Skip to main content
Log in

On the performance of single-layered neural networks

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

This paper studies the performance of single-layered neural networks. This study begins with the performance of single-layered neural networks trained using the outer-product rule. The outer-product rule is a suboptimal learning scheme, resulting under certain assumptions from optimal least-squares training of single-layered neural networks with respect to their analog output. Extensive analysis reveals the improvement on the network performance caused by its optimal least-squares training. The effect of the training scheme on the performance of single-layered neural networks with binary output is exhibited by experimentally comparing the performance of single-layered neural networks trained with respect to their analog and binary output.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Albert A (1972) Regression and the Moore-Penrose pseudoinverse. Academis Press, New York

    Google Scholar 

  • Amari SI, Maginu K (1988) Statistical neurodynamics of associative memory. Neural Networks 1:63–73

    Google Scholar 

  • Anderson JA (1972) Simple neural network generating interactive memory. Math Biosci 14:197–220

    Google Scholar 

  • Gantmacher FR (1977) The theory of matrices. Chelsea Publishing Company, New York

    Google Scholar 

  • Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences U.S.A. 79:2554–2558

    Google Scholar 

  • Karayiannis NB (1991) Artificial neural networks: Learning algorithms, performance evaluation, and applications. Ph.D. dissertation, University of Toronto

  • Karayiannis NB, Venetsanopoulos AN (1990a) Recursive least squares learning algorithms for single-layered neural networks. Proceeding of the IASTED International Conference on Modeling, Simulation, and Optimization, Montreal, Canada pp 162–165

  • Karayiannis NB, Venetsanopoulos AN (1990b) Efficient learning algorithms for single-layered neural networks. In Eckmiller R, Hartman G, Hauske G (eds.) Parallel processing in neural systems and computers. Elsevier Publishers, North Holland, pp. 173–176

    Google Scholar 

  • Kohonen T (1972) Correlation matrix memories. IEEE Trans Comput C-21: 353–359

    Google Scholar 

  • Kohonen T, Ruohonen M (1973) Representation of associated data by matrix operators. IEEE Trans Comput C-22: 701–702

    Google Scholar 

  • McEliece RJ, Posner EC, Rodemich ER, Venkatesh SS (1987) The capacity of the Hopfield associative memory. IEEE Trans Inf Theor IT-33: 461–482

    Google Scholar 

  • Nakano K (1972) Associatron — a model of associative memory. IEEE Trans Syst Man Cybern SMC-2:381–388

    Google Scholar 

  • Noble B, Daniel JW (1977) Applied linear algebra. Prentice-Hall, New York

    Google Scholar 

  • Personnaz L, Guyon I, Dreyfus G (1985) Information storage and retrieval in spin-glass like neural networks. J Phys Lett 46:L359-L365

    Google Scholar 

  • Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. J. Wiley, New York

    Google Scholar 

  • Widrow B, Lehr MA (1990) 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proceedings of the IEEE 78:1415–1442

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karayiannis, N.B., Venetsanopoulos, A.N. On the performance of single-layered neural networks. Biol. Cybern. 68, 31–41 (1992). https://doi.org/10.1007/BF00203135

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00203135

Keywords

Navigation