CUR matrix decompositions for improved data analysis

Proceedings of the National Academy of Sciences of the United States of America

Volumn 106, Issue 3, 2009, Pages 697-702

  Mahoney, Michael W ^a   Drineas, Petros ^b  

^a STANFORD UNIVERSITY   (United States)

^b Rensselaer Polytechnic Institute   (United States)

Author keywords

Interpretation; Principal components analysis; Randomized algorithms; Singular value decomposition; Statistical leverage

Indexed keywords

ALGORITHM; ANALYTICAL ERROR; ARTICLE; CANCER DIAGNOSIS; CANCER GROWTH; CANCER SURVIVAL; COLON ADENOCARCINOMA; COLORECTAL CARCINOMA; DATA ANALYSIS; GASTROINTESTINAL STROMAL TUMOR; GENE EXPRESSION; HUMAN; LEIOMYOSARCOMA; PRINCIPAL COMPONENT ANALYSIS; PRIORITY JOURNAL; REGRESSION ANALYSIS; STATISTICAL ANALYSIS; SYNOVIAL SARCOMA; VARIANCE;

EID: 58849086813     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.0803205106     Document Type: Article

References (32)

1. Golub GH, Van Loan CF (1996) Matrix Computations (Johns Hopkins Univ Press, Baltimore).
2. Gould SJ (1996) The Mismeasure of Man (W. W. Norton, New York).
3. Wall ME, Rechtsteiner A, Rocha LM (2003) Singular value decomposition and principal component analysis. In A Practical Approach to Microarray Data Analysis, eds Berrar DP, Dubitzky W, Granzow M (Kluwer, Boston), pp 91-109.
4. Cho RJ, et al. (1998) A genome-wide transcriptional analysis of the mitotic cell cycle. Mol Cell 2:65-73.
5. Kuruvilla FG, Park PJ, Schreiber SL (2002) Vector algebra in the analysis of genomewide expression data. Genome Biol 3:research0011.1-0011.11.
6. Blinkhorn SF (1995) Burt and the early history of factor analysis. In Cyril Burt: Fraud or Framed? ed Mackintosh NJ (Oxford Univ Press, New York).
7. Stewart GW (1999) Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix. Numer Math 83:313-323.
8. Berry MW, Pulatova SA, Stewart GW (2004) Computing sparse reduced-rank approximations to sparse matrices. Technical Report UMIACS TR-2004-32 CMSC TR-4589 (University of Maryland, College Park, MD).
9. Goreinov SA, Tyrtyshnikov EE, Zamarashkin NL (1997) A theory of pseudoskeleton approximations. Linear Algebra and Its Applications 261:1-21.
10. Goreinov SA, Tyrtyshnikov EE (2001) The maximum-volume concept in approximation by low-rank matrices. Contemp Math 280:47-51.
11. Frieze A, Kannan R, Vempala S (2004) Fast Monte-Carlo algorithms for finding low-rank approximations. J ACM 51(6):1025-1041.
12. Drineas P, Kannan R, Mahoney MW (2006) Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition. SIAM J Comput 36:184-206.
13. Mahoney MW, Maggioni M, Drineas P (2006) Tensor-CUR decompositions for tensorbased data. Proceedings of the 12th Annual ACM SIGKDD Conference (Association for Computing Machinery, New York), pp 327-336.
14. Paschou P, et al. (2007) Intra- and interpopulation genotype reconstruction from tagging SNPs. Genome Res 17:96-107.
15. Drineas P, Mahoney MW, Muthukrishnan S (2008) Relative-error CUR matrix decompositions. SIAM J Matrix Anal Appl 30:844-881.
16. Stewart GW, Sun JG (1990) Matrix Perturbation Theory (Academic, New York).
17. Nashed MZ, ed (1976) Generalized Inverses and Applications (Academic, New York).
18. Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, New York).
19. Hoaglin DC, Welsch RE (1978) The hat matrix in regression and ANOVA. Am Stat 32:17-22.
20. Chatterjee S, Hadi AS (1988) Sensitivity Analysis in Linear Regression (Wiley, New York).
21. Chatterjee S, Hadi AS (1986) Influential observations, high leverage points, and outliers in linear regression. Stat Sci 1:379-393.
22. Velleman PF, Welsch RE (1981) Efficient computing of regression diagnostics. Am Stat 35:234-242.
23. Chatterjee S, Hadi AS, Price B (2000) Regression Analysis by Example (Wiley, New York).
24. Deerwester ST, Dumais ST, Furnas GW, Landauer TK, Harshman R (1990) Indexing by latent semantic analysis. J Am Soc Inf Sci 41:391-407.
25. Landauer TK, Laham D, Derr M (2004) From paragraph to graph: Latent semantic analysis for information visualization. Proc Natl Acad Sci USA 101:5214-5219.
26. Open Directory Project. Available at http://www.dmoz.org/. Accessed October 8, 2007.
27. Gabrilovich E, Markovitch S (2004) Text categorization with many redundant features: using aggressive feature selection to make SVMs competitive with C4.5. Proceedings of the 21th International Conference on Machine Learning (Association for Computing Machinery, New York), pp 41-48.
28. Alter O, Brown PO, Botstein D (2000) Singular value decomposition for genomewide expression data processing and modeling. Proc Natl Acad Sci USA 97:10101-10106.
29. Holter NS, et al. (2000) Fundamental patterns underlying gene expression profiles: Simplicity from complexity. Proc Natl Acad Sci USA 97:8409-8414.
30. Nielsen T, et al. (2002) Molecular characterisation of soft tissue tumours: A gene expression study. Lancet 359:1301-1307.
31. Poole KT, Rosenthal H (1991) Patterns of congressional voting. Am J Political Sci 35:228-278.
32. Porter MA, Mucha PJ, Newman MEJ, Warmbrand CM (2005) A network analysis of committees in the U.S. House of Representatives. Proc Natl Acad Sci USA 102:7057-7062.