Sparse Boolean matrix factorizations

Proceedings - IEEE International Conference on Data Mining, ICDM

Volumn , Issue , 2010, Pages 935-940

  Miettinen, Pauli ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Approximation algorithms; Boolean rank; Matrix decompositions

Indexed keywords

BOOLEAN DECOMPOSITION; BOOLEAN MATRIX; BOOLEAN MATRIX MULTIPLICATION; BOOLEAN RANK; EXISTING METHOD; HARD PROBLEMS; INPUT DATAS; MATRIX DECOMPOSITION; MATRIX DECOMPOSITIONS; MATRIX FACTORIZATIONS; MATRIX MULTIPLICATION; REAL WORLD DATA; SPARSE DATA; SUB-PROBLEMS;

APPROXIMATION ALGORITHMS; DATA MINING; FACTORIZATION;

MATRIX ALGEBRA;

EID: 79951733758     PISSN: 15504786     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICDM.2010.93     Document Type: Conference Paper

References (21)

1. P. Miettinen et al., "The discrete basis problem," IEEE Trans. Knowl. Data Eng., vol. 20, no. 10, pp. 1348-1362, 2008.
2. H. Lu, J. Vaidya, and V. Atluri, "Optimal Boolean matrix decomposition: Application to role engineering," in ICDE, 2008, pp. 297-306.
3. J. Vaidya, V. Atluri, and Q. Guo, "The role mining problem: Finding a minimal descriptive set of roles," in SACMAT, 2007, pp. 175-184. (Pubitemid 47281553)
4. P. O. Hoyer, "Non-negative matrix factorization with sparseness constraints," J. Mach. Learn. Res., vol. 5, pp. 1457-1469, 2004.
5. M. W. Berry, S. A. Pulatova, and G. W. Stewart, "Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices," ACM Trans. Math. Software, vol. 31, no. 2, pp. 252-269, 2005. (Pubitemid 43078387)
6. P. Miettinen, "Matrix decomposition methods for data mining: Computational complexity and algorithms," Ph.D. dissertation, University of Helsinki, 2009.
7. M. W. Berry et al., "Algorithms and applications for approximate nonnegative matrix factorization," Comput. Statist. Data Anal., vol. 52, no. 1, pp. 155-173, 2007. (Pubitemid 47331703)
8. S. D. Monson, N. J. Pullman, and R. Rees, "A survey of clique and biclique coverings and factorizations of (0, 1)-matrices," Bull. ICA, vol. 14, pp. 17-86, 1995.
9. P. Miettinen, "The Boolean column and column-row matrix decompositions," Data Min. Knowl. Discov., vol. 17, no. 1, pp. 39-56, 2008.
10. R. Belohlavek and V. Vychodil, "Discovery of optimal factors in binary data via a novel method of matrix decomposition," J. Comput. System Sci., vol. 76, no. 1, pp. 3-20, 2010.
11. V. Snášel, P. Krömer, J. Platoš, and D. Húsek, "On the implementation of Boolean matrix factorization," in DEXA, 2008, pp. 554-558.
12. F. Geerts, B. Goethals, and T. Mielikäinen, "Tiling databases," in Discovery Science, 2004, pp. 278-289. (Pubitemid 39745469)
13. Z.-Y. Zhang, T. Li, C. Ding, X.-W. Ren, and X.-S. Zhang, "Binary matrix factorization for analyzing gene expression data," Data Min. Knowl. Discov., vol. 20, no. 1, pp. 28-52, 2010.
14. D. S. Nau, G. Markowsky, M. A. Woodbury, and D. B. Amos, "A mathematical analysis of human leukocyte antigen serology," Math. Biosci., vol. 40, pp. 243-270, 1978. (Pubitemid 9045614)
15. L. J. Stockmeyer, "The set basis problem is NP-complete," IBM Thomas J. Watson Research Center, Yorktown Heights, New York, Tech. Rep. RC 5431, 1975.
16. H. U. Simon, "On approximate solutions for combinatorial optimization problems," SIAM J. Discrete Math., vol. 3, no. 2, pp. 294-310, 1990.
17. D. S. Johnson, "Approximation algorithms for combinatiorial problems," J. Comput. System Sci., vol. 9, pp. 256-278, 1974.
18. D. S. Hochbaum, Approximation algorithms for NP-hard problems. PWS Publishing Company, 1996, ch. Approximating covering and packing problems: set cover, vertex cover, independent set, and related problems.
19. D. Lee and H. Seung, "Algorithms for non-negative matrix factorization," NIPS, vol. 13, pp. 556-562, 2001.
20. M. Fortelius et al., "Neogene of the old world database of fossil mammals (NOW)," Online, 2003, http://www.helsinki.fi/science/now/, Accessed 8 December 2008.
21. M. Fortelius, A. Gionis, J. Jernvall, and H. Mannila, "Spectral ordering and biochronology of European fossil mammals," Paleobiology, vol. 32, no. 2, pp. 206-214, 2006. (Pubitemid 43676216)