Diffusion learning algorithms for feedforward neural networks

The problem of training feedforward neural networks is considered. To solve it, new algorithms are proposed. They are based on the asymptotic analysis of the extended Kalman filter (EKF) and on a separable network structure. Linear weights are interpreted as diffusion random variables with zero expectation and a covariance matrix proportional to an arbitrarily large parameter λ. Asymptotic expressions for the EKF are derived as λ→∞. They are called diffusion learning algorithms (DLAs). It is shown that they are robust with respect to the accumulation of rounding errors in contrast to their prototype EKF with a large but finite λ and that, under certain simplifying assumptions, an extreme learning machine (ELM) algorithm can be obtained from a DLA. A numerical example shows that the accuracy of a DLA may be higher than that of an ELM algorithm. © 2013 Springer Science+Business Media New York.