A constructive design method for two-layer perceptrons and its application to the design of modular neural networks

Abstract

A multilayer perceptron is known to be capable of approximating any smooth function to any desired accuracy if it has a sufficient number of hidden neurons. But its training, based on the gradient method, is usually a time consuming procedure that may converge toward a local minimum, and furthermore its performance is greatly influenced by the number of hidden neurons and their initial weights. Usually these crucial parameters are determined based on the trial and error procedure, requiring much experience on the designer's part. In this paper, a constructive design method (CDM) has been propose for a two-layer perceptron that can approximate a class of smooth functions whose feature vector classes are linearly separable. Based on the analysis of a given data set sampled from the target function, feature vectors that can characterize the function 'well' are extracted and used to determine the number of hidden neurons and the initial weights of the network. But when the classes of the feature vectors are not linearly separable, the network may not be trained easily, mainly due to the interference among the hyperplanes generated by hidden neurons. Next, to compensate for this interference, a refined version of the modular neural network (MNN) has been proposed where each network module is created by CDM. After the input space has been partitioned into many local regions, a two-layer perceptron constructed by CDM is assigned to each local region. By doing this, the feature vector classes are more likely to become linearly separable in each local region and as a result, the function may be approximated with greatly improved accuracy by MNN. An example simulation illustrates the improvements in learning speed using a smaller number of neurons.