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arXiv · 1906.05730

The NMF problem and lattice-subspaces

Ioannis A. Polyrakis
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Abstract

Suppose that $A$ is a nonnegative $n\times m$ 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.

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Ioannis A. Polyrakis. 2019-06-11. The NMF problem and lattice-subspaces. https://arxiv.org/abs/1906.05730

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