix decomposition; computer vision applications; data matrix; earth mover distance metric; face recognition; image analysis; image segmentation; linear programming methods; nonnegative matrix factorization; texture classification; Approximation algorithms; Earth; Histograms; Image segmentation; Linear programming; Measurement; Pixel; Nonnegative matrix factorization; earth mover´s distance; image segmentation.;
fLanguage :
English
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publisher :
ieee
ISSN :
0162-8828
Type :
jour
DOI :
10.1109/TPAMI.2011.18
Filename :
5703094
Link To Document :
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