Structured Sparse Principal Component Analysis

Rodolphe Jenatton (1) , Guillaume Obozinski (1) , Francis Bach (1)

1 WILLOW - Models of visual object recognition and scene understanding

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 \emph{structured sparse PCA} is based on a structured regularization recently introduced by [1]. While classical sparse priors only deal with \textit{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, face recognition and the study of the dynamics of a protein complex, demonstrate the benefits of the proposed structured approach over unstructured approaches.

Mots clés: Sparsity; PCA; Dictionary learning; Block coordinate descent

Domaines: Autres [stat.ML]

Rodolphe Jenatton, Guillaume Obozinski, Francis Bach. Structured Sparse Principal Component Analysis. 2009. ⟨hal-00414158v1⟩