Reverse-Convex programming for sparse image codes

Authors:
Matthias Heiler;Christoph Schnörr
Affiliations:
Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany;Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany
Venue:
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Year:
2005

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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 second-order 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.