The NMF problem and lattice-subspaces

06/11/2019

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by   Ioannis A. Polyrakis, et al.

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Suppose that A is a nonnegative n× m real matrix. The NMF problem is the determination of two nonnegative real matrices F, V so that A=FV with intermediate dimension p smaller than min{ n,m}. In this article we present a general mathematical method for the determination of two nonnegative real factors F,V of A. During the first steps of this process the intermediate dimension p of F,V is determined, therefore we have an easy criterion for p. This study is based on the theory of lattice-subspaces and positive bases. Also we give the matlab program for the computation of F,V but the mathematical part is the main part of this article.