Prediction of the chaotic time series using support vector machines for fuzzy rule-based modeling

Abstract

Based on the powerful nonlinear mapping ability of support vector machines and the characteristics of fuzzy logic which can combine a prior knowledge into fuzzy rules, the forecasting model of the support vector machine for fuzzy rules-bas ed model in combination with Takens' delay coordinate phase reconstruction of ch aotic time series has been established; and the least squares method for large-s cale problems is used to train this model. Moreover, based on this model, relati onships among the prediction performances of this model, the embedding dimension and the delay time are discussed. Finally, the Mackey-Glass equation and the t ime series that Lorenz systems generate are applied to test this model, respecti vely, and the results show that the support vector machine for fuzzy rule-based modeling can not only acquire knowledge and generate fuzzy rules from the given data, reduce the number of support vectors greatly, but also predict chaotic ti me series accurately, and even if the embedding dimension is unknown and the del ay time is appropriately selected, the predicted results are satisfactory. These results imply the support vector machine for fuzzy rule-based modeling is a go od tool to study chaotic time series in practice.