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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]].
More control over the non-uniqueness of NMF is obtained with spacity contraints<ref>Julian Eggert, Edgar Körner, "[http:dx.doi.org://10.1109/IJCNN.2004.1381036 Sparse coding and NMF]", ''Proceedings. 2004 IEEE International Joint Conference on Neural Networks, 2004., pp. 2529-2533, 2004.</ref>.
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