A study on neural learning on manifold foliations: The case of the lie group SU(3)

Neural Computation

Volumn 20, Issue 4, 2008, Pages 1091-1117

  Fiori, Simone ^a  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; BRAIN; COMPUTER SIMULATION; LEARNING; NERVE CELL NETWORK; NONLINEAR SYSTEM; PHYSIOLOGY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BRAIN; COMPUTER SIMULATION; LEARNING; NERVE NET; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS;

EID: 41849088853     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2008.03-07-489     Document Type: Article

References (19)

1. Amari, S.-I. (1998). Natural gradient works efficiently in learning. Neural Computation, 10, 251-276.
2. Amari, S.-I., & Fiori, S. (2005). Editorial. Neurocomputing, 67, 1-7.
3. Arfken, G. (1985). Mathematical methods for physicists (3rd ed.). Orlando, FL: Academic Press.
4. Bingham, E., & Hyvärinen, A. (2000). A fast fixed-point algorithm for independent component analysis of complex valued signals. International Journal of Neural Systems, 10, 1-8.
5. Cardoso, J. F., & Laheld, B. (1996). Equivariant adaptive source separation. IEEE Trans, on Signal Processing, 44, 3017-3030.
6. Celledoni, E., & Iserles, A. (2000). Approximating the exponential form of a Lie algebra to a Lie group. Mathematics of Computation, 69, 1457-1480.
7. Fiori, S. (2002). Unsupervised neural learning on Lie group. International Journal of Neural Systems, 22, 219-246.
8. Fiori, S. (2003a). Extended Hebbian learning for blind separation of complex-valued sources. IEEE Trans. on Circuits and Systems - Part 11, 50, 195-202.
9. Fiori, S. (2003b). Singular value decomposition learning on double Stiefel manifold. International Journal of Neural Systems, 13, 155-170.
10. Fiori, S. (2005a). Quasi-geodesic neural learning algorithms over the orthogonal group: A tutorial. Journal of Machine Learning Research, 6, 743-781.
11. Fiori, S. (2005b). Non-linear complex-valued extensions of Hebbian learning: An essay. Neural Computation, 17, 779-838.
12. Fiori, S., & Rossi, R. (2003). Stiefel-manifold learning by improved rigid-body theory applied to ICA. International Journal of Neural Systems, 13, 273-290.
13. Gallot, S., Hulin, D., & Lafontaine, J. (1991). Differential geometry. Berlin: Springer-Verlag.
14. Jing, Y., & Hassibi, B. (2005). Three-transmit-antenna space-time codes based on SU(3). IEEE Trans. on Signal Processing, 53, 3688-3702.
15. Moerdijk, I., & Mrčun, J. (2003). Introduction to foliations and Lie groupoids. Cambridge: Cambridge University Press.
16. Plumbley, M. D. (2005). Geometrical methods for non-negative ICA: Manifolds, Lie groups and Toral subalgebras. Neurocomputing, 67, 161-197.
17. Snoussi, H. (2005). The geometry of prior selection. Neurocomputing, 67, 214-244.
18. Tanaka, T., & Fiori, S. (2006). Simultaneous tracking of the best basis in reduced-rank Wiener filter. In Proceedings of the International Conference on Acoustics, Speech and Signal Processing (IEEE-ICASSP) (Vol. 3, pp. 548-551). Piscataway, NJ: IEEE Press.
19. Varadarajan, V. S. (1984). Lie groups, Lie algebras and their representations. Berlin: Springer.