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2008

On the equivalence between Non-negative Matrix Factorization and Probabilistic Latent Semantic Indexing

11 years 1 months ago
On the equivalence between Non-negative Matrix Factorization and Probabilistic Latent Semantic Indexing
Non-negative Matrix Factorization (NMF) and Probabilistic Latent Semantic Indexing (PLSI) have been successfully applied to document clustering recently. In this paper, we show that PLSI and NMF (with the I-divergence objective function) optimize the same objective function, although PLSI and NMF are different algorithms as verified by experiments. This provides a theoretical basis for a new hybrid method that runs PLSI and NMF alternatively, each jumping out of the local minima of the other method successively, thus achieving a better final solution. Extensive experiments on five real-life datasets show relations between NMF and PLSI, and indicate that the hybrid method leads to significant improvements over NMF-only or PLSI-only methods. We also show that at first-order approximation, NMF is identical to the 2-statistic. c 2008 Published by Elsevier B.V.
Chris H. Q. Ding, Tao Li, Wei Peng
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where CSDA
Authors Chris H. Q. Ding, Tao Li, Wei Peng
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