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Proceedings Paper

Learning hierarchical and topographic dictionaries with structured sparsity
Author(s): Julien Mairal; Rodolphe Jenatton; Guillaume Obozinski; Francis Bach
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Paper Abstract

Recent work in signal processing and statistics have focused on defining new regularization functions, which not only induce sparsity of the solution, but also take into account the structure of the problem. We present in this paper a class of convex penalties introduced in the machine learning community, which take the form of a sum of ℓ2- andℓ- norms over groups of variables. They extend the classical group-sparsity regularization in the sense that the groups possibly overlap, allowing more flexibility in the group design. We review efficient optimization methods to deal with the corresponding inverse problems, and their application to the problem of learning dictionaries of natural image patches: On the one hand, dictionary learning has indeed proven effective for various signal processing tasks. On the other hand, structured sparsity provides a natural framework for modeling dependencies between dictionary elements. We thus consider a structured sparse regularization to learn dictionaries embedded in a particular structure, for instance a tree or a two-dimensional grid. In the latter case, the results we obtain are similar to the dictionaries produced by topographic independent component analysis.

Paper Details

Date Published: 27 September 2011
PDF: 13 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381P (27 September 2011); doi: 10.1117/12.893811
Show Author Affiliations
Julien Mairal, Univ. of California, Berkeley (United States)
Rodolphe Jenatton, Institut National de Recherche en Informatique et en Automatique, CNRS, ENS (France)
Guillaume Obozinski, Institut National de Recherche en Informatique et en Automatique, CNRS, ENS (France)
Francis Bach, Institut National de Recherche en Informatique et en Automatique, CNRS, ENS (France)

Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)

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