A Purely Geometric Approach to Non-Negative Matrix Factorization

We analyze the geometry behind the problem of non-negative matrix factorization (NMF) and devise yet another NMF algorithm. In contrast to the vast majority of algorithms discussed in the literature, our approach does not involve any form of constrained gradient descent or alternating least squares procedures but is of purely geometric nature. In other words, it does not require advanced mathematical software for constrained optimization but solely relies on geometric operations such as scaling, projections, or volume computations.