Abstract
Artificial neural networks (NN) have been successfully applied to solve different problems in recent years, especially in the fields of pattern classification, system identification, and adaptive control. Unlike the traditional methods, the neural network based approach does not require a priori knowledge on the model of the unknown system and also has some other significant advantages, such as adaptive learning ability as well as nonlinear mapping ability. In general, the complexity of a neural network structure is measured by the number of free parameters in the network; that is, the number of neurons and the number and strength of connections between neurons (weights). Network complexity analysis plays an important role in the design and implementation of artificial neural networks - not only because the size of a neural network needs to be predetermined before it can be employed for any application, but also because this dimensionality may significantly affect the neural network learning and generalization ability. This chapter gives a general introduction on neural network complexity analysis. Different pruning algorithms for multi-layer feedforward neural networks are studied and computer simulation results are presented.
An Erratum of this chapter can be found at http://dx.doi.org/10.1007/978-3642-10690-3_12
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Fnaiech, N., Abid, S., Fnaiech, F., Cheriet, M.: A modified version of a formal pruning algorithm based on local relative variance analysis. In: First International Symposium on Control, Communications and Signal Processing, pp. 849–852 (2004)
Rosin, P., Fierens, F.: Improving Neural Network Generalisation. In: International Geoscience and Remote Sensing Symposium, pp. 1255–1257 (1995)
Bevilacqua, V., Mastronardi, G., Menolascina, F., Pannarale, P., Pedone, A.: A novel multi-objective genetic algorithm approach to artificial neural network topology optimisation: the breast cancer classification problem. In: IEEE International Joint Conference on Neural Networks, pp. 1958–1965 (2006)
Narendra, K., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Transaction on Neural Networks 1(1), 4–27 (1990)
Lawrence, S., Giles, C., Tsoi, A.: Lessons in neural network training: overfitting may be harder than expected. In: Proceedings of the Fourteenth National Conference on Artificial Intelligence, pp. 540–545 (1997)
Engelbrecht, A.: A new pruning heuristic based on variance analysis of sensitivity information. IEEE Transactions on Neural Networks 12(6), 1389–1399 (2001)
Giles, C., Lawrence, S.: Overfitting and Neural Networks: Conjugate Gradient and Backpropagation. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 114–119 (2000)
Haykin, S.: Neural networks: a comprehensive foundation. Prentice Hall, New Jersey (1999)
Huynh, T., Setiono, R.: Effective neural network pruning using cross-validation. In: IEEE International Joint Conference on Neural Networks, pp. 972–977 (2005)
Karnin, E.: A simple procedure for pruning back-propagation trained neural networks. IEEE Transactions on Neural Networks 1(2), 239–242 (1990)
Marsland, S., Nehmzow, S., Shapiro, J.: A self-organizing network that grows when required. Neural Networks 15(8-9), 1041–1058 (2002)
Mozer, M., Smolensky, P.: Skeletonization: A technique for trimming the fat from a network via relevance assessment. In: Touretzky, D. (ed.) Advances in Neural Information Processing, pp. 107–115 (1989)
Ponnapalli, P., Ho, K., Thomson, M.: A formal selection and pruning algorithm for feedforward artificial neural network optimization. IEEE Transactions on Neural Networks 10(4), 964–968 (1999)
Yen, G., Lu, H.: Hierarchical genetic algorithm based neural network design. In: IEEE Symposium on Combinations of Evolutionary Computation and Neural Networks, pp. 168–175 (2002)
Chang, S.J., Leung, C.S., Wong, K.W., Sum, J.: A local training and pruning approach for neural networks. International Journal of Neural Networks 10(6), 425–438 (2000)
Chang, S.J., Sum, J., Wong, K.W., Leung, C.S.: Adaptive training and pruning in feedforward networks. Electronics Letters 37(2), 106–107 (2001)
Wan, W., Hirasawa, K., Hu, J., Jin, C.: A new method to prune the neural network. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 449–454 (2000)
