Talk:Non-negative matrix factorization

message: 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)
thread_title:  Non-negative matrix approximation 

message: 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)
replies: text: 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)
thread_title: Equivalences

message: 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)
thread_title:  Minimizing Divergence 

message: I find the following sentence unclear:
When multiplying matrices the factor matrices can be of significantly lower rank than the product matrix and it's this property that forms the basis of NMF. If we can factorize a matrix into factors of significantly lower rank than the original matrix then the column vectors of the first factor matrix can be considered as spanning vectors of the vector space defined by the original matrix.
The rank of the product of two matrices is lower than the minimal rank among the factors, thus the factor matrices cannot have significantly lower rank than the product matrix.  — Preceding unsigned comment added by Mickaël Poussevin (talk • contribs) 08:22, 8 January 2013 (UTC)
thread_title:  Ranks 

message: The article Online NMF discusses NMF at some length, but its content regarding online optimization algorithms can be summarized in a single paragraph. QVVERTYVS (hm?) 15:38, 21 October 2013 (UTC)
thread_title:  Proposed merge with [[Online NMF]] 

message: I miss a section about missing values (NULL values, None, data imputation). --MartinThoma (talk) 09:06, 22 July 2019 (UTC)
thread_title:  Missing values (imputation, null values, None, ...)