Learning method of non-linear network for non-linear function approximation

摘要

A function approximation method is provided which is based on nonparametric estimation by using a network of three layers, such as an input layer, an output layer and a hidden layer. The input and the output layers have linear activation units while the hidden layer has nonlinear activation units which have the characteristics of bounds and locality. The whole learning sequence is divided to two phases. The first phase estimates the number of kernel functions based on a user's requirement on the desired level of accuracy of the network, and the second phase is related to parameter estimation. In the second phase, a linear learning rule is applied between output and hidden layers and a non-linear (piecewise-linear) learning rule is applied between hidden and input layers. Accordingly, an efficient way of function approximation is provided from the view point of the number of kernel functions as well as increased learning speed.