Translated Multiplicative Neuron: An Extended Multiplicative Neuron that can Translate Decision Surfaces

Journal of Advanced Computational Intelligence and Intelligent Informatics

Volumn 8, Issue 5, 2004, Pages 460-468

  Iyoda, Eduardo Masato ^a   Nobuhara, Hajime ^a   Hirota, Kaoru ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

multiplicative neurons; N bit parity problem; neural networks; nonlinear regression; XOR problem

Indexed keywords

BACKPROPAGATION; MULTILAYER NEURAL NETWORKS;

DECISION SURFACES; HIDDEN NEURONS; MULTILAYERS PERCEPTRONS; MULTIPLICATIVE NEURON; MULTIPLICATIVE NEURON MODEL; N-BIT PARITY PROBLEM; NEURAL-NETWORKS; NON-LINEAR REGRESSION; PARITY PROBLEMS; XOR PROBLEM;

NEURONS;

EID: 33747620260     PISSN: 13430130     EISSN: 18838014     Source Type: Journal    
DOI: 10.20965/jaciii.2004.p0460     Document Type: Article

References (23)

1. M. Schmitt, “On the Complexity of Computing and Learning with Multiplicative Neural Networks,” Neural Computation, Vol.14, pp. 241-301, 2001.
2. C. L. Giles, and T. Maxwell, “Learning, Invariance, and Generalization in a High-Order Neural Network,” Applied Optics, Vol.26, pp. 4972-4978, 1987.
3. E. M. Iyoda, and F. J. Von Zuben, “Hybrid neural networks: An evolutionary approach with local search,” Integr. Computer-Aided Eng., Vol.9, pp. 57-72, Jan. 2002.
4. E. M. Iyoda, K. Hirota, and F. J. Von Zuben, “Sigma-pi cascade extended hybrid neural network,” J. Advanced Computational Intell., Vol.6, pp. 126-134, Oct. 2002.
5. B.-T. Zhang, “A Bayesian evolutionary approach to the design and learning of heterogeneous neural trees”, Integr. Computer-Aided Eng., Vol.9, pp. 73-86, Jan. 2002.
6. B.-T. Zhang, P. Ohm, and H. Mühlenbein, “Evolutionary induction of sparse neural trees,” Evol. Comput., Vol.5, pp. 213-236, 1997.
7. D. K. Chaturvedi, P. S. Satsangi, and P. K Kalra, “New neuron models for simulating rotating electrical machines and load forecasting problems,” Electr. Power Syst. Res., Vol.52, pp. 123-131, 1999.
8. T. Poggio, and F. Girosi, “Networks for approximation and learning,” Proc. IEEE, Vol.78, pp. 1481-1497, 1990.
9. J.-N. Hwang, S.-R. Lay, M. Maechler, R. D. Martin, and J. Schimert, “Regression modeling in back-propagation and projection pursuit learning,” IEEE Trans. Neural Networks, Vol.5, pp. 342-353, May 1994.
10. A. F. Rocha, “Neural Nets: A Theory for Brain and Machines,” New York: Springer-Verlag, 1992.
11. W. Duch, and N. Jankowski, “Survey of Neural Transfer Functions,” Neural Computing Surv. [Online]. 2, pp. 163-212, 1999. Available: http://www.ucsc.soe.edu/NCS/
12. R. Durbin, and D. E. Rumelhart, “Product units: A computationally powerful and biological plausible extension to backpropagation networks,” Neural Computation, Vol.1, pp. 133-142, 1989.
13. P. J. Werbos, “Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences,” Ph.D. thesis, Committee on Applied Mathematics, Harvard University, Cambridge, MA, 1974.
14. D. E. Rumelhart, and J. L. McClelland, “Parallel Distributed Processing: Explorations in the Microstructure of Cognition,” Cambridge, MA: MIT Press, 1986.
15. S. Haykin, “Neural Networks – a Comprehensive Foundation,” 2nd ed., Upper Saddle River, NJ: Prentice Hall, 1998, ch. 4.
16. M. S. Bazaraa, H. D. Sheraly, and C. Shetty, “Nonlinear Programming: Theory and Algorithms,” 2nd ed., John Wiley & Sons, 1992.
17. M. F. Møller, “A scaled conjugate gradient algorithm for fast supervised learning”, Neural Networks, Vol.6, pp. 525-533, 1993.
18. E. D. Sontag, “Feedforward nets for interpolation and classification,” J. Comput. Syst. Scie., Vol.45, pp. 20-48, 1992.
19. D. Liu, M. E. Hohil, and S. H. Smith, “N-bit parity neural networks: new solutions based on linear programming,” Neurocomputing, Vol.48, pp. 477-488, Oct. 2002.
20. M. Z. Arslanov, D. U. Ashigaliev, and E. E. Ismail, “N-bit parity ordered neural networks,” Neurocomputing, Vol.48, pp. 1053-1056, Oct. 2002.
21. E. M. Iyoda, H. Nobuhara, and K. Hirota, “A Solution for the N-bit Parity Problem Using a Single Translated Multiplicative Neuron,” Neural Processing Letters (to appear).
22. F. J. Von Zuben, “Parametric and Nonparametric Artificial Neural Network Models and Applications,” Ph.D. thesis, School of Electrical and Computer Engineering, State University of Campinas, Campinas-SP, Brazil, 1996 (in Portuguese).
23. F. J. Von Zuben, and M. L. A. Netto, “Projection pursuit and the solvability condition applied to constructive learning,” Proceedings of the IEEE Joint International Conference on Neural Networks, Vol.2, pp. 1062-1067, 1997.