An hybrid training method for B-spline neural networks

Current and past research has brought up new views related to the optimization of neural networks. For a fixed structure, second order methods are seen as the most promising. From previous works we have shown how second order methods are of easy applicability to a neural network. Namely, we have proved how the Levenberg-Marquard possesses not only better convergence but how it can assure the convergence to a local minima. However, as any gradient-based method, the results obtained depend on the startup point. In this work, a reformulated evolutionary algorithm - the bacterial programming for Levenberg-Marquardt is proposed, as an heuristic which can be used to determine the most suitable starting points, therefore achieving, in most cases, the global optimum.

[1]  Takeshi Furuhashi,et al.  Fuzzy system parameters discovery by bacterial evolutionary algorithm , 1999, IEEE Trans. Fuzzy Syst..

[2]  C. Cabrita,et al.  Design of B-spline neural networks using a bacterial programming approach , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[3]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[4]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.

[5]  László T. Kóczy,et al.  Estimating fuzzy membership functions parameters by the Levenberg-Marquardt algorithm , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[6]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[7]  John R. Koza,et al.  Genetic Programming II , 1992 .

[8]  László T. Kóczy,et al.  Supervised training algorithms for B-Spline neural networks and neuro-fuzzy systems , 2002, Int. J. Syst. Sci..

[9]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[10]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[11]  C. Cabrita,et al.  Single and multi-objective genetic programming design for B-spline neural networks and neuro-fuzzy systems , 2001 .