Unsupervised feature selection for principal components analysis

Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Volumn , Issue , 2008, Pages 61-69

  Boutsidis, Christos ^a   Mahoney, Michael W ^b   Drineas, Petros ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b YAHOO RESEARCH   (United States)

Author keywords

PCA; Random sampling; Subset selection

Indexed keywords

AMOUNT OF INFORMATIONS; APPLICATION DOMAINS; DATA MATRICES; DATA-SETS; EIGENFEATURES; FEATURE MATRIXES; LINEAR DIMENSIONALITY REDUCTIONS; MODERATE VALUES; NUMERICAL LINEAR ALGEBRAS; PCA; PRINCIPAL COMPONENTS ANALYSIS; RANDOM SAMPLING; STATISTICAL DATA ANALYSIS; SUBSET SELECTION; TWO-STAGE ALGORITHMS; UNSUPERVISED FEATURE SELECTIONS;

ALGEBRA; ALGORITHMS; FACE RECOGNITION; FEATURE EXTRACTION; INFORMATION MANAGEMENT; MINING; PRINCIPAL COMPONENT ANALYSIS;

MATRIX ALGEBRA;

EID: 65449139217     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1401890.1401903     Document Type: Conference Paper

References (44)

1. A. d'Aspremont, L. El Ghaoui, M. I. Jordan, and G. R. G. Lanckriet. A Direct Formulation for Sparse PCA Using Semidefinite Programming. SIAM Review, 49(3), July 2007
2. A. Ben-Hur and I. Guyon. Detecting stable clusters using principal component analysis. Methods Mol Biol, 224:159-182, 2003.
3. M.W. Berry, S.A. Pulatova, and G.W. Stewart. Computing sparse reduced-rank approximations to sparse matrices. ACM Trans on Math Soft, 31:252-269, 2005.
4. C. H. Bischof and G. Qintana-Orti. Algorithm 782: codes for rank-revealing QR factorizations of dense matrices. ACM Trans on Math Soft, 24:254-257, 1998.
5. C.H. Bischof and G. Quintana-Orti. Computing rank-revealing QR factorizations of dense matrices. ACM Trans on Math Soft, 24(2):226-253, 1998.
6. C. Boutsidis, M.W. Mahoney, and P. Drineas. Manuscript in preparation, 2008
7. J. Cadima, J. O. Cerdeira, and M. Minhoto. Computational aspects of algorithms for variable selection in the context of principal components. Computational Statistics & Data Analysis, 47(2):225-236, 2004.
8. T. F. Chan. Rank revealing QR factorizations. Linear Algebra Appl, 88/89:67-82, 1987.
9. T.F. Chan and P.C. Hansen. Some applications of the rank revealing QR factorization. SIAM J Sei and Stat Comp, 13:727-741, 1992.
10. T. F. Chan and P.C. Hansen. Low-rank revealing QR factorizations. Linear Algebra Appl, 1:33-44, 1994.
11. S. Chandrasekaran and I. C. F. Ipsen. On rank-revealing factorizations. SIAM J Matrix Anal Appl, 15:592-622, 1994.
12. A. Deshpande, L. Rademacher, S. Vempala, and G. Wang. Matrix approximation and projective clustering via volume sampling. SODA, 2006
13. M. Devaney and A. Ram. Efficient feature selection in conceptual clustering. In ICML, 1997.
14. P. Drineas, M. W. Mahoney, and S. Muthukrishnan. Subspace sampling and relative-error matrix approximation: Column-based methods, APPROX-RANDOM, 2006.
15. P. Drineas, M. W. Mahoney, and S. Muthukrishnan. Relative-error CUR matrix decompositions. http://arxiv.org/abs/0708.3696, 2007.
16. J G. Dy and C. E. Brodley. Feature selection for unsupervised learning. J. Mach. Learn. Res., 5:845-889, 2004.
17. R.D. Fierro, P.C. Hansen, and P. Hansen. UTV tools: Matlab templates for rank-revealing UTV decompositions. Numerical Algorithms, 20(2-3):165-194, 1999.
18. L. V. Foster. Rank and null space calculations using matrix decomposition without column interchanges. Linear Algebra Appl, 74:47-71, 1986.
