DMCA
A randomized algorithm for principal component analysis
| Venue: | SIAM Journal on Matrix Analysis and Applications |
| Citations: | 56 - 0 self |
BibTeX
@ARTICLE{Rokhlin_arandomized,
author = {Vladimir Rokhlin and Arthur Szlam and Mark Tygert},
title = {A randomized algorithm for principal component analysis},
journal = {SIAM Journal on Matrix Analysis and Applications},
year = {},
pages = {2009}
}
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Abstract
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a few digits (measured in the spectral norm, relative to the spectral norm of the matrix being approximated). In such circumstances, existing efficient algorithms have not guaranteed good accuracy for the approximations they produce, unless one or both dimensions of the matrix being approximated are small. We describe an efficient algorithm for the low-rank approximation of matrices that produces accuracy very close to the best possible, for matrices of arbitrary sizes. We illustrate our theoretical results via several numerical examples. 1
