Collaborative Hierarchical Sparse Modeling

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an 1-regularized linear regression problem, commonly referred to as Lasso or basis pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the individual feature level, with the block-sparsity 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 (HiLasso), 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 (inside the group) level, obtaining the collaborative HiLasso model (C-HiLasso). Such signals then share the same active groups, or classes, but not necessarily the same active set. This model is...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Pablo Sprechmann, Ignacio Ramírez, Guillermo Sapiro, Yonina C. Eldar
• Keywords: CORR 2010, Education, Lasso, Lasso Model, Sparsity Pattern