Talk:Non-negative matrix factorization

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Minimizing Divergence

In the section Different cost functions and regularizations it says Each divergence leads to a different NMF algorithm, usually minimizing the divergence using iterative update rules.

This is not true according to:

Amy N. Langville, Michael W. Berry, Murray Browne, V. Paul Pauca, and Robert J. Plemmons. A Survey of Algorithms and Applications for the Nonnegative Matrix Factorization. Computational Statistics and Data Analysis. Elsevier. Submitted Jan. 2006.

»Lee and Seung used the gradient and properties of continual descent (more precisely, continual nonincrease) to claim that the above algorithm converges to a local minimum, which was later shown to be incorrect (Chu et al., 2004; Finesso and Spreij, 2004; Gonzalez and Zhang, 2005; Lin, 2005b). In fact, the proof by Lee and Seung merely shows a continual descent property, which does not preclude descent to a saddle point.«

I think this should be corrected.

--JohKar (talk) 08:04, 7 December 2010 (UTC)[reply]

Equivalences

Also it may not be necessary to keep 2 refs on the NMF-PLSA equivalence. Don't want to offend anybody but it seems the earlier ref. should be enough.

Sunny house 16:03, 15 March 2007 (UTC)[reply]

Did a few edits today. I am a bit confused by the bit about K-means clustering. The formulation and reference [9] seem to imply an equivalence between K-means and NMF. However, in the standard formulation, it can't be so as K-means has no positivity constraints (cf. Lee&Seung's Nature paper). So you need to either relax NMF constraints or add constraints to K-means. Hopefully someone can either correct or clarify the formulation.

Sunny house 16:01, 15 March 2007 (UTC)[reply]

I have been a bit confused too. Please clean up if you like with the K-means and the NMF-PLSA. — fnielsen 20:38, 15 March 2007 (UTC)[reply]

Non-negative matrix approximation

I removed the section about non-negative matrix approximation because there is very little reference to it in the literature (I could only 1 paper linking to this idea). It seems premature to include reference to it at the moment, and its inclusion does not add significantly to the article. Feel free to revert if I am mistaken

--Josephus78 04:18, 22 June 2006 (UTC)[reply]

As you I have only seen the phrase "non-negative matrix approximation" in a single paper, but all the practical applications of NMF that I have seen have been where NMF were approximating the X matrix. -- fnielsen 19:54, 30 June 2006 (UTC)[reply]