Multiplicative updates for non-negative projections

Neurocomputing

Volumn 71, Issue 1-3, 2007, Pages 363-373

  Yang, Zhirong ^a   Laaksonen, Jorma ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Hebbian learning; Matrix factorization; Multiplicative update; Non negative projection; Oja's rule

Indexed keywords

DISCRIMINANT ANALYSIS; FACTORIZATION; ITERATIVE METHODS; KNOWLEDGE BASED SYSTEMS; MATRIX ALGEBRA;

HEBBIAN LEARNING; MATRIX FACTORIZATION; MULTIPLICATIVE UPDATE; NON-NEGATIVE PROJECTION; OJA'S RULE;

LEARNING SYSTEMS;

ALGORITHM; ARTICLE; DISCRIMINANT ANALYSIS; LEARNING; MATHEMATICAL COMPUTING; METHODOLOGY; PRIORITY JOURNAL; STATISTICAL ANALYSIS;

EID: 35648932867     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2006.11.023     Document Type: Article

References (24)

1. Amari S. Natural gradient works efficiently in learning. Neural Comput. 10 2 (1998) 251-276
2. Baudat G., and Anouar F. Generalized discriminant analysis using a kernel approach. Neural Comput. 12 10 (2000) 2385-2404
3. Cristianini N., and Shawe-Taylor J. An Introduction to Support Vector Machines (2000), Cambridge University Press, Cambridge
4. Edelman A. The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20 2 (1998) 303-353
5. T. Feng, S.Z. Li, H.Y. Shum, H.J. Zhang, Local non-negative matrix factorization as a visual representation, in: Proceedings, The Second International Conference on Development and Learning, 2002, pp. 178-183.
6. P.J. Flynn, K.W. Bowyer, P.J. Phillips, Assessment of time dependency in face recognition: an initial study, Audio- and Video-Based Biometric Person Authentication, 2003, pp. 44-51.
7. Haykin S. Neural Networks-A Comprehensive Foundation. second ed. (1998), Prentice-Hall, Englewood Cliffs, NJ
8. Hyvärinen A., and Hoyer P. Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces. Neural Comput. 12 7 (2000) 1705-1720
9. Karhunen J., and Joutsensalo J. Generalizations of principal component analysis, optimization problems, and neural networks. Neural Networks 8 4 (1995) 549-562
10. Kivinen J., and Warmuth M. Exponentiated gradient versus gradient descent for linear predictors. Inf. Comput. 132 1 (1997) 1-63
11. Kohonen T. Emergence of invariant-feature detectors in the adaptive-subspace self-organizing map. Biol. Cybern. 75 (1996) 281-291
12. Lee D.D., and Seung H.S. Learning the parts of objects by non-negative matrix factorization. Nature 401 (1999) 788-791
13. D.D. Lee, H.S. Seung, Algorithms for non-negative matrix factorization, in: NIPS, 2000, pp. 556-562.
14. W. Liu, N. Zheng, X. Lu, Non-negative matrix factorization for visual coding, in: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2003), vol. 3, 2003, pp. 293-296.
15. Mika S., Rtsch G., Weston J., Schölkopf B., and Mller K.-R. Fisher discriminant analysis with kernels. Neural Networks Signal Process. IX (1999) 41-48
16. Nishimori Y., and Akaho S. Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold. Neurocomputing 67 (2005) 106-135
17. Oja E. A simplified neuron model as a principal component analyzer. J. Math. Biol. 15 (1982) 267-273
18. Oja E. Principal components, minor components, and linear neural networks. Neural Networks 5 (1992) 927-935
19. Phillips P.J., Moon H., Rizvi S.A., and Rauss P.J. The FERET evaluation methodology for face recognition algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 22 (2000) 1090-1104
20. Schölkopf B., and Smola A. Learning with Kernels (2002), MIT Press, Cambridge, MA
21. F. Sha, L.K. Saul, D.D. Lee, Multiplicative updates for large margin classifiers, in: COLT, 2003, pp. 188-202.
22. B.W. Xu, J.J. Lu, G.S. Huang, A constrained non-negative matrix factorization in information retrieval, in: Proceedings of the 2003 IEEE International Conference on Information Reuse and Integration (IRI2003), 2003, pp. 273-277.
23. Z. Yuan, E. Oja, Projective nonnegative matrix factorization for image compression and feature extraction, in: Proceedings of 14th Scandinavian Conference on Image Analysis (SCIA 2005), Joensuu, Finland, June 2005, pp. 333-342.
24. S. Zafeiriou, A. Tefas, I. Buciu, I. Pitas, Class-specific discriminant non-negative matrix factorization for frontal face verification, in: Proceedings of Third International Conference on Advances in Pattern Recognition (ICAPR 2005), vol. 2, 2005, pp. 206-215.