Sparse Principal Component Analysis via Rotation and Truncation

Abstract

This chapter begins with the motivation of sparse PCA-to improve the physical interpretation of the loadings. Second, we introduce the issues involved in sparse PCA problem that are distinct from PCA problem. Third, we briefly review some sparse PCA algorithms in the literature, and comment their limitations as well as problems unresolved. Forth, we introduce one of the state-of-the-art algorithms, SPCArt Hu et al. (IEEE Trans. Neural Networks Learn. Syst. 27(4):875-890, 2016), including its motivating idea, formulation, optimization solution, and performance analysis. Along with the introduction, we describe how SPCArt addresses the unresolved problems. Fifth, based on the Eckart-Young Theorem, we provide a unified view to a series of sparse PCA algorithms including SPCArt. Finally, we make a concluding remark.