Minimum-volume-constrained nonnegative matrix factorization: Enhanced ability of learning parts

IEEE Transactions on Neural Networks

Volumn 22, Issue 10, 2011, Pages 1626-1637

  Zhou, Guoxu ^a   Xie, Shengli ^b   Yang, Zuyuan ^a   Yang, Jun Mei ^a   He, Zhaoshui ^b  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b GUANGDONG UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Blind source separation; nonnegative matrix factorization; sparse representation

Indexed keywords

HUMAN FACE IMAGE; LARGE-SCALE PROBLEM; MULTIPLICATIVE UPDATES; NATURAL GRADIENT; NONNEGATIVE MATRIX FACTORIZATION; SPARSE REPRESENTATION;

BLIND SOURCE SEPARATION; FACTORIZATION; SEPARATION;

MATRIX ALGEBRA;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; BIOLOGICAL MODEL; COMPUTER PROGRAM; HUMAN; METHODOLOGY; STANDARD;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; HUMANS; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); PATTERN RECOGNITION, AUTOMATED; SOFTWARE; SOFTWARE DESIGN;

EID: 80053637334     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2011.2164621     Document Type: Article

References (47)

1. D. D. Lee and H. S. Seung, "Learning the parts of objects by nonnegative matrix factorization," Nature, vol. 401, no. 6755, pp. 788-791, 1999.
2. P. O. Hoyer, "Non-negative matrix factorization with sparseness constraints," J. Mach. Learn. Res., vol. 5, pp. 1457-1469, Nov. 2004.
3. D. Lee and S. Seung, "Algorithms for non-negative matrix factorization," in Proc. Adv. Neural Inf. Process. Syst. 13, 2001, pp. 556-562.
4. F. Y. Wang, C. Y. Chi, T. H. Chan, and Y. Wang, "Nonnegative leastcorrelated component analysis for separation of dependent sources by volume maximization," IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, no. 5, pp. 875-888, May 2010.
5. S. Zafeiriou, "Discriminant nonnegative tensor factorization algorithms," IEEE Trans. Neural Netw., vol. 20, no. 2, pp. 217-235, Feb. 2009.
6. I. Buciu, N. Nikolaidis, and I. Pitas, "Nonnegative matrix factorization in polynomial feature space," IEEE Trans. Neural Netw., vol. 19, no. 6, pp. 1090-1100, Jun. 2008.
7. Z. R. Yang and E. Oja, "Linear and nonlinear projective nonnegative matrix factorization," IEEE Trans. Neural Netw., vol. 21, no. 5, pp. 734-749, May 2010.
8. S. Zafeiriou, A. Tefas, I. Buciu, and I. Pitas, "Exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification," IEEE Trans. Neural Netw., vol. 17, no. 3, pp. 683-695, May 2006.
9. D. Donoho and V. Stodden, "When does non-negative matrix factorization give a correct decomposition into parts?" in Proc. Adv. Neural Inf. Process. Syst. 16, 2003, pp. 1141-1148.
10. A. Cichocki, A. Phan, R. Zdunek, and L.-Q. Zhang, "Flexible component analysis for sparse, smooth, nonnegative coding or representation," in Proc. Neural Inf. Process., 2008, pp. 811-820.
11. M. Heiler and C. Schnorr, "Learning sparse representations by nonnegative matrix factorization and sequential cone programming," J. Mach. Learn. Res., vol. 7, pp. 1385-1407, Jul. 2006. (Pubitemid 44024595)
12. K. Stadlthanner, D. Lutter, F. J. Theis, E. W. Lang, A. M. Tome, P. Georgieva, and C. G. Puntonet, "Sparse nonnegative matrix factorization with genetic algorithms for microarray analysis," in Proc. Int. Joint Conf. Neural Netw., Orlando, FL, Aug. 2007, pp. 294-299.
13. J. Eggert and E. Korner, "Sparse coding and NMF," in Proc. IEEE Int. Joint Conf. Neural Netw., vol. 4. Jul. 2004, pp. 2529-2533. (Pubitemid 40011434)
14. F. J. Theis, K. Stadlthanner, and T. Tanaka, "First results on uniqueness of sparse non-negative matrix," in Proc. 13th Eur. Signal Process. Conf., 2005, pp. 1-4.
15. H. Laurberg and L. K. Hansen, "On affine non-negative matrix factorization," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., Honolulu, HI, Apr. 2007, pp. 653-656.
16. P. O. Hoyer, "Non-negative sparse coding," in Proc. 12th IEEE Workshop Neural Netw. Signal Process., Nov. 2002, pp. 557-565.
17. L. Weixiang, Z. Nanning, and L. Xiaofeng, "Non-negative matrix factorization for visual coding," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 3. Apr. 2003, pp. 293-296.
18. D. L. Donoho and M. Elad, "Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization," Proc. Nat. Acad. Sci. United States Amer., vol. 100, no. 5, pp. 2197-2202, Mar. 2003. (Pubitemid 36297476)
19. M. D. Craig, "Minimum-volume transforms for remotely sensed data," IEEE Trans. Geosci. Remote Sens., vol. 32, no. 3, pp. 542-552, May 1994.
20. J. M. P. Nascimento and J. M. B. Dias, "Vertex component analysis: A fast algorithm to unmix hyperspectral data," IEEE Trans. Geosci. Remote Sens., vol. 43, no. 4, pp. 898-910, Apr. 2005. (Pubitemid 40476033)
