A Selective Overview of Sparse Principal Component Analysis

Principal component analysis (PCA) is a widely used technique for dimension reduction, data processing, and feature extraction. The three tasks are particularly useful and important in high-dimensional data analysis and statistical learning. However, the regular PCA encounters great fundamental challenges under high dimensionality and may produce "wrong" results. As a remedy, sparse PCA (SPCA) has been proposed and studied. SPCA is shown to offer a "right" solution under high dimensions. In this paper, we review methodological and theoretical developments of SPCA, as well as its applications in scientific studies.