Convex Optimization Based High-Order Fuzzy Cognitive Map Modeling and Its Application in Time Series Predicting

Abstract

As a soft computing method, applying fuzzy cognitive map (FCM) to time series prediction has become a timely issue pursued by numerous researchers. Although many FCM construction methods have emerged, most of them exhibit obvious limitations in weight learning especially for long-term or complex time series. Either the weight calculation is computationally expensive, or it cannot achieve gratifying accuracy. In this paper, a new method for constructing FCM is proposed which extracts concepts from data by exploiting triangular membership function, and the weights of high-order FCM are subtly obtained by transforming the learning problem of FCM into a convex optimization problem with constraints. Since then, FCM with optimized weights is used to represent fuzzy logical relationships of time series and implement prediction further. Fifteen benchmark time series,such as Soybean Price time series, Yahoo stock time series, Condition monitoring of hydraulic systems time series etc. are applied to verify prediction performance of the proposed method. Accordingly, experiment results show that the proposed numerical prediction method of time series is effective and can acquire better prediction accuracy with lower computation time than other recent advanced methods. In addition, the influence of parameters of the method is analyzed individually.

Keywords

• Fuzzy cognitive map
• convex optimization
• time series