Output power statistical analysis of the neural network with LMS algorithm tuning with square constraint with weight vector jitter

S.V. Zimina

Output power statistical analysis of the neural network with LMS algorithm tuning with square constraint with weight vector jitter

S.V. Zimina¹

research article Pages: 12-18

¹ Ph. D. (Phys.-Math.), Associate Professor, National Research Lobachevsky State University of Nizhny Novgorod

Keywords: neural networks LMS algorithm weight coefficients jitter

Abstract

In this article the results of statistical analysis of neural network (NN) with LMS algorithm tuning with square constraint for weight coefficients jitter are represented. The task was solved by the methods of perturbation theory for the coefficient adap-tation of the LMS algorithm with quadratic constraint, which was supposed to be small. The result are presented in the first (born) approximation. The expressions for output power of some neuron of the different neural network layers are obtained. It is shown, that the weight vector jitter leads to distortions of output signal of neural network and these distortions depends on number of neural network layer.

How to cite

Зимина С.В. Статистический анализ выходной мощности искусственной нейронной сети, настраивающейся по алгоритму LMS с квадратичным ограничением, с учетом флуктуаций весовых коэффициентов // Нейрокомпьютеры: разработка, применение. 2015. № 12. С. 12–18.

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[1] Haykin S. Neural Networks: A comprehensive Foundation. New York: Macmillan College Publishing Company. 1994.

[2] Galushkin A.I.Teorija nejjronnykh setejj. M.: IPRZHR, 2000. 416 s.

[3] Zimina S.V.Statisticheskie kharakteristiki iskusstvennojj nejjronnojj seti s diskretnym gradientnym algoritmom nastrojjki s uchetom fluktuacijj vesovykh koehfficientov // Nejjrokompjutery: razrabotka i primenenie. 2006. № 10. C. 9-15.

[4] Zimina S.V.Vlijanie fluktuacijj vesovykh koehfficientov na statisticheskie kharakteristiki iskusstvennojj nejjronnojj seti s algoritmom rekurrentnogo obrashhenija vyborochnojj ocenki korreljacionnojj matricy vkhodnykh signalov // Nejjrokompjutery: razrabotka i primenenie 2007. № 5. C. 3-7.

[5] Litvinov O.S., Zimina S.V. Statisticheskijj analiz fluktuacijj vesovykh koehfficientov iskusstvennojj nejjronnojj seti, nastraivajushhejjsja po algoritmu KHehbba // Nejjrokompjutery: razrabotka i primenenie. 2009. № 3. C. 33-43.

[6] Oreshkin B.N., Bakulev P.A. Algoritm LMS s kvadratichnym ogranicheniem // Antenny. 2007. № 9. C. 29-34.

[7] Pupkov K.A., Kapalin V.I., JUshhenko A.S. Funkcionalnye rjady v teorii nelinejjnykh sistem. M.: Nauka. 1976.

[8] Uidrou B., Stirnz S. Adaptivnaja obrabotka signalov. M.: Radio i svjaz. 1989.

[9] Ignatenko S.V., Malcev A.A. Statisticheskie kharakteristiki adaptivnykh antennykh reshetok pri obrabotke diskretnykh signalov s korrelirovannymi otschetami // Izv. vuzov. Radiofizika. 1994. T. 37. № 12. C. 1532-1545.