Nonnegative sparse PCA with provable guarantees

31st International Conference on Machine Learning, ICML 2014

Volumn 5, Issue , 2014, Pages 3717-3735

  Asteris, Megasthenis ^a   Papailiopoulos, Dimitris S ^a   Dimakis, Alexandras G ^a  

^a The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; EIGENVALUES AND EIGENFUNCTIONS; LEARNING SYSTEMS; MATRIX ALGEBRA;

DATA DEPENDENT; INPUT MATRICES; NOVEL ALGORITHM; POSITIVE SEMIDEFINITE MATRICES; PRINCIPAL COMPONENTS; SPECTRAL PROFILE; STATE OF THE ART; TIME POLYNOMIALS;

APPROXIMATION ALGORITHMS;

EID: 84919822057     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. Allen, Genevera I. and Maletič-Savatič, Mirjana. Sparse nonnegative generalized pea with applications to metabolomics. Bioinformatics, 2011.
2. Armstrong, Scott A, Staunton, Jane E, Silverman, Lewis B, Pieters, Rob, den Boer, Monique L, Minden, Mark D, Sallan, Stephen E, Lander, Eric S, Golub, Todd R, and Korsmeyer, Stanley J. Mil translocations specify a distinct gene expression profile that distinguishes a unique leukemia. Nature genetics, 30(1):41-47, 2001.
3. Asteris, M., Papailiopoulos, D.S., and Karystinos, G.N. Sparse principal component of a rank-deficient matrix. In Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on, pp. 673-677, 2011.
4. Bache, K. and Lichman, M. UCI machine learning repository, 2013. URL http://archive.ics.uci.edu/ml.
5. Badea, Liviu and Tilivea, Doina. Sparse factorizations of gene expression guided by binding data. In Pacific Symposium on Biocomputing, 2005.
6. d'Aspremont, A., El Ghaoui, L., Jordan, M.I., and Lanckriet, G.R.G. A direct formulation for sparse pea using semidefinite programming. SIAM review, 49(3):434-448, 2007a.
7. d'Aspremont, Alexandre, Bach, Francis R., and Ghaoui, Laurent El. Full regularization path for sparse principal component analysis. In Proceedings of the 24th international conference on Machine learning, ICML '07, pp. 177-184, New York, NY, USA, 2007b. ACM.
8. d'Aspremont, Alexandre, Bach, Francis, and Ghaoui, Laurent El. Optimal solutions for sparse principal component analysis. J. Mach. Learn. Res., 9:1269-1294, Jun 2008.
9. Hoyer, Patrik O. Non-negative matrix factorization with sparse-ness constraints. Journal of Machine Learning Research, 5: 1457-1469, 2004.
10. Jolliffe, IT. Rotation of principal components: choice of normalization constraints. Journal of Applied Statistics, 22(l).29-35, 1995.
11. Jolliffe, I.T, Trendafilov, N.T., and Uddin, M. A modified principal component technique based on the lasso. Journal of Computational and Graphical Statistics, 12(3):531-547, 2003.
12. Karystinos, G.N. and Liavas, A.P. Efficient computation of the binary vector that maximizes a rank-deficient quadratic form. Information Theory, IEEE Transactions on, 56(7):3581-3593, 2010.
13. Kim, Hyunsoo and Park, Haesun. Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics, 23(12): 1495-1502, 2007.
14. Lee, Daniel D and Seung, H Sebastian. Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755): 788-791, 1999.
15. Mackey, Lester. Deflation methods for sparse pea. In Advances in Neural Information Processing Systems 21, NIPS '08, pp. 1-8, Vancouver, Canada, Dec 2008.
16. Moghaddam, B., Weiss, Y, and Avidan, S. Spectral bounds for sparse pea: Exact and greedy algorithms. Advances in neural information processing systems, 18:915, 2006a.
17. Moghaddam, Baback, Weiss, Yair, and Avidan, Shai. Generalized spectral bounds for sparse Ida. In Proceedings of the 23rd international conference on Machine learning, ICML '06, pp. 641-648, 2006b.
18. Murty, Katta G. and Kabadi, Santosh N. Some np-complete problems in quadratic and nonlinear programming. Mathematical Programming, 39(2): 117-129, 1987.
19. Papailiopoulos, D. S., Dimakis, A. G., and Korokythakis, S. Sparse pea through low-rank approximations. In Proceedings of the 30th International Conference on Machine Learning, ICML '13, pp. 767-774. ACM, 2013.
20. Parrilo, Pablo A. Structured Semidenite Programs and Semialge-braic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology Pasadena, California, 2000.
21. Sigg, Christian D. and Buhmann, Joachim M. Expectation-maximization for sparse and non-negative pea. In Proceedings of the 25th International Conference on Machine Learning, ICML '08, pp. 960-967, New York, NY, USA, 2008. ACM.
22. Sung, Kah-Kay. Learning and example selection for object and pattern recognition. PhD thesis, PhD thesis, MIT, Artificial Intelligence Laboratory and Center for Biological and Computational Learning, Cambridge, MA, 1996.
23. Zass, Ron and Shashua, Amnon. Nonnegative sparse pea. In Advances in Neural Information Processing Systems 19. pp. 1561-1568, Cambridge, MA, 2007. MIT Press.
24. Zhang, Y, d'Aspremont, A., and Ghaoui, L.E. Sparse pea: Convex relaxations, algorithms and applications. Handbook on Semidefinite, Conic and Polynomial Optimization, pp. 915-940, 2012.
25. Zou, H., Hastie, T., and Tibshirani, R. Sparse principal component analysis. Journal of computational and graphical statistics, 15 (2):265-286, 2006.