Math @ Duke

Publications [#265064] of Guillermo Sapiro
Papers Published
 Sprechmann, P; Ramirez, I; Sapiro, G; Eldar, Y, Collaborative hierarchical sparse modeling,
2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
(2010) [doi]
(last updated on 2018/03/21)
Abstract: Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an ℓ1regularized linear regression problem, usually called Lasso. In this work we first combine the sparsityinducing property of the Lasso model, at the individual feature level, with the blocksparsity property of the group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the hierarchical Lasso, which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level but not necessarily at the lower one. Signals then share the same active groups, or classes, but not necessarily the same active set. This is very well suited for applications such as source separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the new framework and optimization approach is complemented with experimental examples and preliminary theoretical results. ©2010 IEEE.


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