19. L. V. Foster and Xinrong Liu. Comparison of rank revealing algorithms applied to matrices with well defined numerical ranks, manuscript, 2006.
20. A. Frieze, R. Kannan, and S. Vempala. Fast Monte-Carlo algorithms for finding low-rank approximations, FOCS, 1998
21. E. Gabrilovich and S. Markovitch. Text categorization with many redundant features: using aggressive feature selection to make SVMs competitive with C4.5. ICML, 2004
22. G. H. Golub. Numerical methods for solving linear least squares problems. Numer Math, 7:206-216, 1965.
23. G.H. Golub and C.F. Van Loan. Matrix Computations. Johns Hopkins University Press, Baltimore, 1989.
24. M. Gu and S.C. Eisenstat. Efficient algorithms for computing a strong rank-revealing QR factorization. SIAM J Sci Comp, 17:848-869, 1996.
25. Y. P. Hong and C. T. Pan. Rank-revealing QR factorizations and the singular value decomposition. Math Comp, 58:213-232, 1992.
26. W. J. Krzanowski. Selection of variables to preserve multivariate data structure, using principal components. Applied Statistics, 36(1):22-33, 1987.
27. F.G. Kuruvilla and P.J. Park and S.L. Schreiber. Vector algebra in the analysis of genome-wide expression data. Genome Biology, 3, 2002.
28. K. Z. Mao. Identifying critical variables of principal components for unsupervised feature selection. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 35(2):339-344, 2005.
29. M.W. Mahoney, M. Maggioni, and P. Drineas. Tensor-CUR decompositions for tensor-based data, KDD, 2006.
30. P. Menozzi, A. Piazza, and L. Cavalli-Sforza. Synthetic maps of human gene frequencies in Europeans . Science, 201(4358):786-792, 1978.
31. P. Mitra, C. A. Murthy, and S. K. Pal. Unsupervised feature selection using feature similarity. IEEE Trans. Pattern Anal. Mach. Intell., 24(3):301-312, 2002.
32. Open Directory Project, http://www.dmoz.org/
33. C. T. Pan. On the existence and computation of rank-revealing LU factorizations. Linear Algebra Appl, 316:199-222, 2000.
34. C. T. Pan and P. T. P. Tang. Bounds on singular values revealed by QR factorizations. BIT Numerical Mathematics, 39:740-756, 1999.
35. P. Paschou, E. Ziv, E.G. Burchard, S. Choudhry, W.R. Cintron, M.W Mahoney, and P. Drineas. PCA-Correlated SNPs for Structure Identification in Worldwide Human Populations, PLoS Genetics, 9(3), 2007.
36. P. Paschou, M.W. Mahoney, A. Javed, J.R. Kidd, A.J. Pakstis, S. Gu, K.K. Kidd, and P. Drineas. Intra- and Inter-population genotype reconstruction from tagging SNPs, Genome Research, 17: 96-107, 2007.
37. N.A. Rosenberg, L.M. Li, R. Ward, and J.K. Pritchard. Informativeness of genetic markers for inference of ancestry. Am J Hum Genet, 73(6):1402-1422, 2003.
38. G.W. Stewart. Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix. Num Math, 83:313-323, 1999.
39. H. Stoppiglia, G. Dreyfus, R. Dubois, and Y. Oussar. Ranking a random feature for variable and feature selection. J. Mach. Learn. Res., 3:1399-1414, 2003.
40. J. Sun, Y. Xie, H. Zhang, and C. Faloutsos. Less is more: Compact matrix decomposition for large sparse graphs, SDM, 2007.
41. The International HapMap Consortium. A haplotype map of the human genome. Nature, 437:1299-1320, 2005.
42. L. Wolf and A. Shashua. Feature selection for unsupervised and supervised inference: The emergence of sparsity in a weight-based approach. J. Mach. Learn. Res., 6:1855-1887, 2005.
43. Z. Zhao and H. Liu. Spectral feature selection for supervised and unsupervised learning. In ICML, 2007.
44. http://finance.yahoo.com/