Prediction of chaotic time series using Cascade Correlation: effects of number of inputs and training set size
Dale E. Nelson, David Ensley, Steven K. Rogers · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
Most neural networks have been used for problems of classification. We have undertaken a study using neural networks to predict continuous valued functions which are aperiodic or chaotic. In addition, we are considering a relatively new class of neural networks, ontogenic neural networks. Ontogenic neural networks are networks which generate their own topology during training. Cascade Correlation is one such network. In this study we used the Cascade Correlation neural network to answer two questions regarding prediction. First, how do the number of inputs affect prediction accuracy. Second, how do the number of training exemplars affect prediction accuracy. For these experiments, the Mackey-Glass equation was used with a Tau value of 17 which yields a correlation dimension of 2.1. Takens' theorem for this data set states that the number of inputs to obtain a smooth mapping should be 3 to 5. We were experimentally able to verify this. Experiments were run varying the number of training exemplars from 50 to 450. The results showed that there is an overall trend towards lower predictive rms error with a greater number of exemplars. However, there are good results obtained with only 50 exemplars which we are unable to explain at this time. In addition to these results, we discovered that the way in which predictive accuracy is generally represented, a graph of Mackey-Glass with the network output superimposed, can lead to erroneous conclusions