Structured Sparse Principal Component Analysis

Abstract

We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This structured sparse PCA is based on a structured regularization recently introduced by Jenatton 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 optimization procedure to solve this problem. Experiments with two practical tasks, the denoising of sparse structured signals and face recognition, demonstrate the benefits of the proposed structured approach over unstructured approaches.