A New Algorithm for Initialization and Training of Beta Multi-Library Wavelets Neural Network
Wajdi Bellil, Mohamed Ali Othmani, Chokri Ben, Mohamed Adel · InTech eBooks · 2008
In this chapter, we described a new training algorithm for multi library wavelets network. We needed a selection procedure, a cost function and an algorithm of minimization for the evaluation. To succeed a good training, we showed that it was necessary to unite good ingredients. Indeed, a good algorithm of minimization finds a minimum quickly; but this one is not necessarily satisfactory. The use of a selection algorithm is fundamental. Indeed, the good choice of regressors guarantees a more regular shape of the cost function; the global minima correspond well to the "true" values of the parameters, and avoid the local minimum multiplication. So the cost function present less local minima and the algorithms of evaluation find the global minimum more easily. For the validation of this algorithm we have presented a comparison between the CWNN and MLWNN algorithm in the domain of 1D, 2D and 3D function approximation. Many examples permitted to compare the capacity of approximation of MLWNN and CWNN. We deduce from these examples that: ? The choice of the reconstruction method essentially depends on the type of data that we treat, ? The quality of reconstruction depends a lot on the number of samples used and on their localizations. Also we have define a new Beta wavelets family that some one can see that they are more superior then the classic one in term of approximation and we demonstrate in [BELLIL07] that they have the capacity of universal approximation. As future work we propose a hybrid algorithm, based on MLWNN and genetic algorithm and the GCV (Generalised Cross validation) procedure to fix the optimum number of wavelets in hidden layer of the network, in order to model and synthesis PID controller for non linear dynamic systems.