Tikhonov training of the CMAC neural network

IEEE Transactions on Neural Networks

Volumn 17, Issue 3, 2006, Pages 613-622

  Weruaga, Luis ^a   Kieslinger, Barbara ^b  

^a ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^b Centre for Social Innovation   (Austria)

Author keywords

Cerebellar model articulation controller (CMAC); Generalization; Overfitting; Tikhonov regularization

Indexed keywords

COMPUTATIONAL METHODS; LEARNING SYSTEMS; OPTIMIZATION; THEOREM PROVING;

CEREBELLAR MODEL ARTICULATION CONTROLLER; OVERFITTING; TIKHONOV TRAINING;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; INFORMATION RETRIEVAL; METHODOLOGY; SYSTEMS THEORY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; INFORMATION STORAGE AND RETRIEVAL; NEURAL NETWORKS (COMPUTER); PATTERN RECOGNITION, AUTOMATED; SYSTEMS THEORY;

EID: 33646518523     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2006.872348     Document Type: Article

References (31)

1. J. S. Albus, "A new approach to manipulator control: The cerebellar model articulation controller (CMAC)," J. Dyn. Syst., Measure. Contr., vol. 97, pp. 220-227, 1975.
2. W. T. Miller, F. H. Glanz, and L. G. Kraft, "CMAC: An associative neural network alternative to backpropagation," Proc. IEEE, vol. 78, no. 10, pp. 1561-1567, Oct. 1990.
3. M. Brown, C. J. Harris, and P. C. Parks, "The interpolation capabilities of the binary CMAC," Neural Netw., vol. 6, no. 3, pp. 429-440, 1993.
4. F. J. González, A. R. Figueiras, and A. Artés, "Fourier analysis of the generalized CMAC neural network," Neural Netw., vol. 11, no. 3, pp. 391-396, Apr. 1998.
5. H. Chao, X. Lixin, and Z. Yuhe, "Learning convergence of CMAC algorithm," Neural Process. Lett., vol. 14, no. 1, pp. 61-74, 2001.
6. D. E. Thompson and S. Kwon, "Neighborhood sequential and random training techniques for CMAC," IEEE Trans. Neural Netw., vol. 6, no. 1, pp. 196-202, Jan. 1995.
7. C. S. Lin and H. Kim, "Selection of learning parameters for CMAC-based adaptive critic learning," IEEE Trans. Neural Netw., vol. 6, no. 3, pp. 642-647, May 1995.
8. S. Zhong and V. Cherkassky, "Factors controlling generalization ability of MLP networks," in Proc. IEEE Int. Joint Conf. Neural Netw., 1999, pp. 625-630.
9. M. T. Musavi, K. H. Chan, D. M. Hummels, and K. Kalantri, "On the generalization ability of neural network classifiers," IEEE Trans. Pattern Anal. Mach. Intell., vol. 16, no. 6, pp. 659-663, Jun. 1994.
10. A. S. Weigend, D. E. Rumelhart, and B. A. Huberman, "Generalization by weight-elimination with application to forecasting," in Advances in Neural Information Processing Systems. San Mateo, CA: Morgan Kaufmann, 1991, vol. 3.
11. C. M. Bishop, "Curvature-driven smoothing: A learning algorithm for feedforward networks," IEEE Trans. Neural Netw., vol. 4, no. 5, pp. 882-884, Sep. 1993.
12. C. M. Bishop, "Training with noise is equivalent to Tikhonov regularization," Neural Comput., vol. 7, no. 1, pp. 108-116, Jan. 1995.
13. F. Girosi, M. Jones, and T. Poggio, "Regularization theory and neural networks architectures," Neural Comput., vol. 7, no. 2, pp. 219-269, Mar. 1995.
14. V. Vapnik, Statistical Learning Theory. New York: Wiley, 1998.
15. J. Pallotta and L. G. Kraft, "Two dimensional function learning using CMAC neural network with optimized weight smoothing," in Proc. Amer. Contr. Conf., 1999, pp. 373-377.
16. C. S. Lin and C. K. Li, "A new neural network structure composed of small CMACs," in Proc. IEEE Int. Conf. Neural Netw., 1996, pp. 1777-1783.
17. G. Horváth, "Kernel CMAC with improved capability," in Proc. Int. Joint Conf. Neural Netw., 2004, pp. 681-686.
18. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. New York: Wiley, 1977.
19. C. T. Chiang and C. S. Lin, "CMAC with general basis functions," Neural Netw., vol. 9, no. 7, pp. 1199-1211, 1996.
20. F. J. González, A. Artés, and A. R. Figueiras, "Generalizing CMAC architecture and training," IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1509-1514, Nov. 1998.
21. G. H. Golub and C. F. van Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkin Univ. Press, 1996.
22. "Integral equations and inverse theory," in Numerical Recipes in C++, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 2002, ch. 18.
23. J. Liang, T. McInerney, and D. Terzopoulos, "United snakes," in Proc. 7th IEEE Int. Conf. Comput. Vision, 1999, pp. 933-940.
24. L. Weruaga, R. Verdú, and J. Morales, "Frequency domain formulation of active deformable models," IEEE Trans. Pattern Anal. Mach. Intell., vol. 26, no. 12, pp. 1568-1578, Dec. 2004.
25. S. Haykin, Adaptive Filter Theory, 4th ed: Prentice Hall, 2001.
26. J. Park and I. W. Sandberg, "Universal approximation using radial-basis function networks," Neural Comput., vol. 3, no. 2, pp. 246-257, 1991.
27. P. Zamperoni, "Plus ça va, moins ça va," Pattern Recognit. Lett., vol. 17, no. 7, pp. 671-677, Jun. 1996.
28. L. Prechelt, "A quantitative study of experimental evaluations of neural network learning algorithms: Current research practice," Neural Netw., vol. 9, no. 3, pp. 457-462, Apr. 1996.
29. C. S. Lin and C. K. Li, "A sum-of-product neural network (SOPNN)," Neurocomputing, vol. 30, pp. 273-291, Jan. 2000.
30. Y. Morimoto, H. Ishii, and S. Morishita, "Efficient construction of regression trees with range and region splitting," Mach. Learning, vol. 45, no. 3, pp. 235-259, Dec. 2001.
31. R. Verdú and L. Weruaga, "Convergence analysis of active contours in image segmentation," in Proc. IEEE Int. Conf. Image Process., 2004, pp. 2749-2752.