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.