Structured Sparse Principal Component Analysis

TL;DR

This paper introduces structured sparse PCA, which incorporates higher-order data information through regularization, improving performance in tasks like face recognition and protein dynamics analysis.

Contribution

It extends sparse PCA by integrating structured regularization, enabling the encoding of higher-order data patterns and demonstrating practical benefits.

Findings

Structured sparse PCA outperforms unstructured methods.

Efficient optimization procedure developed.

Improved results in face recognition and protein studies.

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 \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.