Randomized algorithms for distributed computation of principal component analysis and singular value decomposition

Huamin Li; Yuval Kluger; Mark Tygert

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arXiv · 1612.08709

Randomized algorithms for distributed computation of principal component analysis and singular value decomposition

Huamin Li·Yuval Kluger·Mark Tygert

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Abstract

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a low-rank approximation (in the form of a singular value decomposition) to an arbitrary matrix. Carefully honed algorithms yield results that are uniformly superior to those of the stock, deterministic implementations in Spark (the popular platform for distributed computation); in particular, whereas the stock software will without warning return left singular vectors that are far from numerically orthonormal, a significantly burnished randomized implementation generates left singular vectors that are numerically orthonormal to nearly the machine precision.

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BibTeX RIS

Huamin Li, Yuval Kluger, Mark Tygert. 2016-12-27. Randomized algorithms for distributed computation of principal component analysis and singular value decomposition. https://arxiv.org/abs/1612.08709

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