Bernoulli neural network with weights directly determined and with the number of hidden- layer neurons automatically determined

Abstract

Conventional back-propagation (BP) neural networks have some inherent weaknesses such as slow convergence and local-minima existence. Based on the polynomial interpolation and approximation theory, a special type of feedforward neural-network is constructed in this paper with hidden-layer neurons activated by Bernoulli polynomials. Different from conventional BP and gradient-based training algorithms, a weights-direct-determination (WDD) method is proposed for the Bernoulli neural network (BNN) as well, which determines the neural-network weights directly (just in one general step), without a lengthy iterative BP-training procedure. Moreover, by analyzing the relationship between BNN performance and its different number of hidden-layer neurons, a structure-automatic-determination (SAD) algorithm is further proposed, which could obtain the optimal number of hidden-layer neurons in a constructed Bernoulli neural network in the sense of achieving the highest learning-accuracy for a specific data problem or target function/system. Computer-simulations further substantiate the efficacy of such a Bernoulli neural network and its deterministic algorithms. © 2009 Springer Berlin Heidelberg.