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

TL;DR

This paper introduces advanced randomized algorithms for distributed principal component analysis and singular value decomposition, demonstrating superior accuracy and orthonormality over traditional methods in distributed computing environments.

Contribution

The paper presents novel randomized algorithms that improve the accuracy and orthonormality of distributed PCA and SVD computations compared to existing deterministic methods.

Findings

Randomized algorithms outperform deterministic methods in distributed PCA/SVD.

Generated singular vectors are nearly orthonormal to machine precision.

Algorithms are effective on highly rectangular matrices in distributed settings.

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.