Abstract
In this paper, the behavior of the Sanger hebbian artificial neural networks [6] is analyzed. Hebbian neural networks are employed in communications and signal processing applications, among others, due to their capability to implement Principal Component Analysis (PCA). Different improvements over the original model due to Oja have been developed in the last two decades. Among them, Sanger model was designed to directly provide the eigenvectors of the correlation matrix[8]. The behavior of these models has been traditionally considered on a continuous-time formulation whose validity is justified via some analytical procedures that presume, among other hypotheses, an specific asymptotic behavior of the learning gain. In practical applications, these assumptions cannot be guaranteed. This paper addresses the study of a deterministic discrete-time (DDT) formulation that characterizes the average evolution of the net, preserving the discrete-time form of the original network and gathering a more realistic behavior of the learning gain[13]. The dynamics behavior Sanger model is analyzed in this more realistic context. The results thoroughly characterize the relationship between the learning gain and the eigenvalue structure of the correlation matrix.
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Berzal, J.A., Zufiria, P.J.: Algorithms and Implementation Architectures for Hebbian Neural Networks. In: Mira, J., Prieto, A.G. (eds.) IWANN 2001. LNCS, vol. 2084, pp. 166–173. Springer, Heidelberg (2001)
Berzal, J.A., Zufiria, P.J.: Linearized Trainning of Hebbian Neural Networks: Aplication to Multispectral Image Processing. In: Proceedings of the International Conference on Engineering Applications of Neural Networks, EANN 1998, Gibraltar, June 10-12, pp. 1–8 (1998)
Berzal, J.A., Zufiria, P.J., Cires, J.: Analysis of Hebbian Neural Networks and their Application to Video Sequence Compression. In: Proceedings of the International Conference on Engineering Applications of Neural Networks (EANN 1997), Estocolmo, Sweden, June 16-18, pp. 127–136 (1997)
Berzal, J.A., Zufiria, P.J., Rodríguez, L.: Implementing the Karhunen-Loeve Transform via Improved Neural Networks. In: Proceedings of the International Conference on Engineering Applications of Neural Networks (EANN 1996), London, UK, June 15-17, pp. 375–378 (1996)
Chen, T., Hua, Y., Yan, W.-Y.: Global Convergence of Oja’s Subspace Algorithm for Principal Component Extraction. IEEE Transactions on Neural Networks, 58–67 (January 1998)
Diamantaras, K.I., Kung, S.Y.: Principal Component Neural Networks: Theory and Applications. John Wiley & Sons, Inc, Chichester (1994)
Kushner, H.J., Yin, G.G.: Stochastic Approximation Algorithms and Applications. Springer, New York (1997)
Sanger, T.D.: Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Networks 2, 459–473 (1992)
Weingessel, A., Hornik, K.: Local PCA Algorithms. IEEE Transactions on Neural Networks, 1242–1250 (November 2000)
Yan, W.-Y., Helmke, U., Moore, J.B.: Global Analysis of Oja’s Flow for Neural Networks. IEEE Transactions on Neural Networks, 674–683 (September 1994)
Zufiria, P.J., Berzal, J.A., Martínez, M.A., Fernández, J.M.: Neural Network Processing of Satellite Data for the Nowcasting and Very Short Range Forecasting. In: Proceedings of the International Conference on Engineering Applications of Neural Networks (EANN 1999), Varsovia, Polonia, September 13-15, pp. 241–246 (1999)
Zufiria, P.J., Berzal, J.A.: Satellite Data Processing for Meteorological Nowcasting and Very Short Range Forecasting Using Neural Networks. Intelligent Data Analysis 5(1), 3–21 (2001)
Zufiria, P.J.: On the Discrete-Time Dynamics of the Basic Hebbian Neural-Network Node. IEEE Transactions on Neural Networks, 1342–1352 (November 2002)
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Berzal, J.A., Zufiria, P.J. (2005). Analysis of the Sanger Hebbian Neural Network. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_2
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DOI: https://doi.org/10.1007/11494669_2
Publisher Name: Springer, Berlin, Heidelberg
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