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Asymptotic Performance Analysis of Subspace Adaptive Algorithms Introduced in the Neural Network Literature

Jean-Pierre Delmas 1, 2 Florence Alberge 
2 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications
SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
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.
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https://hal.archives-ouvertes.fr/hal-03435761
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Submitted on : Thursday, November 18, 2021 - 7:39:07 PM
Last modification on : Friday, April 22, 2022 - 11:18:01 AM
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  • HAL Id : hal-03435761, version 1

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Jean-Pierre Delmas, Florence Alberge. Asymptotic Performance Analysis of Subspace Adaptive Algorithms Introduced in the Neural Network Literature. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 1998. ⟨hal-03435761⟩

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