Algorithms for nonnegative matrix factorization with the β-divergence

Neural Computation

Volumn 23, Issue 9, 2011, Pages 2421-2456

  Févotte, Cédric ^a   Idier, Jérôme ^b  

^a INSTITUT TELECOM   (France)

^b UNIVERSITÉ DE NANTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80051594038     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00168     Document Type: Letter

References (53)

1. Badeau, R., Bertin, N., & Vincent, E. (2010). Stability analysis of multiplicative update algorithms and application to non-negative matrix factorization. IEEE Transactions on Neural Networks, 21(12), 1869-1881.
2. Basu, A., Harris, I. R., Hjort, N. L., & Jones, M. C. (1998). Robust and efficient estimation by minimising a density power divergence. Biometrika, 85(3), 549-559.
3. Berry, M. W., Browne, M., Langville, A. N., Pauca, V. P., & Plemmons, R. J. (2007). Algorithms and applications for approximate nonnegative matrix factorization. Computational Statistics and Data Analysis, 52(1), 155-173.
4. Bertin, N., Févotte, C., & Badeau, R. (2009). A tempering approach for Itakura-Saito non-negative matrix factorization. With application to music transcription. In Proc. International Conference on Acoustics, Speech and Signal Processing (pp. 1545-1548). Piscataway, NJ: IEEE.
5. Brunet, J.-P., Tamayo, P., Golub, T. R.,&Mesirov, J. P. (2004).Metagenes and molecular pattern discovery using matrix factorization. In Proceedings of the NationalAcademy of Sciences, 101, 4164-4169.
6. Cao, Y., Eggermont, P. P. B., & Terebey, S. (1999). Cross Burg entropy maximization and its application to ringing suppression in image reconstruction. IEEE Transactions on Image Processing, 8(2), 286-292.
7. Cemgil, A. T. (2009). Bayesian inference for nonnegative matrix factorisation models. Computational Intelligence and Neuroscience, 2009, 785152. doi:10.1155/2009/785152.
8. Cichocki, A., & Amari, S. (2010). Families of alpha- beta- and gamma-divergences: Flexible and robust measures of similarities. Entropy, 12(6), 1532-1568.
9. Cichocki, A., Lee, H.,Kim, Y.-D.,&Choi, S. (2008). Non-negativematrix factorization with α-divergence. Pattern Recognition Letters, 29(9), 1433-1440.
10. Cichocki, A., Zdunek, R., & Amari, S. (2006). Csiszar's divergences for non-negative matrix factorization: Family ofnewalgorithms. In Proc. 6th InternationalConference on Independent Component Analysis and Blind Signal Separation (ICA'06) (pp. 32-39). Berlin: Springer.
11. Daube-Witherspoon, M., & Muehllehner, G. (1986). An iterative image space reconstruction algorithm suitable for volume ECT. IEEE Transactions on Medical Imaging, 5(5), 61-66.
12. De Pierro, A. R. (1993). On the relation between the ISRA and the EM algorithm for positron emission tomography. IEEE Trans. Medical Imaging, 12(2), 328-333.
13. Dessein, A., Cont, A., & Lemaitre, G. (2010). Real-time polyphonic music transcription with non-negative matrix factorization and beta-divergence. In Proc. 11th International Society for Music Information Retrieval Conference. Society for Music Information Retrieval.
14. Dhillon, I. S., & Sra, S. (2005). Generalized nonnegative matrix approximations with Bregman divergences. In B. Schölkopf, J. Platt, & T. Hoffman (Eds.), Advances in neural information processing systems, 19. Cambridge, MA: MIT Press.
15. Ding, C. H. Q., Li, T., & Jordan, M. I. (2010). Convex and semi-nonnegative matrix factorizations. IEEE Transactions on Pattern Analysis andMachine Intelligence, 32(1), 45-55.
16. Donoho, D., & Stodden, V. (2004). When does non-negative matrix factorization give a correct decomposition into parts? In S. Thrun, L. Saul, & B. Schölkopf (Eds.), Advances in neural information processing systems, 16. Cambridge, MA: MIT Press.
17. Drakakis, K., Rickard, S., de Frein, R., & Cichocki, A. (2007). Analysis of financial data using non-negative matrix factorization. International Mathematical Forum, 3, 1853-1870.
18. Eggermont, P. P. B., & LaRiccia, V. N. (1998). On EM-like algorithms for minimum distance estimation. http://www.udel.edu/FREC/eggermont/Preprints/emlike.pdf.
19. Eguchi, S., & Kano, Y. (2001). Robustifying maximum likelihood estimation. (Tech. Rep. Research Memo 802). Tokyo: Institute of Statistical Mathematics.
20. Févotte, C., Bertin, N., & Durrieu, J.-L. (2009). Nonnegative matrix factorization with the Itakura-Saito divergence. With application to music analysis. Neural Computation, 21(3), 793-830.
21. Févotte, C.,&Cemgil, A. T. (2009). Nonnegative matrix factorisations as probabilistic inference in composite models. In Proc. 17th European Signal Processing Conference (EUSIPCO) (pp. 1913-1917). EURASIP.
22. FitzGerald, D., Cranitch, M., & Coyle, E. (2009). On the use of the beta divergence for musical source separation. In Proc. Irish Signals and Systems Conference.
23. Gao, Y., & Church, G. (2005). Improving molecular cancer class discovery through sparse non-negative matrix factorization. Bioinformatics, 21, 3970-3975.
24. Gonzalez, E. F.,&Zhang,Y. (2005). Accelerating the Lee-Seung algorithm for non-negative matrix factorizations (Tech. Rep.). Houston, TX: Rice University.
