June 15, 2009

Non-negative Matrix Factorization

Non-negative matrix factorization (NMF) is a group of algorithms in multivariate analysis and linear algebra where a matrix, X, is factorized into (usually) two matrices, W and H.

A( M by N ) = W(M by K) X H( K by N )

W,H : Initialize W and H to random positive matrices.
W = ||W*H-A||
H = ||H(T)W(T)-A(T)||

Iterates W*H until convergence.

See also,
- http://en.wikipedia.org/wiki/Non-negative_matrix_factorization, WIKIPEDIA
- Non-Negative Matrix Factorization with sparseness constraints
- Non-Negative Matrix Factorization Techniques and Optimizations
- Document Clustering Based On Non-negative Matrix Factorization

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