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Algorithms for Non-negative Matrix Factorization (2001)
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| Venue: | In NIPS |
| Citations: | 1213 - 5 self |
BibTeX
@INPROCEEDINGS{Lee01algorithmsfor,
author = {Daniel D. Lee and H. Sebastian Seung},
title = {Algorithms for Non-negative Matrix Factorization},
booktitle = {In NIPS},
year = {2001},
pages = {556--562},
publisher = {MIT Press}
}
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Abstract
Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the ExpectationMaximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.
Keyphrases
non-negative matrix factorization different multiplicative algorithm expectationmaximization algorithm generalized kullback-leibler divergence useful decomposition monotonic convergence gradient descent multiplicative factor multivariate data rescaling factor update rule auxiliary function
