Algorithm 971: An implementation of a randomized algorithm for principal component analysis

ACM Transactions on Mathematical Software

Volumn 43, Issue 3, 2017, Pages

  Li, Huamin ^a   Linderman, George C ^a   Szlam, Arthur ^b   Stanton, Kelly P ^a   Kluger, Yuval ^a   Tygert, Mark ^a  

^a YALE UNIVERSITY   (United States)

^b FACEBOOK   (United States)

Author keywords

PCA; Principal component analysis; Singular value decomposition; SVD

Indexed keywords

APPROXIMATION ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL EFFICIENCY; DIGITAL FILTERS; MATLAB; SINGULAR VALUE DECOMPOSITION;

DETERMINISTIC TECHNIQUE; LANCZOS ITERATIONS; LOW RANK APPROXIMATIONS; NUMERICAL COMPUTATIONS; RANDOMIZED ALGORITHMS; SINGULAR SUBSPACES; SOFTWARE PLATFORMS; TRUNCATED SINGULAR VALUE DECOMPOSITION;

PRINCIPAL COMPONENT ANALYSIS;

EID: 85011340773     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/3004053     Document Type: Article

References (18)

1. Alliance for Telecommunications Industry Solutions Committee PRQC. 2011. ATIS Telecom Glossary, American National Standard T1.523. Alliance for Telecommunications Industry Solutions (ATIS), American National Standards Institute (ANSI), Washington, DC.
2. Edward Anderson, Zhaojun Bai, Christian Bischof, Laura Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, and Daniel Sorensen. 1999. LAPACK User's Guide. SIAM, Philadelphia, PA.
3. Haim Avron, Costas Bekas, Christos Boutsidis, Kenneth Clarkson, Prabhanjan Kambadur, Giorgos Kollias, Michael Mahoney, Ilse Ipsen, Yves Ineichen, Vikas Sindhwani, and David Woodruff. 2014. Lib-Skylark: Sketching-Based Matrix Computations for Machine Learning. IBM Research, in collaboration with Bloomberg Labs, NCSU, Stanford, UC Berkeley, and Yahoo Labs. Retrieved from http://xdataskylark.github.io/libskylark.
4. Michael Berry, Dany Mezher, Bernard Philippe, and Ahmed Sameh. 2003. Parallel computation of the singular value decomposition. Research report RR-4694, INRIA.
5. Timothy A. Davis and Yifan Hu. 2011. The university of Florida sparse matrix collection. ACM Trans. Math. Softw. 38, 1 (2011), 1:1-1:25.
6. Leslie V. Foster and Timothy A. Davis. 2013. Algorithm 933: Reliable calculation of numerical rank, null space bases, pseudoinverse solutions, and basic solutions using SuiteSparseQR. ACM Trans. Math. Softw. 40, 1 (Sep. 2013), 1-23. DOI:http://dx.doi.org/10.1145/2513109.2513116
7. Gene Golub and Charles Van Loan. 2012. Matrix Computations (4th ed.). Johns Hopkins University Press.
8. Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp. 2011. Finding structure with randomness: Probabilistic algorithms for constructing approximatematrix decompositions. SIAM Rev. 53, 2 (2011), 217-288.
9. Jacek Kuczyński and Henryk Woźniakowski. 1992. Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start. SIAM J. Matrix Anal. Appl. 13, 4 (1992), 1094-1122.
10. Rasmus Larsen. 2001. Combining implicit restart and partial reorthogonalization in Lanczos bidiagonalization. Presentation at U.C. Berkeley, sponsored by Stanford's Scientific Computing and Computational Mathematics (succeeded by the Institute for Computational and Mathematical Engineering). Retrieved from http://sun.stanford.edu/∼rmunk/PROPACK/talk.rev3.pdf.
11. Richard Lehoucq, Daniel Sorensen, and Chao Yang. 1998. ARPACK User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, Philadelphia, PA.
12. Per-Gunnar Martinsson and Sergey Voronin. 2015. A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices.1-12.
13. Frank McSherry and Dimitris Achlioptas. 2007. Fast computation of low-rank matrix approximations. J. ACM 54, 2 (Apr. 2007), 1-19.
14. Srinivas Rachakonda, Rogers F. Silva, Jingyu Liu, and Vince Calhoun. 2014. Memory-efficient PCA approaches for large-group ICA. (2014). fMRI Toolbox, Medical Image Analysis Laboratory, University of New Mexico.
15. Gil Shabat, Yaniv Shmueli, and Amir Averbuch. 2013. Randomized LU Decomposition. Technical Report 1310.7202. arXiv.
16. RafiWitten and Emmanuel Candes. 2015. Randomized algorithms for low-rank matrix factorizations: Sharp performance bounds. Algorithmica 72, 1 (May 2015), 264-281.
17. Herman Wold. 1966. Estimation of principal components and related models by iterative least squares. In Multivariate Analysis, Parachuri R. Krishnaiaah (Ed.). Academic Press, 391-420.
18. David Woodruff. 2014. Sketching as a Tool for Numerical Linear Algebra. Foundations and Trends in Theoretical Computer Science, Vol. 10. Now Publishers.