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Asymptotic distributions associated to unsupervised Oja's learning equation

  • Part IV: Signal Processing: Blind Source Separation, Vector Quantization, and Self Organization
  • Conference paper
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Artificial Neural Networks — ICANN'97 (ICANN 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1327))

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Abstract

In this paper, we perform a complete asymptotic performance analysis of the stochastic approximation algorithm (denoted Subspace Network Learning algorithm) derived from Oja's learning equation, in the case where the learning rate is constant and a large number of patterns is available. Using a general result of Gaussian approximation theory, we derive the asymptotic distribution of the estimated projection matrix WW T associated to the connection weight matrix W. Closed form expressions of the asymptotic covariance of the projection matrix estimated by the SNL algorithm, and by the smoothed SNL algorithm that we introduce, are given.

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References

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Authors and Affiliations

  1. Dèpartement Signal et Image, Institut National des Télécommunications, 9 rue Charles Fourier, 91011, Evry Cedex, France

    Jean Pierre Delmas

Authors
  1. Jean Pierre Delmas
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Editor information

Wulfram Gerstner Alain Germond Martin Hasler Jean-Daniel Nicoud

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© 1997 Springer-Verlag Berlin Heidelberg

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Delmas, J.P. (1997). Asymptotic distributions associated to unsupervised Oja's learning equation. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020227

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  • DOI: https://doi.org/10.1007/BFb0020227

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63631-1

  • Online ISBN: 978-3-540-69620-9

  • eBook Packages: Springer Book Archive

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