Modelo no lineal basado en redes neuronales de unidades producto para clasificación. Una aplicación a la determinación del riesgo en tarjetas de crédito // Non-linear model for classification based on product-unit neural networks. An application to determine credit card risk

F. J. Martínez-Estudillo, C. Hervás-Martínez, M. Torres-Jiménez, A. C. Martínez-Estudillo


El principal objetivo de este trabajo es mostrar un tipo de redes neuronales denominadas redes neuronales basadas en unidades producto (RNUP) como un modelo no lineal que puede ser utilizado para la resolución de problemas de clasificación en aprendizaje. Proponemos un método evolutivo en el que simultáneamente se diseña la estructura de la red y se calculan los correspondientes pesos. La metodología que presentamos se basa, por tanto, en la combinación del modelo no lineal RNUP y del algoritmo evolutivo; se aplica a la resolución de un problema de clasificación de índole económica, surgido del mundo de las finanzas. Para evaluar el rendimiento de los modelos de clasificación obtenidos, comparamos nuestra propuesta con varias técnicas clásicas, como la regresión logística o el análisis discriminante, y con el clásico modelo de perceptrón multicapa de redes neuronales basado en unidades sigmoides y el algoritmo de aprendizaje de retropropagación (MLPBP).


The main aim of this work is to show a neural network model called product unit neural network (PUNN), which is a non-linear model to solve classification problems. We propose an evolutionary algorithm to simultaneously design the topology of the network and estimate its corresponding weights. The methodology proposed combines a non-linear model and an evolutionary algorithm and it is applied to solve a real economic problem that occurs in the financial management. To evaluate the performance of the classification models obtained, we compare our approach with several classic statistical techniques such us logistic regression and linear discriminat analysis, and with the multilayer perceptron neural network model based on sigmoidal units trained by means of Back-Propagation algorithm (MLPBP).

Palabras clave

Clasificación; redes neuronales de unidades producto; redes neuronales evolutivas; classification; product unit neural networks; evolutionary neural networks

Texto completo:



Hawley, D., Johnson, J., y Raina, D., Artificial Neural System: A new tool for financial decision-making. Financial Analysts Journal 23 (1990) 63-72.

Refenes, A.P., Neural networks in the capital markets, New York Wiley (1995).

Parisi, A., Parisi, F., y Díaz, D., Modelos de Algoritmos Genéticos y Redes Neuronales en la Predicción de Índices Bursátiles Asiáticos. Cuadernos de Economía, 43 (2006) 251-284.

Baesens, B., Setiono, R., Mues, C., y Vanthienen, J., Using neural network rule extraction and decision tables for credit-risk evaluation. Management Science, 49 (2003) 312-329.

Mcnelis, P.D., Neural Networks in Finance: Gaining Predictive Edge in the Market. Advanced Finance Series Elsevier Academic Press (2005).

Coleman, K.G., Graettinger, T.J., y Lawrence, W.F., Neural Networks for Bankruptcy Prediction: The Power to Solve Financial Problems. AI Review, (1991) 48-50.

Brockett, P.W., Cooper, W.W., Golden, L.L., y Pitaktong, U., A neural network method for obtaining an early warning of insurer insolvency. The Journal of Risk and Insurance, 6 (1994) 402-424.

Martín-del Brio, B. y Serrano-Cinca, C., Self-organizing Neural networks: The financial State of Spanisch Companies, in Neural networks in the Capital Markets, A.P. Refenes, Editor: Wiley. 341-357 (1995).

Herbrich, D., Keilbach, M., Graepel, T., Bollmann-Sdorra, P., y Obermayer, K., Neural Networks in Economics: Background, applications and new developments, in Advances in Computational Economics: Computational techniques for Modelling Learning in Economics, T. Brenner, Editor, Kluwer Academics. 169-196 (2000).

Durbin, R. y Rumelhart, D., Products Units: A computationally powerful and biologically plausible extension to backpropagation networks. Neural Computation, 1 (1989) 133-142.

Hastie, T., Tibshirani, R.J., y Friedman, J., The Elements of Statistical Learning. Data mining, Inference and Prediction, in Springer. (2001).

McCullagh, P. y Nelder, J.A., Generalized Linear Models, 2nd edn., ed. C. Hall, London (1989).

Schumacher, M., Robner, R., y Vach, W., Neural networks and logistic regression: Part I. Computational Statistics & Data Analysis, 21 (1996) 661-682.

Vach, W., Robner, R., y Schumacher, M., Neural Networks and logistic regression: Part II. Computational Statistics & Data Analysis, 21 (1996) 683-701.

Friedman, J. y Stuetzle, W., Proyection pursuit regression. Journal of the American Statistical Association, 76 (376) (1981) 817-823.

Hastie, T.J. y Tibshirani, R.J., Generalized Additive Models, London Chapman & Hall (1990).

Kooperberg, C., Bose, S., y Stone, C.J., Polychotomous Regression. Journal of the American Statistical Association, 92 (1997) 117-127.

Friedman, J., Multivariate adaptive regression splines (with discussion). Ann. Stat., 19 (1991) 1-141.

Bose, S., Classification using splines. Computational Statistics & Data Analysis, 22 (1996) 505-525.

Bose, S., Multilayer statistical classifiers. Computational Statistics & Data Analysis, 42 (2003) 685-701.

Bishop, M., Neural Networks for Pattern Recognition Oxford University Press (1995).

