Sparse nonnegative matrix factorization with ℓ 0-constraints

Neurocomputing

Volumn 80, Issue , 2012, Pages 38-46

  Peharz, Robert ^a   Pernkopf, Franz ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

NMF; Nonnegative least squares; Sparse coding

Indexed keywords

BASIS MATRIX; COEFFICIENT MATRIX; LEAST SQUARE; MULTIPLICATIVE UPDATES; NMF; NONNEGATIVE LEAST SQUARES; NONNEGATIVE MATRIX FACTORIZATION; PART-BASED REPRESENTATION; SPARSE CODING; SPARSE NON-NEGATIVE MATRIX FACTORIZATIONS;

FACTORIZATION;

MATRIX ALGEBRA;

ARTICLE; IMAGE QUALITY; IMAGE RECONSTRUCTION; INFORMATION PROCESSING; INTERMETHOD COMPARISON; MACHINE LEARNING; MATHEMATICAL ANALYSIS; NONNEGATIVE MATRIX FACTORIZATION; PRIORITY JOURNAL; REGRESSION ANALYSIS; SIGNAL NOISE RATIO;

EID: 84855246748     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2011.09.024     Document Type: Article

References (40)

1. Lee D.D., Seung H.S. Algorithms for non-negative matrix factorization. NIPS 2001, 556-562.
2. Dhillon I.S., Sra S. Generalized nonnegative matrix approximations with Bregman divergences. NIPS 2005, 283-290.
3. Cichocki A., Lee H., Kim Y.D., Choi S. Non-negative matrix factorization with α-divergence. Pattern Recognition Lett. 2008, 29(9):1433-1440.
4. Paatero P., Tapper U. Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 1994, 5:111-126.
5. Lee D.D., Seung H.S. Learning the parts of objects by nonnegative matrix factorization. Nature 1999, 401:788-791.
6. Smaragdis P., Brown J. Non-negative matrix factorization for polyphonic music transcription. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics 2003, 177-180.
7. Virtanen T. Monaural sound source separation by nonnegative matrix factorization with temporal continuity and sparseness criteria. IEEE Trans. Audio Speech Lang. Process. 2007, 15(3):1066-1074.
8. Févotte C., Bertin N., Durrieu J.L. Nonnegative matrix factorization with the Itakura-Saito divergence: with application to music analysis. Neural Comput. 2009, 21(3):793-830.
9. Peharz R., Stark M., Pernkopf F. A factorial sparse coder model for single channel source separation. Proceedings of Interspeech 2010, 386-389.
10. Xu W., Liu X., Gong Y. Document clustering based on non-negative matrix factorization. Proceedings of ACM SIGIR'03 2003, 267-273.
11. Hoyer P.O. Non-negative sparse coding. Proceedings of Neural Networks for Signal Processing 2002, 557-565.
12. Eggert J., Koerner E. Sparse coding and NMF. International Joint Conference on Neural Networks 2004, 2529-2533.
13. Hoyer P.O. Non-negative matrix factorization with sparseness constraints. J. Mach. Learn. Res. 2004, 5:1457-1469.
14. 1 minimization. Proc. Natl. Acad. Sci. 2003, 100(5):2197-2202.
15. Tropp J. Just relax: convex programming methods for identifying sparse signals. IEEE Trans. Inf. Theory 2006, 51:1030-1051.
16. Vavasis S. On the complexity of nonnegative matrix factorization. SIAM J. Matrix Anal. Appl. J. Optim. 2009, 20(3):1364-1377.
17. Aharon M., Elad M., Bruckstein A. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 2006, 54:4311-4322.
18. Aharon M., Elad M., Bruckstein A. K-SVD and its non-negative variant for dictionary design. Proceedings of the SPIE Conference, Curvelet, Directional, and Sparse Representations II 2005, vol. 5914:11.1-11.13.
19. D. Dueck, B. Frey, Probabilistic Sparse Matrix Factorization, Technical Report PSI TR 2004-023, Department of Computer Science, University of Toronto, 2004.
20. 0 constrained non-negative matrix and tensor factorization. Proceedings of ISCAS 2008, 1328-1331.
21. Efron B., Hastie T., Johnstone I., Tibshirani R. Least angle regression. Ann. Stat. 2004, 32:407-499.
22. Yang Z., Chen X., Zhou G., Xie S. Spectral unmixing using nonnegative matrix factorization with smoothed L0 norm constraint. Proceedings of SPIE 2009.
23. Davis G., Mallat S., Avellaneda M. Adaptive greedy approximations. J. Constr. Approx. 1997, 13:57-98.
24. Pati Y.C., Rezaiifar R., Krishnaprasad P.S. Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. Proceedings of 27th Asilomar Conference on Signals, Systems and Computers 1993, 40-44.
25. Tropp J. Greed is good: algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 2004, 50(10):2231-2242.
26. Bruckstein A.M., Elad M., Zibulevsky M. On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations. IEEE Trans. Inf. Theory 2008, 54:4813-4820.
27. Lawson C., Hanson R. Solving Least Squares Problems 1974, Prentice-Hall.
28. Chen S., Donoho D., Saunders M. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 1998, 20(1):33-61.
29. Van Benthem M., Keenan M. Fast algorithm for the solution of large-scale non-negativity-constrained least-squares problems. J. Chemometrics 2004, 18:441-450.
30. Kim H., Park H. Non-negative matrix factorization based on alternating non-negativity constrained least squares and active set method. SIAM J. Matrix Anal. Appl. 2008, 30:713-730.
31. Lin C.J. Projected gradient methods for nonnegative matrix factorization. Neural Comput. 2007, 19:2756-2779.
32. Li S., Hou X., Zhang H., Cheng Q. Learning spatially localized, parts-based representation. Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR) 2001.
33. Pascual-Montano A., Carazo J., Kochi K., Lehmann D., Pascual-Marqui R. Nonsmooth nonnegative matrix factorization (NSNMF). Transactions on Pattern Analysis and Machine Intelligence 2006.
34. Yang A.Y., Maji S., Hong K., Yan P., Sastry S.S. Distributed compression and fusion of nonnegative sparse signals for multiple-view object recognition. International Conference on Information Fusion 2009.
35. 0-constraints. Proceedings of MLSP 2010, 83-88.
36. Donoho D.L., Tanner J. Sparse nonnegative solutions of underdetermined linear equations by linear programming. Proc. Natl. Acad. Sci. 2005, 102(27):9446-9451.
37. Boyd S., Vandenberghe L. Convex Optimization 2004, Cambridge University Press.
38. Wächter A., Biegler L.T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programming 2006, 106:25-57.
39. Cooke M.P., Barker J., Cunningham S.P., Shao X. An audio-visual corpus for speech perception and automatic speech recognition. J. Am. Stat. Assoc. 2006, 120:2421-2424.
40. Samaria F.S., Harter A. Parameterisation of a stochastic model for human face identification. Proceedings of the 2nd IEEE Workshop on Applications of Computer Vision 1994, 138-142.