The nonlinear PCA learning rule in independent component analysis

Neurocomputing

Volumn 17, Issue 1, 1997, Pages 25-45

  Oja, Erkki ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Independent component analysis; Principal component analysis; Signal separation; Unsupervised learning

Indexed keywords

ALGORITHMS; MATRIX ALGEBRA; NEURAL NETWORKS; NUMERICAL ANALYSIS; PROBABILITY DENSITY FUNCTION; SIGNAL THEORY; VECTORS;

INDEPENDENT COMPONENT ANALYSIS; PRINCIPAL COMPONENT ANALYSIS; SIGNAL SEPARATION; UNSUPERVISED LEARNING;

LEARNING SYSTEMS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER PROGRAM; INFORMATION PROCESSING; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL;

EID: 0343416807     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-2312(97)00045-3     Document Type: Article

References (16)

1. J.-F. Cardoso, B. Laheld, Equivariant adaptive source separation, IEEE Trans. Signal Process. 44 (1996) 3017-3030.
2. P. Comon, Independent component analysis - a new concept?, Signal Process. 36 (1994) 287-314.
3. J. Friedman, Exploratory projection pursuit, J. Amer. Statist. Assoc. 82 (1987) 249-266.
4. C. Fyfe, R. Baddeley, Nonlinear data structure extraction using simple hebbian networks, Biol. Cybernet. 72 (1995) 533-541.
5. P. Huber, Projection pursuit, Ann. Statist. 13 (1985) 435-475.
6. C. Jutten, J. Herault, Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture, Signal Process. 24(1) (1991) 1-10.
7. J. Karhunen, J. Joutsensalo, Representation and separation of signals using nonlinear PCA type learning, Neural Networks 7(1) (1994) 113-127.
8. J. Karhunen, J. Joutsensalo, Generalizations of principal component analysis, optimization problems, and neural networks, Neural Networks 8 (1995) 549-562.
9. J. Karhunen, E. Oja, L. Wang, R. Vigario, J. Joutsensalo, A class of neural networks for Independent Component Analysis, IEEE Trans. Neural Networks 8 (1997) 486-504.
10. C. Nikias, J. Mendel, Signal processing with higher-order spectra, IEEE Signal Proc. Mag. July 1993, 10-37.
11. E. Oja, Principal components, minor components, and linear neural networks, Neural Networks 5 (1992) 927-935.
12. E. Oja, J. Karhunen, On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix, J. Math. Anal. Appl. 106 (1985) 69-84.
13. E. Oja, J. Karhunen, L. Wang, R. Vigario, Principal and independent components in neural networks - recent developments, in: M. Marinaro, R. Tagliaferri (Eds.), Neural Nets WIRN Vietri-95, World Scientific, Singapore, 1996, pp. 16-35.
14. E. Oja, H. Ogawa, J. Wangviwattana, Learning in nonlinear constrained Hebbian networks, in: T. Kohonen, K. Mäkisara, O. Simula, J. Kangas (Eds.), Artificial Neural Networks, Elsevier, Amsterdam, 1991, pp. 385-390.
15. L. Wang, J. Karhunen, E. Oja, R. Vigario, Blind separation of sources using nonlinear PCA type learning algorithms, in: Proc. Int. Conf. on Neural Networks and Signal Processing ICNNSP95, 10-13 December 1995, Nanjing, P.R. China, 1995, pp. 847-850.
16. L. Xu, Least mean square error reconstruction principle for self-organizing neural nets, Neural Networks 6 (1993) 627-648.