A Literature Survey on High-Dimensional Sparse Principal Component Analysis

Abstract

Principal Component Analysis (PCA) is a classical method for dimensionality reduction, data pre-processing, compression and visualization of multivariate data for different applications in biology, social science and engineering. The limitation of PCA is lacking of interpretation due to the non-zero loadings and the inconsistence for highdimensional data. Sparse principal component analysis (sparse PCA) is proposed mainly for the challenges of PCA above. For the past decades, many works of the development methods and theoretical analysis for sparse PCA have been presented. The goal of this paper is to give a comprehensive literatures review to recent progress in highdimensional sparse PCA from algorithm and statistical theory. Firstly we give the overview for PCA and sparse PCA. Secondly the algorithms of sparse PCA are categorized into different classes and provide detailed descriptions for typical formulations and methods in each category, and the typical packages of sparse PCA are also given. Considering that statistical analysis in high dimension becomes more involved in sparse PCA, and then the survey of theoretical analysis of sparse PCA is also presented. Finally the future trends as well as challenges are given.