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.
Bibliographical noteFunding Information:
Manuscript received January 30, 2018; revised May 28, 2018; accepted June 8, 2018. Date of current version August 2, 2018. The work of H. Zou was supported in part by the National Science Foundation (NSF) under Grant DMS-1505111. The work of L. Xue was supported by the National Science Foundation (NSF) under Grant DMS-1505256. (Corresponding author: Hui Zou.) H. Zou is with the Department of Statistics, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: firstname.lastname@example.org). L. Xue is with the Pennsylvania State University, State College, PA 16801 USA (e-mail: email@example.com).
- Covariance matrices
- mathematical programming
- principal component analysis (PCA)
- statistical learning