Earticle

초록

영어

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.

목차

Abstract
 1. Introduction
 2. Overview of PCA and Sparse PCA
  2.1. Notation
  2.2. Formulations of PCA
  2.3. Basic Formulations of Sparse PCA
 3. Sparse PCA: Formulations and Algorithms
  3.1. Sparse PCA from Data-Variance-Maximization View
  3.2. Sparse PCA from Data-Variance-Maximization View
  3.3. Sparse PCA from Data-Variance-Maximization View
 4. Sparse PCA Software Package
 5. Theoretical Analysis of High-Dimensional Sparse PCA
  5.1. Spiked-Covariance Model
  5.2. Statistical Properties of High-Dimensional Sparse PCA
 6. Discussions and Challenges
  6.1. Performance Improvements of Algorithms (Sparse PCA)
  6.2. Trade-Off Theoretical and Computational Sparse PCA
  6.3. Extending the Application of Sparse PCA
 References

키워드

저자

• Shen Ning-min [ College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China ]
• Li Jing [ College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China ]

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Database Theory and Application

• 간기

  격월간

• pISSN

  2005-4270

• 수록기간

  2008~2016

• 십진분류

  KDC 505 DDC 605