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Reverse-Convex Programming for Sparse Image Codes

  • Matthias Heiler
  • Christoph Schnörr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)

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.

Keywords

Positive Matrix Factorization Order Cone Sparsity Measure Sparse Image Project Gradient Descent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Matthias Heiler
    • 1
  • Christoph Schnörr
    • 1
  1. 1.Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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