Non-negative matrix factorization

Non-negative matrix factorization (NMF) is a group of algorithms in multivariate analysis and linear algebra where a matrix, <math>\mathbf{X}</math>, is factorized into two matrices, <math>\mathbf{W}</math> and <math>\mathbf{H}</math> : <math>\operatorname{nmf} \rightarrow \mathbf{WH} </math> Factorization of matrices is generally non-unique, and a number of different methods of doing so have been developed by incorporating different constraints; non-negative matrix factorization differs from these methods in that it enforces the constraint that the factors W and H must be non-negative, i.e., all elements must be equal to or greater than zero.