The UD RLS algorithm for training feedforward neural networks
A new algorithm for training feedforward multilayer neural networks is proposed. It is based on recursive least squares procedures and U-D factorization, which is a well-known technique in filter theory. It will be shown that due to the U-D factorization method, our algorithm requires fewer computations than the classical RLS applied to feedforward multilayer neural network training.
- Abid S., Fnaiech F. and Najim M. (2001): A fast feedforward training algorithm using a modified form of the standard backpropagation algorithm. - IEEE Trans. Neural Netw., Vol. 12, No. 2, pp. 424-434.
- Ampazis N. and Perantonis J. (2002): Two highly efficient second-order algorithms for training feedforward networks. - IEEE Trans. Neural Netw., Vol. 13, No. 5, pp. 1064-1074.
- Azimi-Sadjadi M.R. and Liou R.J. (1992): Fast learning process of multi-layer neural network using recursive least squares method. - IEEE Trans. Signal Process., Vol. 40, No. 2, pp. 443-446.
- Bilski J. (1995): Fast learning procedures for neural networks. - Ph.D. Thesis, AGH University of Science and Technology, (in Polish).
- Bilski J. and Rutkowski L. (1996): The recursive least squares method versus the backpropagation learning algorithms. - Second Conf. Neural Networks and Their Applications, Szczyrk, Poland, pp. 25-31.
- Bilski J. and Rutkowski L. (1998): A fast training algorithm for neural networks. - IEEE Trans. Circuits Syst. II, Vol. 45, No. 6, pp. 749-753,
- Bilski J. and Rutkowski L. (2003): A family of the RLS neural network learning algorithms. - Techn. Report, Dept. Comp. Eng., Technical University of Częstochowa, Poland.
- Bishop C.M. (1995): Neural Networks for Pattern Recognition. -Oxford: Clarendon Press.
- Bojarczak O.S.P. and Stodolski M. (1996): Fast second-order learning algorithm for feedforward multilayer neural networks and its application. - Neural Netw. Vol. 9, No. 9, pp. 1583-1596.
- Chen X.- H.Y.G.- A. (1992): Efficient backpropagation learning using optimal learning rate and momentum. - Neural Netw., Vol. 10, No. 3, pp. 517-527.
- Joost M. and Schiffmann W. (1998): Speeding up backpropagation algorithms by using cross-entropy combined with pattern normalization. - Int. J.Uncert. Fuzz. Knowledge-Based Syst., Vol. 6, No. 2, pp. 117-126.
- Karayiannis N.B. and Venetsanopoulos A.N. (1993): Efficient Learning Algorithms for Neural Networks (ELEANNE). - IEEE Trans. Syst. Man Cybern., Vol. 23, No. 5, pp. 1372-1383.
- Kitano H. (1994): Neurogenetic learning: an integrated method of designing and training neural networks using genetic algorithms. - Physica D., Vol. 75, No. 1-3, pp. 225-238.
- Korbicz J., Obuchowicz A., Uciński D. (1994): Artificial Neural Networks. Fundamentals and Applications. - Warsaw: Akademicka Oficyna Wydawnicza PLJ, (in Polish).
- Lera G. and Pinzolas M. (2002): Neighbourhood based Levenberg-Marquardt algorithm for neural network training. - IEEE Trans. Neural Netw., Vol. l3, No. 5, pp. 1200-1203.
- Leung Ch.S., Tsoi Ah.Ch. and Chan L. W. (2001): Two regularizers for recursive least squared algorithms in feedforward multilayered neural networks. - IEEE Trans. Neural Netw., Vol. 12, No. 6, pp. 1314-1332.
- Moller M. (1993): A scaled conjugate gradient algorithm for fast supervised learning. - Neural Netw., Vol. 6, No. 4, pp. 525-533.
- Perantonis S. and Karras D. (1995): An efficient constrained learning algorithm with momentum acceleration. - Neural Netw., Vol. 8, No. 2, pp. 237-249.
- Rutkowski L. (1994): Adaptive Signal Processing: Theory and Applications. -Warsaw: WNT, (in Polish).
- Strobach P. (1990): Linear Prediction Theory - A Mathematical Basis for Adaptive Systems. - New York: Springer-Verlag.
- Sum J., Chan L.W., Leung C.S. and Young G. (1998): Extended Kalman filter-based pruning method for recurrent neural networks. - Neural Comput., Vol. 10, No. 6, pp. 1481-1505.
- Sum J., Leung C., Young G.H. and Kan W. (1999): On the Kalman filtering method in neural-network training and pruning. - IEEE Trans. Neural Netw., Vol. 10, No. 1, pp. 161-166.
- Wellstead P.E. and Zarrop M.B. (1991): Self-Tuning Systems Control and Signal Processing. - Chichester Wiley.
- Yao X. (1999): Evolving artificial neural networks. - Proc. IEEE, Vol. 87, No. 9, pp. 1423-1447.
- Zhang Y. and Li R. (1999): A fast U-D factorization-based learning algorithm with applications to nonlinear system modelling and identification. - IEEE Trans. Neural Netw., Vol. 10, No. 4, pp. 930-938.