Comparison on Prediction Abilities of Single-Input Neuronets Activated by Different Polynomials
Zhang Yu-non · Jisuanji fangzhen · 2014
Based on the theory of function approximation and polynomial interpolation, polynomial neuronets are constructed by using linearly independent or orthogonal polynomials as activation functions of hidden-layer neurons. After using Legendre polynomials, Hermite polynomials, Chebyshev polynomials of class I, Chebyshev polynomials of class II, Bernoulli polynomials and power functions as activation functions to construct single-input neuronets, a weights-and-structure-determination algorithm of growing type is proposed, which can be applied to these six aforementioned neuronets to determine the optimal structure and weights. With this algorithm, the abilities of learning and prediction of these six neuronets activated by different polynomials are further investigated. Simulation results show that, though the Hermite polynomial neuronet and the Bernoulli polynomial neuronet perform relatively ordinarily, other four neuronets possess superior abilities of learning and prediction. Finally, the neuronet using Chebyshev polynomials of class I is used to simulate the trend of the world population.