Learning Linear and Nonlinear PCA with Linear Programming

Authors:
Rui Zhang;Wenjian Wang
Affiliations:
School of Science, Shandong University of Technology, Zibo, P. R. China 255049;Key Laboratory of Computational Intelligence & Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, P. R. China 30006
Venue:
Neural Processing Letters
Year:
2011

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Abstract

An SVM-like framework provides a novel way to learn linear principal component analysis (PCA). Actually it is a weighted PCA and leads to a semi-definite optimization problem (SDP). In this paper, we learn linear and nonlinear PCA with linear programming problems, which are easy to be solved and can obtain the unique global solution. Moreover, two algorithms for learning linear and nonlinear PCA are constructed, and all principal components can be obtained. To verify the performance of the proposed method, a series of experiments on artificial datasets and UCI benchmark datasets are accomplished. Simulation results demonstrate that the proposed method can compete with or outperform the standard PCA and kernel PCA (KPCA) in generalization ability but with much less memory and time consuming.