On relative convergence properties of principal component analysis algorithms

IEEE Transactions on Neural Networks

Volumn 9, Issue 2, 1998, Pages 319-329

  Chatterjee, Chanchal ^a,b   Roychowdhury, Vwani P ^c   Chong, Edwin K P ^a,d  

^a IEEE   (United States)

^b GDE Systems Inc   (United States)

^c University of California   (United States)

^d PURDUE UNIVERSITY   (United States)

Author keywords

Adaptive eigen decomposition algorithms; PCA algorithms; Rates of convergence

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; ITERATIVE METHODS;

ASYMPTOTIC MEAN SQUARE ERRORS (AMSE); PRINCIPAL COMPONENT ANALYSIS (PCA);

ADAPTIVE ALGORITHMS;

EID: 0032022550     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.661126     Document Type: Article

References (17)

1. P. Baldi and K. Hornik, "Learning in linear neural networks: A survey," IEEE Trans. Neural Networks, vol. 6, pp. 837-857, 1995.
2. A. Benveniste, A. Metivier, and P. Priouret, Adaptive Algorithms and Stochastic Approximations. New York: Springer-Verlag, 1990.
3. V. Fabian, "On asymptotic normality in stochastic approximation," Ann. Math. Statist., vol. 39, no. 4, pp. 1327-1332, 1968.
4. G. H. Golub and C. F. VanLoan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1983.
5. J. K. Hale, Ordinary Differential Equations. New York: Wiley, 1969.
6. S. Haykin, Neural Networks - A Comprehensive Foundation. New York: Macmillan, 1994.
7. L. Ljung, "Analysis of recursive stochastic algorithms," IEEE Trans. Automat. Contr., vol. AC-22, pp. 551-575, 1977.
8. L. Ljung, G. Pflug, and H. Walk, Stochastic Approximation and Optimization of Random Systems. Boston, MA: Birkhauser, 1992.
9. J. Karhunen, "Stability of Oja's PCA subspace rule," Neural Computa., vol. 6, pp. 739-747, 1994.
10. E. Oja, "Principal components, minor components, and linear neural networks," Neural Networks, vol. 5, pp. 927-935, 1992.
11. E. Oja and J. Karhunen, "On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix," J. Math. Anal. Applicat., vol. 106, pp. 69-84, 1985.
12. T. Okada and S. Tomita, "An optimal orthonormal system for discriminant analysis," Pattern Recognition, vol. 18, no. 2, pp. 139-144, 1985.
13. J. Rubner and P. Tavan, "A self-organizing network for principal component analysis," Europhys. Lett., vol. 10, no. 7, pp. 693-698, 1989.
14. T. D. Sanger, "Optimal unsupervised learning in a single-layer linear feedforward neural network," Neural Networks, vol. 2, pp. 459-473, 1989.
15. R. L. Wheeden and A. Zygmund, Measure and Integral - An Introduction to Real Analysis. New York: Marcel Dekker, 1977.
16. L. Xu, "Least mean square error reconstruction principle for self-organizing neural-nets," Neural Networks, vol. 6, pp. 627-648, 1993.
17. L. Xu and A. L. Yuille, "Robust principal component analysis by self-organizing rules based on statistical physics approach," IEEE Trans. Neural Networks, vol. 6, pp. 131-143, 1995.