Algorithm 971 swMATH ID: 22686 Software Authors: H. Li, G. C. Linderman, A. Szlam, K. P. Stanton, Y. Kluger, M. Tygert Description: Algorithm 971: An implementation of a randomized algorithm for principal component analysis. Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis and the calculation of truncated singular value decompositions. The present article presents an essentially black-box, foolproof implementation for Mathworks’ MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical deterministic techniques (such as Lanczos iterations run to convergence) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces). Homepage: https://dl.acm.org/citation.cfm?id=3004053 Keywords: Statistical Software; Principal component analysis; PCA; singular value decomposition; SVD; TOMS_publication Related Software: ARPACK; LSRN; Blendenpik; LAPACK; SparseMatrix; rsvd; RandNLA; UTV; JDQR; JDQZ; ASKIT; SPQR_RANK; LibSkylark; SDPLR; ProxSDP; SE-Sync; SDPNAL+; Manopt; DIMACS; Mosek Cited in: 10 Documents Standard Articles 1 Publication describing the Software Year all top 5 Cited by 25 Authors 3 Kluger, Yuval 3 Tropp, Joel A. 2 Cevher, Volkan 2 Li, Huamin 2 Linderman, George C. 2 Tygert, Mark 2 Udell, Madeleine 2 Yurtsever, Alp 1 Bjarkason, Elvar K. 1 Buhr, Andreas 1 Fercoq, Olivier 1 Floater, Michael S. 1 Gu, Yu 1 Jaffe, Ariel 1 Li, Yaohang 1 Manni, Carla 1 Martinsson, Per-Gunnar 1 Mishne, Gal 1 Sande, Espen 1 Smetana, Kathrin 1 Speleers, Hendrik 1 Stanton, Kelly P. 1 Steinerberger, Stefan 1 Szlam, Arthur D. 1 Yu, Wenjian all top 5 Cited in 7 Serials 3 SIAM Journal on Matrix Analysis and Applications 2 SIAM Journal on Scientific Computing 1 ACM Transactions on Mathematical Software 1 Journal of Applied Probability 1 Advances in Computational Mathematics 1 Acta Numerica 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 9 Fields 9 Numerical analysis (65-XX) 3 Computer science (68-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Approximations and expansions (41-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year