Non-negative matrix factorization: Difference between revisions

Revision as of 16:50, 6 June 2007

Revision as of 03:36, 28 June 2007

Line 1:

: ''NMF redirects here. For the [[contract bridge|bridge]] convention, see [[new minor forcing]].''

'''Non-negative matrix factorization''' (NMF)''' is a group of [[algorithm]]s in [[multivariate analysis]] and [[linear algebra]] where a [[matrix (mathematics)|matrix]], <math>\mathbf{X}</math>, is factorized into (usually) two matrices, <math>\mathbf{W}</math> and <math>\mathbf{H}</math> : <math>\operatorname{nmf}(\mathbf{X}) \rightarrow \mathbf{WH} </math>

Factorization of matrices is generally non-unique, and a number of different methods of doing so have been developed (e.g. [[principal component analysis]] and [[singular value decomposition]]) by incorporating different constraints; non-negative matrix factorization differs from these methods in that it enforces the constraint that all three matrices must be [[non-negative matrix|non-negative]], i.e., all elements must be equal to or greater than zero.