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It was used by a Finish group of researchers in the middle of the 1990s under the name ''positive matrix factorization''.
It became more widely known after Lee and Seung's investigations of the properties of the algorithm, and after they published a simple usefull algorithm.
== Uniqueness ==
The factorization is not unique: A matrix and its [[inverse matrix|inverse]] can be used to transform the two factorization matrix, e.g.,
: <math>\mathbf{WH} = \mathbf{WBB}^{-1}\mathbf{H}</math>
If the two new matrices <math>\mathbf{\tilde{W} = WB}</math> and <math>\mathbf{\tilde{H}}=\mathbf{B}^{-1}\mathbf{H}</math> are [[non-negative matrix|non-negative]] they form another parametrization of the factorization.
The non-negativity of <math>\mathbf{\tilde{W}}</math> and <math>\mathbf{\tilde{H}}</math> applies at least if <b>B</b> is a non-negative [[monomial matrix]].
In this simple case it will just correspond to a scaling and a [[permutation]].
== Sources and external links ==
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