Back Propagation Learning of an Affordable Neural Network for Chaotic Time Series

In Japan, cramming of too much knowledge into students was criticized and more relaxed education policy has been introduced to develop the individuality of each student. If students can afford to study carefully, creativity of the individual is fostered. We consider that it is very important to pay attention to “Affordable” concept in the field of engineering. In our previous research, we have proposed a new network structure with chaotically-selected affordable neurons in the hidden layer of the feedforward neural network for more efficient BP learning [1]. By computer simulations, the proposed neural network has been confirmed to gain better performance for the BP learning on both convergence speed and learning efficiency, when we set the feedforward neural network producing outputs x for inputs data x as a learning example. However, only the results on one learning example can not conclude that the affordable neural network has an excellent ability for convergence speed and learning efficiency. In this study, we investigate the performance of this neural network with chaotically-selected affordable neurons for unknown data which is chaotic time series generated by a skew tent map. Further, in order to confirm the effectiveness of the chaotic selection of the affordable neurons, we investigate performance of the network with affordable neurons selected regularly and at random. Computer simulated results show that the affordable neural network exhibits a good performance for the unknown input data.