Asymptotic performance analysis of subspace adaptive algorithms introduced in the neural network literature

IEEE Transactions on Signal Processing

Volumn 46, Issue 1, 1998, Pages 170-182

  Delmas, J P ^a   Alberge, F ^b  

^a INSTITUT NATIONAL DES TÉLÉCOMMUNICATIONS   (France)

^b TELECOM PARISTECH   (France)

Author keywords

Adaptive estimation; Array signal processing; Covariance matrices; Eigenvalues eigenfunctions; Neural networks, principal component analysis; Subspace adaptive algorithm

Indexed keywords

ADAPTIVE ALGORITHMS; ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; PERFORMANCE; SIGNAL PROCESSING;

ARRAY SIGNAL PROCESSING;

NEURAL NETWORKS;

EID: 0031674037     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.651207     Document Type: Article

References (27)

1. E. Moulines, P. Duhamel, J. F. Cardoso, and S. MayrargueSubspace methods for blind identification of multichannel FIR filtersIEEE Trans. Signal Processing, vol. 43, pp. 516-525, Feb. 1995.
2. E. OjaPrincipal components, minor components and linear neural networksNeural Networks, vol. 5, pp. 927-935, 1992.
3. J. DehaeneContinuous-time matrix algorithms, systolic algorithms and adaptive neural networks Ph.D. dissertation, Katholieke Univ. Leuven, Leuven, Belgium, Oct. 1995.
4. P. Comon and G. H. GolubTracking a few extreme singular values and vectors in signal processingProc. IEEE, vol. 78, pp. 1327-1343, Aug. 1990.
5. C. M. Kuan and K. HornikConvergence of learning algorithms with constant learning ratesIEEE Trans. Neural Networks, vol. 2, pp. 484-489, Sept. 1991.
6. B. Yang and F. GersemskyAsymptotic distribution of recursive subspace estimatorsProc. ICASSP, Atlanta, GA, May 1996, pp. 1764-1767.
7. J. P. DelmasPerformance analysis of parametrized adaptive eigensubspace algorithmsProc. ICASSP, Detroit, MI, May 1995, pp. 2056-2059.
8. J. P. Delmas and J. F. CardosoPerformance analysis of an adaptative algorithm for tracking dominant subspaces submitted for publication.
9. H. RutishauserComputational aspects of F. L. Bauer's simultaneous iteration methodNumer. Math. vol. 13 pp. 4-13, 1969.
10. R. WilliamsFeature discovery through error-correcting learning Inst. Cognitive Sei., Univ. California, San Diego, Tech. Rep. 8501, 1985.
11. W.-Y. Yan, U. Helmke, and J. B. MooreGlobal analysis of Oja's flow for neural networksIEEE Trans. Neural Networks, vol. 5, pp. 674-683, Sept. 1994.
12. B. YangProjection approximation subspace trackingIEEE Trans. Signal Processing, vol. 43, pp. 95-107, Jan. 1995.
13. _Convergence analysis of the subspace tracking algorithms PAST and PASTdProc. ICASSP, Atlanta, GA, May 1996, pp. 1760-1763.
14. E. Oja, Subspace Methods of Pattern Recognition. Letchworth, U.K.: Res. Studies/Wiley, 1983.
15. T. D. SangerOptimal unsupervised learning in a single-layer linear feedforward networkNeural Networks, vol. 2, pp. 459-473, 1989.
16. E. Oja, H. Ogawa, and J. WangviwattanaPrincipal component analysis by homogeneous neural networks, Part I: The weighted subspace criterionIEICE Trans. Inform. Syst., vol. E75-D, pp. 366-375, 1992.
17. _Principal component analysis by homogeneous neural networks, Part II: Analysis and extensions of the learning algorithmsIEICE Trans. Inform. Syst., vol. E75-D, no. 3, pp. 376-382, 1992.
18. E. OjaA simplified neuron model as a principal components analyzerJ. Math. Biol, vol. 15, pp. 267-273, 1982.
19. C. Riou, T. Chonavel, and P. Y. CochetAdaptive subspace estimation-Application to moving sources localization and blind channel identificationProc. ICASSP, Atlanta, GA, May 1996, pp. 1649-1652.
20. L. Xu, E. Oja, and C. SuenModified Hebbian learning for curve and surface fittingNeural Networks, vol. 5, no. 3, pp. 441-457, 1992.
21. A. Benveniste, M. Métivier, and P. Priouret, Adaptive Algorithms and Stochastic Approximations. New York: Springer-Verlag, 1990.
22. N. Delfosse and P. LoubatonAdaptive blind separation of independent sources: A deflation approachSignal Process., vol. 45, pp. 59-83, 1995.
23. K. Hornik and C. M. KuanConvergence analysis of local feature extraction algorithmsNeural Networks, vol. 5, pp. 229-240, 1992.
24. E. Oja and J. KarhunenOn stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrixJ. Math. Anal. Appl., vol. 106, pp. 69-84, 1985.
25. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 2nd ed. New York: Wiley, 1984.
26. C. R. Rao, Linear Statistical Inference and Its Applications. New York: Wiley, 1973.
27. D. R. Brillinger, Times Series, Data Analysis and Theory. San Francisco, CA: Holden-Day, 1980.