Learning Sparse Representations by Non-Negative Matrix Factorization and Sequential Cone Programming

Matthias Heiler, Christoph Schnörr.

Year: 2006, Volume: 7, Issue: 51, Pages: 1385−1407


We exploit the biconvex nature of the Euclidean non-negative matrix factorization (NMF) optimization problem to derive optimization schemes based on sequential quadratic and second order cone programming. We show that for ordinary NMF, our approach performs as well as existing state-of-the-art algorithms, while for sparsity-constrained NMF, as recently proposed by P. O. Hoyer in JMLR 5 (2004), it outperforms previous methods. In addition, we show how to extend NMF learning within the same optimization framework in order to make use of class membership information in supervised learning problems.