Learning hierarchical and topographic dictionaries with structured sparsity

Julien Mairal; Rodolphe Jenatton; Guillaume Obozinski; Francis Bach

doi:10.1117/12.893811

27 September 2011 Learning hierarchical and topographic dictionaries with structured sparsity

Julien Mairal, Rodolphe Jenatton, Guillaume Obozinski, Francis Bach

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81381P (2011) https://doi.org/10.1117/12.893811
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

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.

Citation Download Citation

Julien Mairal, Rodolphe Jenatton, Guillaume Obozinski, and Francis Bach "Learning hierarchical and topographic dictionaries with structured sparsity", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381P (27 September 2011); https://doi.org/10.1117/12.893811

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