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.
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Albert A (1972) Regression and the Moore-Penrose pseudoinverse. Academis Press, New York
Amari SI, Maginu K (1988) Statistical neurodynamics of associative memory. Neural Networks 1:63–73
Anderson JA (1972) Simple neural network generating interactive memory. Math Biosci 14:197–220
Gantmacher FR (1977) The theory of matrices. Chelsea Publishing Company, New York
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
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
Kohonen T (1972) Correlation matrix memories. IEEE Trans Comput C-21: 353–359
Kohonen T, Ruohonen M (1973) Representation of associated data by matrix operators. IEEE Trans Comput C-22: 701–702
McEliece RJ, Posner EC, Rodemich ER, Venkatesh SS (1987) The capacity of the Hopfield associative memory. IEEE Trans Inf Theor IT-33: 461–482
Nakano K (1972) Associatron — a model of associative memory. IEEE Trans Syst Man Cybern SMC-2:381–388
Noble B, Daniel JW (1977) Applied linear algebra. Prentice-Hall, New York
Personnaz L, Guyon I, Dreyfus G (1985) Information storage and retrieval in spin-glass like neural networks. J Phys Lett 46:L359-L365
Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. J. Wiley, New York
Widrow B, Lehr MA (1990) 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proceedings of the IEEE 78:1415–1442
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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
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DOI: https://doi.org/10.1007/BF00203135