  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.
