March 31, 2010 : Francis Bach

INRIA - Willow project
Laboratoire d'Informatique de l'Ecole Normale Supérieure

Structured Sparse Principal Component Analysis and Dictionary Learning

We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements or decomposition coefficients are structured and constrained to belong to a prespecified set of shapes. This structured sparse PCA is based on a struc- tured regularization recently introduced by Jenat- ton et al. (2009). While classical sparse priors only deal with cardinality, the regularization we use encodes higher-order information about the data. We propose an efficient and simple opti- mization procedure to solve this problem. Ex- periments with three practical tasks, the denoising of sparse structured signals, face recognition, and topic models for text documents, demonstrate the benefits of the proposed structured approach over unstructured approaches.

(joint work with R. Jenatton, J. Mairal and G. Obozinski)

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