Learning computationally efficient dictionaries and their implementation as fast transforms

Luc Le Magoarou 1 Rémi Gribonval 1
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. In this paper, inspired by usual fast transforms, we consider a general dictionary structure that allows cheaper manipulation, and propose an algorithm to learn such dictionaries --and their fast implementation-- over training data. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments.
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https://hal.inria.fr/hal-01010577
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Submitted on : Thursday, February 26, 2015 - 2:31:22 PM
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  • HAL Id : hal-01010577, version 3
  • ARXIV : 1406.5388

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Luc Le Magoarou, Rémi Gribonval. Learning computationally efficient dictionaries and their implementation as fast transforms. 2015. ⟨hal-01010577v3⟩

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