Neruda, R., Stedry, A., Drkosova, J.: Kolmogorov learning for feedforward networks. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 77–81 (2001)
Kamran, F., Harley, R.G., Burton, B., Habetler, T.G., Brooke, M.A.: A fast on-line neural-network training algorithm for a rectifier regulator. IEEE Trans on Power Electronics 13(2), 366–371 (1998)
Hecht-Nielsen, R.: Kolmogorov’s mapping neural network existence theorem. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 11–14 (1987)
Li, W.: A neural network controller for a class of phase-shifted full-bridge DC-DC converter. PhD thesis, California Polytechnic State University, San Luis Obispo (2006)
Li, W., Yu, X.: Improving DC power supply efficiency with neural network controller. In: Proceedings of the IEEE International Conference on Control and Automation, pp. 1575–1580 (2007)
Li, W., Yu, X.: A self-tuning controller for real-time voltage regulation. In: Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 2010–2014 (2007)
Quero, J.M., Carrasco, J.M., Franquelo, L.G.: Implementation of a neural controller for the series resonant converter. IEEE Trans on Industrial Electronics 49(3), 628–639 (2002)
Leshno, M., Lin, V., Pinkus, A., Shocken, S.: Multilayer feedforward networks with a non-polynomial activation function can approximate any function. Neural Networks 6, 861–867 (1993)
Lin, F., Ye, H.: Switched inductor two-quadrant DC-DC converter with neural network control. In: IEEE International Conference on Power Electronics and Drive Systems, pp. 1114–1119 (1999)
El-Sharkh, M.Y., Rahman, A., Alam, M.S.: Neural networks-based control of active and reactive power of a stand-alone PEM fuel cell power plant. Journal of Power Resources 135(1-2), 88–94 (2004)
Bebis, G., Georgiopoulo, M., Kasparis, T.: Coupling weight elimination with genetic algorithms to reduce network size and preserve generalization. Neurocomputing 17, 167–194 (1997)
Sabo, D.: A Modified Iterative Pruning Algorithm for Neural Network Dimension Analysis. PhD thesis, California Polytechnic State University, San Luis Obispo (2007)
Sabo, D., Yu, X.: A New Pruning Algorithm for Neural Network Dimension Analysis. In: Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 3312–3317 (2008)
Kopel, A., Yu, X.: Optimize Neural Network Controller Design Using Genetic Algorithm. In: Proceedings of the World Congress on Intelligent Control and Automation, pp. 2012–2016 (2008)
Yu, X.: Reducing neural network size for dynamical system identification. In: Proceedings of the IASTED International Conference on Intelligent Systems and Control, pp. 328–333 (2000)
Yu, X.: Adaptive Neural Network Structure Based on Sensitivity Analysis. In: Proceedings of the World Forum on Smart Materials and Smart Structures Technology (2007)
Brouwer, R.: Automatic growing of a Hopfield style net-work during training for classification. Neural Networks 10(3), 529–537 (1997)
Vonk, E., Jain, L., Johnson, R.: Automatic generation of neural network architecture using evolutionary computation. World Scientific Publishing Co., Singapore (1997)
Huberman, B., Rumelhart, D.: Generalization by weight elimination with applications to forecasting. In: Lippmann, R., Moody, J. (eds.) Advances in neural information processing III, pp. 875–882. Morgan Kaufmann, San Francisco (1991)
Gupta, A., Lam, S.: Weight decay backpropagation for noisy data. Neural Networks 11, 1127–1137 (1998)
Reed, R., Marks, R.: Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks. MIT Press, Cambridge (1999)
Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)
Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1994)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Yu, H. (2010). Network Complexity Analysis of Multilayer Feedforward Artificial Neural Networks. In: Schumann, J., Liu, Y. (eds) Applications of Neural Networks in High Assurance Systems. Studies in Computational Intelligence, vol 268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10690-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-10690-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10689-7
Online ISBN: 978-3-642-10690-3
eBook Packages: EngineeringEngineering (R0)