Learning Hierarchical and Topographic Dictionaries with Structured Sparsity

Details Learning Hierarchical and Topographic Dictionaries with Structured Sparsity Learning Hierarchical and Topographic Dictionaries with Structured Sparsity

2011-10-20

arxiv.org/abs/1110.4481v1

SPIE Wavelets and Sparsity XIV 81381P (2011)

Computer Science

Learning

Scientific paper

10.1117/12.893811

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 l_2 and l_infinity-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.

Affiliated with

Also associated with

No associations

Rating

Learning Hierarchical and Topographic Dictionaries with Structured Sparsity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Learning Hierarchical and Topographic Dictionaries with Structured Sparsity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Learning Hierarchical and Topographic Dictionaries with Structured Sparsity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-551588