Integrating KPCA and LS-SVM for Chaotic Time Series Forecasting Via Similarity Analysis

Abstract

A novel approach is presented to reconstruct the phase space using kernel principal component analysis (KPCA) with similarity analysis and forecast chaotic time series based on a least squares support vector machines (LS-SVM) in the phase space. A three-stage architecture is proposed to improve its prediction accuracy and generalization performance for chaotic time series forecasting. In the first stage, KPCA is adopted to extract features and obtain kernel principal components. Then, in the second stage, the similarity is analyzed between every principal components and output variable, and some principal components are chosen to construct the phase space of chaotic time series according to their similarity degree to the model output. LS-SVM is employed in the third stage for forecasting the chaotic time series. The method was evaluated by coal mine gas concentration in experiment. The simulation shows that LS-SVM by phase space reconstruction using KPCA with similarity analysis performs much better than that without similarity analysis.