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Titre du document / Document title

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

Auteur(s) / Author(s)

DELMAS J.-P. (1) ; ALBERGE F. (2) ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

(1) Institut National des Telecommunications, Evry, FRANCE
(2) Ecole Nationale Supérieure des Télécommunications, Paris, FRANCE

Résumé / Abstract

In the neural network literature, many algorithms have been proposed for estimating the eigenstructure of covariance matrices. We first show that many of these algorithms, when presented in a common framework, show great similitudes with the gradient-like stochastic algorithms usually encountered in the signal processing literature. We derive the asymptotic distribution of these different recursive subspace estimators. A closed-form expression of the covariances in distribution of eigenvectors and associated projection matrix estimators are given and analyzed. In particular, closed-form expressions of the mean square error of these estimators are given. It is found that these covariance matrices have a structure very similar to those describing batch estimation techniques. The accuracy of our asymptotic analysis is checked by numerical simulations, and it is found to be valid not only for a small step size but in a very large domain. Finally, convergence speed and deviation from orthonormality of the different algorithms are compared, and several tradeoffs are analyzed.

Revue / Journal Title

IEEE transactions on signal processing    ISSN  1053-587X   CODEN ITPRED 

Source / Source

1998, vol. 46, no1, pp. 170-182 (27 ref.)

Langue / Language

Anglais

Editeur / Publisher

Institute of Electrical and Electronics Engineers, New York, NY, ETATS-UNIS  (1991) (Revue)

Mots-clés anglais / English Keywords

Signal processing

;

Adaptive estimation

;

Covariance matrix

;

Eigenvalue

;

Eigenfunction

;

Neural network

;

Principal component analysis

;

Adaptive algorithm

;

Performance analysis

;

Mots-clés français / French Keywords

Traitement signal

;

Estimation adaptative

;

Matrice covariance

;

Valeur propre

;

Fonction propre

;

Réseau neuronal

;

Analyse composante principale

;

Algorithme adaptatif

;

Analyse performance

;

Mots-clés espagnols / Spanish Keywords

Procesamiento señal

;

Estimación adaptativa

;

Matriz covariancia

;

Valor propio

;

Función propia

;

Red neuronal

;

Análisis componente principal

;

Algoritmo adaptativo

;

Análisis eficacia

;

Localisation / Location

INIST-CNRS, Cote INIST : 222 E3, 35400007743355.0160

Nº notice refdoc (ud4) : 2127481



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