25. Greene, D.,Cagney, G.,Krogan, N.,&Cunningham, P. (2008). Ensemble non-negative matrix factorization methods for clustering protein-protein interactions. Bioinformatics, 24(15), 1722-1728.
26. Hennequin, R., Badeau, R.,&David, B. (2010). NMF with time-frequency activations to model non stationary audio events. In Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'10) (pp. 445-448). Piscataway, NJ: IEEE.
27. Ho, N.-D. (2008). Nonnegative matrix factorization algorithms and applications. Unpublished doctoral dissertation, Université Catholique de Louvain.
28. Hunter,D. R.,&Lange, K. (2004). Atutorial on MM algorithms. American Statistician, 58, 30-37.
29. Kim, D., Sra, S., & Dhillon, I. S. (2008). Fast projection-based methods for the least squares nonnegative matrix approximation problem. Statistical Analysis and Data Mining, 1, 38-51.
30. Kompass, R. (2007). A generalized divergence measure fon nonnegative matrix factorization. Neural Computation, 19(3), 780-791.
31. Lantéri, H., Roche, M., Cuevas, O., & Aime, C. (2001). A general method to devise maximum-likelihood signal restoration multiplicative algorithms with nonnegativity constraints. Signal Processing, 81(5), 945-974.
32. Lantéri, H., Theys, C., Richard, C., & Févotte, C. (2010). Split gradient method for nonnegative matrix factorization. In Proc. 18th European Signal Processing Conference (EUSIPCO). EURASIP.
33. Laurberg,H., Christensen, M., Plumbley, M. D., Hansen, L. K., & Jensen, S. H. (2008). Theorems on positive data: On the uniqueness ofNMF. Computational Intelligence and Neuroscience, article 764206.
34. Le Roux, J., Kameoka, H.,Ono, N., de Cheveigné, A.,&Sagayama, S. (2008). Computational auditory induction by missing-data non-negative matrix factorization. In Proc. ISCA Workshop on Statistical and Perceptual Audition (SAPA) (pp. 1-6).
35. Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects with nonnegative matrix factorization. Nature, 401, 788-791.
36. Lee, D. D., & Seung, H. S. (2001). Algorithms for non-negative matrix factorization. In T. K. Leen, T. G. Dietterich, & K.-R. Müller (Eds.), Advances in neural and information processing systems, 13 (pp. 556-562). Cambridge, MA: MIT Press.
37. Lin, C.-J. (2007a). On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Transactions on Neural Networks, 18, 1589-1596.
38. Lin, C.-J. (2007b). Projected gradient methods for nonnegative matrix factorization. Neural Computation, 19, 2756-2779.
39. Lucy, L. B. (1974). An iterative technique for the rectification of observed distributions. Astronomical Journal, 79, 745-754.
40. Mairal, J., Bach, F., Ponce, J., & Sapiro, G. (2010). Online learning for matrix factorization and sparse coding. Journal of Machine Learning Research, 11, 10-60.
41. Minami, M., & Eguchi, S. (2002). Robust blind source separation by beta-divergence. Neural Computation, 14, 1859-1886.
42. Mørup, M., & Clemmensen, L. H. (2007). Multiplicative updates for the LASSO. In Proc. IEEE Workshop on Machine Learning for Signal Processing. Piscataway, NJ: IEEE.
43. Mørup, M., & Hansen, L. K. (2009). Tuning pruning in sparse non-negative matrix factorization. In Proc. 17th European Signal Processing Conference (EUSIPCO'09). EURASIP.
44. Nakano, M., Kameoka, H., Le Roux, J., Kitano, Y., Ono, N., & Sagayama, S. (2010). Convergence-guaranteed multiplicative algorithms for non-negative matrix factorization with beta-divergence. In Proc. IEEE International Workshop on Machine Learning for Signal Processing. Piscataway, NJ: IEEE.
45. O'Grady, P. D. (2007). Sparse separation of under-determined speech mixtures. Unpublished doctoral dissertation, National University of Ireland Maynooth.
46. O'Grady, P. D., & Pearlmutter, B. A. (2008). Discovering speech phones using convolutive non-negative matrix factorisation with a sparseness constraint. Neurocomputing, 72(1-3), 88-101.
47. Pauca, V. P., Piper, J., & Plemmons, R. J. (2006). Nonnegative matrix factorization for spectral data analysis. Linear Algebra and Its Applications, 416, 29-47.
48. Richardson, W. H. (1972). Bayesian-based iterative method of image restoration. Journal of the Optical Society of America, 62, 55-59.
49. Salakhutdinov, R., & Roweis, S. (2003). Adaptive overrelaxed bound optimization methods. In Proc. International Conference on Machine Learning (pp. 664-671). CSREA Press.
50. Smaragdis, P., & Brown, J. C. (2003). Non-negative matrix factorization for polyphonic music transcription. In IEEE Workshop on Applications of Signal Processing to Audio and Acoustics. Piscataway, NJ: IEEE Press.
51. Smaragdis, P., Raj, B., & Shashanka, M. (2009). Missing data imputation for spectral audio signals. In IEEE International Workshop on Machine Learning for Signal Processing. Piscataway, NJ: IEEE Press.
52. Titterington, D.M. (1987). On the iterative image space reconstruction algorithm for ECT. IEEE Trans. Medical Imaging, 6(1), 52-56.
53. Vincent, E., Bertin, N., & Badeau, R. (2010). Adaptive harmonic spectral decomposition for multiple pitch estimation. IEEE Trans. Audio, Speech and Language Processing, 18, 528-537.