An improvement of a back propagation algorithm by the extended Kalman filter and demand forecasting by layered neural networks

Recently, Watanabe et al. proposed a back propagation algorithm via the extended Kalman filter, in which the learning rate was time-varying. In their algorithm the weights and biases are treated as independent variables. It is, however, natural that the weights and biases are not always independent, and generally have mutual correlation. In this paper, we improve the back propagation algorithm by considering that there is mutual correlation among the weights and bias directly connected to the unit. Through some numerical examples, our improved learning algorithm is compared with Watanabe et al.’s algorithm in learning ability. Furthermore, we consider demand forecasting as a kind of pattern recognition, and propose a demand forecasting method using layered neural networks with the improved learning algorithm. The effectiveness of this demand forecasting method is also discussed through some simulations.