The minimum number of errors in the N-parity and its solution with an incremental neural network

Neural Processing Letters

Volumn 16, Issue 3, 2002, Pages 201-210

  Torres Moreno, J Manuel ^a   Aguilar, Julio C ^b   Gordon, Mirta B ^c  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^b National Laboratory of Advanced Informatics Xalapa   (Mexico)

^c Laboratoire Leibniz   (France)

Author keywords

Classification tasks; Minimerror; Monoplan; Parity problem; Perceptrons; Supervised learning

Indexed keywords

BACKPROPAGATION; ERRORS; GRADIENT METHODS; HEURISTIC METHODS; LEARNING SYSTEMS; PATTERN RECOGNITION; PROBLEM SOLVING;

INCREMENTAL NEURAL NETWORKS; MINIMUM ERROR; MONOPLAN; PARITY PROBLEM; SUPERVISED LEARNING;

FEEDFORWARD NEURAL NETWORKS;

EID: 0036970554     PISSN: 13704621     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021726007566     Document Type: Article

References (22)

1. Minsky, M. and Papert, S.: Perceptrons. MIT Press, Cambridge 1969.
2. Gordon, M. B. and Berchier, D.: Minimerror: A perceptron learning rule that finds the optimal weights. In: Michel Verleysen, (ed.), European Symposium on Artificial Neural Networks, pp. 105-110, Brussels, 1993. D facto.
3. Raffin, B. and Gordon, M. B.: Learning and generalization with minimerror, a temperature dependent learning algorithm. Neural Comput. 7(6) (1995), 1206-1224.
4. Torres Moreno, J.-M. and Gordon, M.: An evolutive architecture coupled with optimal perceptron learning for classification. In: Michel Verleysen, (ed.), European Symposium on Artificial Neural Networks, pp. 365-370, Brussels, 1995. D facto.
5. Torres Moreno, J.-M.: Apprentissage et Généralisation par des Réseaux de Neurones: étude de nouveaux algorithmes constructifs. Ph. D. these INPG, Grenoble, France, 1997.
6. Cover, T. M.: Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Transactions on Electronic Computers, EC-14 (1965), 326-334.
7. Gardner, E.: Maximum storage capacity in neural networks. Europhysics Letters, 4 (1987), 481-485.
8. Torres Moreno, J. M. and Gordon, M. B.: Efficient adaptive learning for classification tasks with binary units. Neural Comput. 10(4) (1997), 1007-1030.
9. Torres Moreno, J. M. and Gordon, M. B.: Characterization complete of the sonar benchmark. Neural Processing Letters 7(1) (1998), 1-4.
10. Gordon, M. B.: A convergence theorem for incremental learning with real-valued inputs. In IEEE International Conference on Neural Networks, pp. 381-386, Washington 1996.
11. Martinez, D. and Estéve, D.: The offset algorithm: building and learning method for multilayer neural networks. Europhysics Letters, 18 (1992), 95-100.
12. Biehl, M. and Opper, M.: Tilinglike learning in the parity machine. Physical Review A, 44 (1991), 6888.
13. Peretto, P.: An Introduction to the Modeling of Neural Networks. Cambridge, University Press, 1992.
14. Gorman, R. P. and Sejnowski, T. J.: Analysis of hidden units in a layered network trained to classify sonar targets. Neural Networks, 1 (1988), 75-89.
15. Berthold, M. A.: probabilistic extension for the DDA algorithm. In: IEEE International Conference on Neural Networks, pp. 341-346, Washington, 1996.
16. Berthold, M. R. and Diamond, J.: Boosting the performance of RBF networks with dynamic decay adjustment. In: G. Tesauro, D. Touretzky, and T. Leen, (eds.), Advances in Neural Information Processing Systems, 7, pp. 521-528. The MIT Press, 1995.
17. Bruske, J. and Sommer, G.: Dynamic cell structures. In: G. Tesauro, D. Touretzky, and T. Leen, (eds.), Advances in Neural Information Processing Systems, volume 7, pp. 497-504. The MIT Press, 1995.
18. Chakraborty, B. and Sawada, Y.: Fractal connection structure: Effect on generalization supervised feed-forward networks. In: IEEE International Conference on Neural Networks, pp. 264-269 Washington, 1996.
19. Karouia, M., Lengellé, R. and Denoeux, T.: Performance analysis of a MLP weight initialization algorithm. In: Michel Verleysen, (ed.), European Symposium on Artificial Neural Networks, pp. 347-352 Brussels, D facto, 1995.
20. Hasenäger, M. and Ritter H.: Perceptron Learning Revisited: The Sonar Targets Problem. Neural Processing Letters. 10(1) (1999), 1-8.
21. Perantonis, S. J. and Virvilis, V.: Input Feature Extraction for Multilayered Perceptrons Using Supervised Principal Component Analysis. Neural Processing Letters. 10(3) (1999), 243-252.
22. Kim, J. H. and Kwong-Park, S.: The Geometrical Learning of Binary Neural Networks. IEEE Transactions on Neural Networks. 6(1) (1995), 237-247.