Principal Component Analysis

Efficient, accurate principal component analysis

Description

The enclosed function PCA implements what is probably the method of choice for computing principal component analyses fairly efficiently, while guaranteeing nearly optimal accuracy. The enclosed function DIFFSNORM provides an efficient, reliable means for checking the accuracies of the low-rank approximations produced by PCA (often the accuracies are slightly better than recently proven bounds guarantee).  
 
Though recently obtained proofs guarantee the accuracy and efficiency of the algorithms implemented in these functions, the enclosed m-files should be considered to be in the beta-testing phase. Although the author has subjected the routines to a battery of tests, he would not be surprised if the functions respond inappropriately to sufficiently bizarre errant input.  
 
Please note that these functions are tailored for the low-rank approximation of large matrices (both dense and sparse).

• MATLAB release: MATLAB 7.6 (R2008a)
• Other Files: pca.m, ; diffsnorm.m

[Mark Tygert]

Sometimes the QR decomposition in the function PCA takes inordinately long compared to squaring a matrix of the same size. This presumably will not change until the recently introduced communication-avoiding QR decompositions become part of the LAPACK suites.