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

As illustrated via numerical experiments with an implementation in Spark (the popular platform for distributed computation), randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a full 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; for instance, 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.