Abstract. This article surveys recent research on Non-Negative Matrix Factorization (NNMF), a relatively new technique for dimensionality reduction. It is based on the idea that, in many data-processing tasks, negative numbers are physically meaningless. The NNMF technique addresses this problem by placing non-negativity constraints on the data model. I discuss the applications of NNMF, the proposed algorithms and the qualitative results. Since many of the algorithms suggested for NNMF seem to lack a firm theoret-ical foundation, this article also surveys techniques for proving that iterative algorithms converge. It concludes with a description of additional investigations which are presently underway. 2. NON-NEGATIVE MATRIX FACTORIZATION 3 1.