## On the equivalence between non-negative matrix factorization and probabilistic latent semantic indexing.(English)Zbl 1452.62053

Summary: 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 $$\chi ^{2}$$-statistic.

### MSC:

 62-08 Computational methods for problems pertaining to statistics

WebACE
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### References:

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