Recursive principal components analysis using eigenvector matrix perturbation

作     者：Erdogmus, D Rao, YN Peddaneni, H Hegde, A 

作者机构：Oregon Hlth Sci Univ Oregon Grad Inst Dept Comp Sci & Engn Beaverton OR 97006 USA Univ Florida Dept Elect & Comp Engn CNEL Gainesville FL 32611 USA 

出 版 物：《EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING》 (EURASIP信号处理进展杂志)

年 卷 期：2004年第2004卷第13期

页      面：2034-2041页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 

基　　金：National Science Foundation  NSF  (0300340) 

主　　题：PCA recursive algorithm rank-one matrix update 

摘      要：Principal components analysis is an important and well-studied subject in statistics and signal processing. The literature has an abundance of algorithms for solving this problem, where most of these algorithms could be grouped into one of the following three approaches: adaptation based on Hebbian updates and deflation, optimization of a second-order statistical criterion (like reconstruction error or output variance), and fixed point update rules with deflation. In this paper, we take a completely different approach that avoids deflation and the optimization of a cost function using gradients. The proposed method updates the eigenvector and eigenvalue matrices simultaneously with every new sample such that the estimates approximately track their true values as would be calculated from the current sample estimate of the data covariance matrix. The performance of this algorithm is compared with that of traditional methods like Sanger s rule and APEX, as well as a structurally similar matrix perturbation-based method.