Abstract
Conventional back-propagation (BP) neural networks have some inherent weaknesses such as slow convergence and local-minima existence. Based on the polynomial interpolation and approximation theory, a special type of feedforward neural-network is constructed in this paper with hidden-layer neurons activated by Bernoulli polynomials. Different from conventional BP and gradient-based training algorithms, a weights-direct-determination (WDD) method is proposed for the Bernoulli neural network (BNN) as well, which determines the neural-network weights directly (just in one general step), without a lengthy iterative BP-training procedure. Moreover, by analyzing the relationship between BNN performance and its different number of hidden-layer neurons, a structure-automatic-determination (SAD) algorithm is further proposed, which could obtain the optimal number of hidden-layer neurons in a constructed Bernoulli neural network in the sense of achieving the highest learning-accuracy for a specific data problem or target function/system. Computer-simulations further substantiate the efficacy of such a Bernoulli neural network and its deterministic algorithms.
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References
Zhang, Y., Wang, J.: Recurrent Neural Networks for Nonlinear Output Regulation. Automatica 37(8), 1161–1173 (2001)
Zhang, Y., Wang, J.: Global Exponential Stability of Recurrent Neural Networks for Synthesizing Linear Feedback Control Systems via Pole Assignment. IEEE Transactions on Neural Networks 13(3), 633–644 (2002)
Zhang, Y., Jiang, D., Wang, J.: A Recurrent Neural Network for Solving Sylvester Equation with Time-Varying Coefficients. IEEE Transactions on Neural Networks 13(5), 1053–1063 (2002)
Zhang, Y., Ge, S.S.: Design and Analysis of a General Recurrent Neural Network Model for Time-Varying Matrix Inversion. IEEE Transactions on Neural Networks 16(6), 1477–1490 (2005)
Steriti, R.J., Fiddy, M.A.: Regularized Image Reconstruction Using SVD and a Neural Network Method for Matrix Inversion. IEEE Transactions on Signal Processing 41(10), 3074–3077 (1993)
Zhang, Y., Ge, S.S., Lee, T.H.: A Unified Quadratic-Programming-Based Dynamical System Approach to Joint Torque Optimization of Physically Constrained Redundant Manipulators. IEEE Transactions on Systems, Man, and Cybernetics 34(5), 2126–2132 (2004)
Sadeghi, B.H.M.: A BP-Neural Network Predictor Model for Plastic Injection Molding Process. Journal of Materials Processing Technology 103, 411–416 (2000)
Demuth, H., Beale, M., Hagan, M.: Neural Network Toolbox 5 User’s Guide. MathWorks Inc., Natick (2007)
Zhang, Y., Li, W., Yi, C., Chen, K.: A Weights-Directly-Determined Simple Neural Network for Nonlinear System Identification. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 455–460. IEEE Press, Los Alamitos (2008)
Zhang, Y., Zhong, T., Li, W., Xiao, X., Yi, C.: Growing Algorithm of Laguerre Orthogonal Basis Neural Network with Weights Directly Determined. In: Huang, D.-S., Wunsch II, D.C., Levine, D.S., Jo, K.-H. (eds.) ICIC 2008. LNCS (LNAI), vol. 5227, pp. 60–67. Springer, Heidelberg (2008)
Mathews, J.H., Fink, K.D.: Numerical Methods Using MATLAB. Pearson Education Inc., Beijing (2004)
Mo, G., Liu, K.: Function Approximation Method. Science Press, Beijing (2003)
Costabile, F.A., Dell’Accio, F.: Expansion over a Rectangle of Real Functions in Bernoulli Polynomials and Application. BIT Numerical Mathematics 41(3), 451–464 (2001)
Costabile, F.A., Dell’Accio, F., Gualtieri, M.I.: A New Approach to Bernoulli Polynomials. Rendiconti di Matematica 26(7), 1–12 (2006)
Lin, C.S.: Numerical Analysis. Science Press, Beijing (2007)
Kincaid, D., Cheney, W.: Numerical Analysis: Mathematics of Scientific Computing. China Machine Press, Beijing (2003)
Leithead, W.E., Zhang, Y.: O(N 2)-Operation Approximation of Covariance Matrix Inverse in Gaussian Process Regression Based on Quasi-Newton BFGS Methods. Communications in Statistics - Simulation and Computation 36(2), 367–380 (2007)
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Zhang, Y., Ruan, G. (2009). Bernoulli Neural Network with Weights Directly Determined and with the Number of Hidden- Layer Neurons Automatically Determined. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_5
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DOI: https://doi.org/10.1007/978-3-642-01507-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01506-9
Online ISBN: 978-3-642-01507-6
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