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Pré-Publication, Document De Travail Année : 2008

Convex Sparse Matrix Factorizations

Résumé

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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Dates et versions

hal-00345747 , version 1 (09-12-2008)

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