Zhang Yunong

An algorithm for designing Chebyshev neural network

In this paper, a Chebyshev neural network is constructed, of which the hidden neurons are activated with Chebyshev orthogonal polynomials. Based on the special structure, the weight-direct-determination method for the constructed neural network is introduced, which could obtain the optimal weights of such a neural network directly. Furthermore, a novel algorithm based on exponential-growth and binary-pruning search strategy is proposed to determine the optimal number of hidden neurons. Theoretical analysis and simulation results substantiate that our algorithm can adaptively, quickly and efficiently determine the number of hidden neurons in Chebyshev neural network for a given task.

Sieve-Decrease Algorithms of Polynomial Neural Networks

To overcome the problem of determining the number of hidden-layer neurons in feed-forward neural networks, a polynomial feed-forward neural network with a single hidden layer is presented based on the theory of polynomial approximation, where the polynomials are employed as the activation functions of hidden-layer neurons, and the weights between input layer and hidden layer are set to be 1. We only need to adjust the weights between hidden layer and output layer. Then, using the least square method, we could deduce the formula of computing weights directly. Furthermore, the basic ideas of the sieve-decrease algorithm of polynomial neural networks are described and discussed in details, together with several new concepts, such as weight-sieve, sieve-pore diameter, sieve-decrease rate,etc. Two illustrative computer-simulations substantiate that the improved polynomial feed-forward neural networks possess superior performance, and show that the number of hidden neurons decreases respectively by 98.19% and 80%, as compared to primal neural networks.