Convex Sparse Matrix Factorizations

Francis Bach 1 Julien Mairal 1 Jean Ponce 1
1 WILLOW - Models of visual object recognition and scene understanding
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In particular, our formulation introduces an explicit trade-off between size and sparsity of the decomposition of rectangular matrices. Using a large set of synthetic examples, we compare the estimation abilities of the convex and non-convex approaches, showing that while the convex formulation has a single local minimum, this may lead in some cases to performance which is inferior to the local minima of the non-convex formulation.
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Submitted on : Tuesday, December 9, 2008 - 5:54:43 PM
Last modification on : Wednesday, January 30, 2019 - 11:07:29 AM
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  • HAL Id : hal-00345747, version 1
  • ARXIV : 0812.1869



Francis Bach, Julien Mairal, Jean Ponce. Convex Sparse Matrix Factorizations. 2008. ⟨hal-00345747⟩



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