Reverse-Convex Programming for Sparse Image Codes

Abstract. Reverse-convex programming (RCP) concerns global optimization of a specific class of non-convex optimization problems. We show that a recently proposed model for sparse non-negative matrix factorization (NMF) belongs to this class. Based on this result, we design two algorithms for sparse NMF that solve sequences of convex secondorder cone programs (SOCP). We work out some well-defined modifications of NMF that leave the original model invariant from the optimization viewpoint. They considerably generalize the sparse NMF setting to account for uncertainty in sparseness, for supervised learning, and, by dropping the non-negativity constraint, for sparsity-controlled PCA.

• Type: Conference
• Year: 2005
• Where: EMMCVPR
• Authors: Matthias Heiler, Christoph Schnörr
• Keywords: EMMCVPR 2005, Non-convex Optimization Problems, Sparse Nmf, Sparse Non-negative Matrix