{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T05:42:45Z","timestamp":1648532565235},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T00:00:00Z","timestamp":1483920000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"US DoD DARPA Young Faculty Award, U.S.NIH","award":["R0-1 CA158167"]},{"name":"U.S. NIH","award":["1R01HG008383-01A1"]},{"name":"U.S. NIH MSTP Training","award":["T32GM007205"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2017,1,16]]},"abstract":"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\u2019 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).<\/jats:p>","DOI":"10.1145\/3004053","type":"journal-article","created":{"date-parts":[[2017,1,10]],"date-time":"2017-01-10T15:41:17Z","timestamp":1484062877000},"page":"1-14","source":"Crossref","is-referenced-by-count":20,"title":["Algorithm 971"],"prefix":"10.1145","volume":"43","author":[{"given":"Huamin","family":"Li","sequence":"first","affiliation":[{"name":"Yale University Program in Applied Mathematics, New Haven, CT"}]},{"given":"George C.","family":"Linderman","sequence":"additional","affiliation":[{"name":"Yale University Program in Applied Mathematics, New Haven, CT"}]},{"given":"Arthur","family":"Szlam","sequence":"additional","affiliation":[{"name":"Facebook Artificial Intelligence Research"}]},{"given":"Kelly P.","family":"Stanton","sequence":"additional","affiliation":[{"name":"Yale University Department of Pathology and Program in Applied Mathematics"}]},{"given":"Yuval","family":"Kluger","sequence":"additional","affiliation":[{"name":"Yale University Department of Pathology, Program in Applied Mathematics, and Interdepartmental Program in Computational Biology and Bioinformatics"}]},{"given":"Mark","family":"Tygert","sequence":"additional","affiliation":[{"name":"Facebook Artificial Intelligence Research and Yale University"}]}],"member":"320","reference":[{"key":"e_1_2_2_1_1","volume-title":"American National Standard T1.523. Alliance for Telecommunications Industry Solutions (ATIS)","author":"Alliance for Telecommunications Industry Solutions Committee PRQC. 2011."},{"key":"e_1_2_2_2_1","volume-title":"James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, and Daniel Sorensen.","author":"Anderson Edward","year":"1999"},{"key":"e_1_2_2_3_1","unstructured":"Haim Avron Costas Bekas Christos Boutsidis Kenneth Clarkson Prabhanjan Kambadur Giorgos Kollias Michael Mahoney Ilse Ipsen Yves Ineichen Vikas Sindhwani and David Woodruff. 2014. LibSkylark: Sketching-Based Matrix Computations for Machine Learning. IBM Research in collaboration with Bloomberg Labs NCSU Stanford UC Berkeley and Yahoo Labs. Retrieved from http:\/\/xdata-skylark.github.io\/libskylark. Haim Avron Costas Bekas Christos Boutsidis Kenneth Clarkson Prabhanjan Kambadur Giorgos Kollias Michael Mahoney Ilse Ipsen Yves Ineichen Vikas Sindhwani and David Woodruff. 2014. LibSkylark: Sketching-Based Matrix Computations for Machine Learning. IBM Research in collaboration with Bloomberg Labs NCSU Stanford UC Berkeley and Yahoo Labs. Retrieved from http:\/\/xdata-skylark.github.io\/libskylark."},{"key":"e_1_2_2_4_1","unstructured":"Michael Berry Dany Mezher Bernard Philippe and Ahmed Sameh. 2003. Parallel computation of the singular value decomposition. Research report RR-4694 INRIA. Michael Berry Dany Mezher Bernard Philippe and Ahmed Sameh. 2003. Parallel computation of the singular value decomposition. Research report RR-4694 INRIA."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2049662.2049663"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2513109.2513116"},{"key":"e_1_2_2_7_1","volume-title":"Matrix Computations","author":"Golub Gene","edition":"4"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/090771806"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/0613066"},{"key":"e_1_2_2_10_1","volume-title":"Combining implicit restart and partial reorthogonalization in Lanczos bidiagonalization. Presentation at U.C","author":"Larsen Rasmus"},{"key":"e_1_2_2_11_1","volume-title":"ARPACK User\u2019s Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods","author":"Lehoucq Richard"},{"key":"e_1_2_2_12_1","unstructured":"Per-Gunnar Martinsson and Sergey Voronin. 2015. A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. 1--12. Per-Gunnar Martinsson and Sergey Voronin. 2015. A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. 1--12."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1219092.1219097"},{"key":"e_1_2_2_14_1","volume-title":"Medical Image Analysis Laboratory","author":"Rachakonda Srinivas"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-014-9891-7"},{"key":"e_1_2_2_17_1","volume-title":"Estimation of principal components and related models by iterative least squares","author":"Wold Herman"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1561\/0400000060"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3004053","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T12:06:27Z","timestamp":1614600387000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3004053"}},"subtitle":["An Implementation of a Randomized Algorithm for Principal Component Analysis"],"short-title":[],"issued":{"date-parts":[[2017,1,16]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,1,16]]}},"alternative-id":["10.1145\/3004053"],"URL":"http:\/\/dx.doi.org\/10.1145\/3004053","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":["Applied Mathematics","Software"],"published":{"date-parts":[[2017,1,16]]}}}