21. R. Schachtner, G. Popel, and E. W. Lang, "Toward unique solutions of non-negative matrix factorization problems by a determinant criterion," Digital Signal Process., vol. 21, no. 4, pp. 528-534, Jul. 2011.
22. G. Zhou, Z. Yang, S. Xie, J.-M. Yang, "Online blind source separation using incremental nonnegative matrix factorization with volume constraint," IEEE Trans. Neural Netw., vol. 22, no. 4, pp. 550-560, Apr. 2011.
23. T. H. Chan, C. Y. Chi, Y. M. Huang, and W. K. Ma, "A convex analysisbased minimum-volume enclosing simplex algorithm for hyperspectral unmixing," IEEE Trans. Signal Process., vol. 57, no. 11, pp. 4418-4432, Nov. 2009.
24. A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. New York: Wiley, 2003.
25. V. Zarzoso and P. Comon, "Robust independent component analysis by iterative maximization of the kurtosis contrast with algebraic optimal step size," IEEE Trans. Neural Netw., vol. 21, no. 2, pp. 248-261, Feb. 2010.
26. Y. Washizawa, Y. Yamashita, T. Tanaka, and A. Cichocki, "Blind extraction of global signal from multi-channel noisy observations," IEEE Trans. Neural Netw., vol. 21, no. 9, pp. 1472-1481, Sep. 2010.
27. G. X. Zhou, S. L. Xie, Z. Y. Yang, and J. Zhang, "Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers," IEEE Trans. Neural Netw., vol. 20, no. 11, pp. 1810-1819, Nov. 2009.
28. G. X. Zhou, Z. Y. Yang, S. L. Xie, and J. M. Yang, "Mixing matrix estimation from sparse mixtures with unknown number of sources," IEEE Trans. Neural Netw., vol. 22, no. 2, pp. 211-221, Feb. 2011.
29. D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization," in Proc. Adv. Neural Inf. Process. Syst. 13, 2000, pp. 556-562.
30. S. A. Robila and L. G. Maciak, "Considerations on parallelizing nonnegative matrix factorization for hyperspectral data unmixing," IEEE Geosci. Remote Sens. Lett., vol. 6, no. 1, pp. 57-61, Jan. 2009.
31. R. Schachtner, G. Pöppel, A. Tomé, and E. Lang, "Minimum determinant constraint for non-negative matrix factorization," in Proc. Independ. Comp. Anal. Signal Separat., 2009, pp. 106-113.
32. D. P. Bertsekas, Nonlinear Programming, 2nd ed. Belmont, MA: Athena Scientific, 1999.
33. B. Nils, "The gramian and K-volume in N-space: Some classical results in linear algebra," J. Young Investigat., vol. 2, no. 1, pp. 1-4, 1999.
34. A. Cichocki, R. Zdunek, and S. I. Amari, "Nonnegative matrix and tensor factorization [lecture notes]," IEEE Signal Process. Mag., vol. 25, no. 1, pp. 142-145, Jan. 2008.
35. S. Amari, "Natural gradient works efficiently in learning," Neural Comput., vol. 10, no. 2, pp. 251-276, Mar. 1998. (Pubitemid 128463152)
36. C. J. Lin, "On the convergence of multiplicative update algorithms for nonnegative matrix factorization," IEEE Trans. Neural Netw., vol. 18, no. 6, pp. 1589-1596, Nov. 2007.
37. R. Badeau, N. Bertin, and E. Vincent, "Stability analysis of multiplicative update algorithms and application to nonnegative matrix factorization," IEEE Trans. Neural Netw., vol. 21, no. 12, pp. 1869-1881, Dec. 2010.
38. R. Zdunek and A. Cichocki, "Nonnegative matrix factorization with constrained second-order optimization," Signal Process., vol. 87, no. 8, pp. 1904-1916, Aug. 2007. (Pubitemid 46590394)
39. C. Boutsidis and E. Gallopoulos, "SVD based initialization: A head start for nonnegative matrix factorization," Pattern Recognit., vol. 41, no. 4, pp. 1350-1362, 2008. (Pubitemid 350212975)
40. Y. Xue, C. S. Tong, Y. Chen, and W. S. Chen, "Clustering-based initialization for non-negative matrix factorization," Appl. Math. Comput., vol. 205, no. 2, pp. 525-536, Nov. 2008.
41. T. H. Chan, W. K. Ma, C. Y. Chi, and Y. Wang, "A convex analysis framework for blind separation of non-negative sources," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 5120-5134, Oct. 2008.
42. M. D. Plumbley and E. Oja, "A 'nonnegative PCA' algorithm for independent component analysis," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 66-76, Jan. 2004.
43. P. Hoyer. (2004). NMFpack (1.1st ed.) [Online]. Available: http://www.cs.helsinki.fi/patrik.hoyer
44. A. Cichocki and R. Zdunek. (2006). NMFLAB for Signal Processing NMFLAB - MATLAB Toolbox for Non-Negative Matrix Factorization [Online]. Available: http://www.bsp.brain.riken.jp/ICALAB/nmflab.html
45. A. Hyvarinen, "The fixed-point algorithm and maximum likelihood estimation forindependent component analysis," Neural Process. Lett., vol. 10, no. 1, pp. 1-5, Aug. 1999.
46. H. Shen, M. Kleinsteuber, and K. Huper, "Local convergence analysis of fastICA and related algorithms," IEEE Trans. Neural Netw., vol. 19, no. 6, pp. 1022-1032, Jun. 2008.
47. C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, "The quickhull algorithm for convex hulls," ACM Trans. Math. Softw., vol. 22, no. 4, pp. 469-483, Dec. 1996. (Pubitemid 126417394)