Schmitt, M., On the Complexity of Computing and Learning with Multiplicative Neural Networks. Neural Computation, 14 (2001) 241-301.

Martinez-Estudillo, A., Martinez-Estudillo, F., Hervas-Martinez, C., y Garcia-Pedrajas, N., Evolutionary product unit based neural networks for regression. Neural Networks, 19 (4) (2006) 477-486.

Ismail, A. y Engelbrecht, A.P. Training products units in feedforward neural networks using particle swarm optimisation. in Development and practice of Artificial Intelligence Techniques, Proceeding of the International Conference on Artificial Intelligence Durban, South Africa In V.B. Bajic & D. Sha (Eds). (1999)

Ismail, A. y Engelbrecht, A.P. Global optimization algorithms for training product units neural networks. in International Joint Conference on Neural Networks IJCNN`2000 Como, Italy. (2000)

Janson, D.J. y Frenzel, J.F., Training product unit neural networks with genetic algorithms. IEEE Expert, 8 (5) (1993) 26-33.

Ismail A., E.A.P. Pruning product unit neural networks. in Proceedings of the International Conference on Neural Networks Honolulu, Hawai. (2002)

Leerink, L.R., Giles, C.L., Horne, B.G., y Jabri, M.A., Learning with products units. Advances in Neural Networks Processing Systems, 7 (1995) 537-544.

Saito, K. y Nakano, R., Extracting Regression Rules From Neural Networks. Neural Networks, 15 (2002) 1279-1288.

Saito, K. y Nakano, R. Numeric law discovery using neural networks. in Proc. of the 4th International Conference on Neural Information Processing (ICONIP97). (1997)

Engelbrecht, A.P. y Ismail, A., Training product unit neural networks. Stability and Control: Theory and Applications, 2 (1-2) (1999) 59-74.

Martinez-Estudillo, A.C., Hervas-Martinez, C., Martinez-Estudillo, F.J., y Garcia-Pedrajas, N., Hybridization of evolutionary algorithms and local search by means of a clustering method. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 36 (3) (2006) 534-545.

Joost, M. y Schiffmann, W., Speeding up backpropagation algorithms by using Cross-Entropy combined with Pattern Normalization. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 6 (2) (1998) 117-126.

Bishop, C.M., Pattern Recognition and Machine Learning. Information Science and Statistics, ed. M. Jordan Springer (2006).

Baldi, P., Brunak, S., Chauvin, Y., Andersen, C.A.F., y Nielsen, H., Assessing the accuracy of prediction algorithms for classification: an overview. Bioinformatics, 16 (5) (2000) 412-424.

Reed, R., Pruning algorithms-A survey. IEEE Transactions on Neural Networks, 4 (1993) 740-747.

Setiono, R. y Hui, L.C.K., Use of quasinewton method in a feedforward neural-network construction algorithm. IEEE Trans. Neural Networks, 6 (1995) 273-277.

Yao, X., Evolving artificial neural network. Proceedings of the IEEE, 9 (87) (1999) 1423-1447.

García-Pedrajas, N., Hervás-Martínez, C., y Muñoz-Pérez, J., Multiobjetive cooperative coevolution of artificial neural networks. Neural Networks, 15 (10) (2002) 1255-1274.

Yao, X. y Liu, Y., Making use of population information in evolutionary artificial neural networks. IEEE Transactions and System Man and Cybernetics-Part B: Cybernetics, 28 (3) (1998) 417-425.

Yan, W., Zhu , Z., y Hu, R. Hybrid genetic /BP algorithm and its application for radar target classification. in Proceedings of the IEEE National Aerospace Electronics Conference Piscataway, NJ, USA IEEE Press. (1997)

Fogel, D.B. Using evolutionary programming to greater neural networks that are capable of playing Tic-Tac-Toe. in International Conference on Neural Networks San Francisco, CA IEEE Press. (1993)

Yao, X. y Liu, Y., A new evolutionary system for evolving artificial neural networks. IEEE Transactions on Neural Networks, 8 (3) (1997) 694-713.

Angeline, P.J., Saunders, G.M., y Pollack, J.B., An evolutionary algorithm that constructs recurrent neural networks. IEEE Transactions on Neural Networks, 5 (1) (1994) 54-65.

Fogel, D.B., Owens, A.J., y Wals, M.J., Artificial Intelligence Throught Simulated Evolution, New York Wiley (1966).

Fogel, D.B., Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, New York IEEE Press (1995).

Kirkpatrick, S., Gellat, C.D.J., y Vecchi, M.P., Optimization by simulated annealing. Science, 220 (1983) 671-680.

Otten, R.H.J.M. y van Ginneken, L.P.P.P., The annealing algorithm, Boston, MA. Ed. Kluwer (1989).

Rechenberg, I., Evolutionstrategie: Optimierung technischer Systeme nach Prinzipien der Biologischen Evolution, Stuttgart Framman-Holzboog Verlag (1975).

Enlaces refback

  • No hay ningún enlace refback.

Copyright (c) 2007 Revista de Métodos Cuantitativos para la Economía y la Empresa

URL de la licencia:

Licencia Creative Commons CC-BY-SA de tipo Reconocimiento-CompartirIgual. Se permite el uso comercial de la obra, reconociendo su autoría, y de las posibles obras derivadas, la distribución de las cuales se debe hacer con una licencia igual a la que regula la obra original.