An algorithm for the principal component analysis of large data sets

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy -- even on parallel processors -- unlike the classical (deterministic) alternatives. We adapt one of these randomized methods for use with data sets that are too large to be stored in random-access memory (RAM). (The traditional terminology is that our procedure works efficiently out-of-core.) We illustrate the performance of the algorithm via several numerical examples. For example, we report on the PCA of a data set stored on disk that is so large that less than a hundredth of it can fit in our computer's RAM. Key words. algorithm, principal component analysis, PCA, SVD, singular value decomposition, low rank AMS subject classifications. 65F15, 65C60, 68W20

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Nathan Halko, Per-Gunnar Martinsson, Yoel Shkolnisky, Mark Tygert
• Keywords: CORR 2010, Education, Optimal Accuracy, Principal Component Analysis, Randomized