New algorithm for training neural networks based on generalized Чебышев polynomials
Daiyuan Zhang · Systems engineering and electronics · 2008
A new learning algorithm based on the generalizedЧебышевpolynomials is introduced for train-ing neural networks.AtЧебышевnodes,the values of functions are found by the cubic spline interpolation forthe given patterns(or the given set of data points).TheЧебышевnodes and the obtained values are the newtraining patterns of the networks.By using the orthogonal property ofЧебышевpolynomials,each weight func-tion can be expressed as a generalizedЧебышевpolynomial,therefore,the weight function is a optimal approxi-mation polynomial in the least-squares sense.Compared with the cubic spline learning algorithm,the proposedfinal expressions are more convenient for generalization and have less information to be stored in each weightfunction.In addition,the new algorithm has no problems such as local minima,slow convergence arising fromthe steepest descent-like algorithms.Finally,to illustrate the power of the new learning algorithm,a simulationexample is presented to show good performance that extracts useful information from the weight functions(gen-eralizedЧебышевpolynomials)for understanding relations inherent in the given patterns,and the trained net-work has good performance both on generalization and calculating precision.