Feature Analysis And Modeling Of Multivariate Time Series

Multivariate time series widely exist in practical complex systems,in which there are complex coupling relationships among multiple variables.Mining useful information contained in time series data is of great significance for the analysis and modeling of practical complex systems.This paper takes the multivariate time series generated by complex systems as the research object,and studies the feature selection,causality analysis and feature extraction of multivariate time series,which will construct appropriate input features for the model and finally improve the accuracy and computational efficiency of the model.The research content of this paper includes the following three aspects:(1)For the feature selection problem of multivariate time series,a global mutual information feature selection method is proposed.The method transforms the mutual information feature selection into a global optimization problem and applies the global search strategy to solve it.Thus,global mutual information feature selection algorithms based on single-objective and multi-objective optimization are proposed.Then,the optimal feature subset is determined according to the hybrid feature selection framework that combines filter and wrapper.The proposed method provides a new solution for the feature selection problems.In addition,for the multivariable chaotic systems,a nonuniform state space reconstruction method based on joint mutual information is proposed.The method combines nonuniform embedding and feature selection.First,the low-dimensional approximation of joint mutual information criterion is derived to select the delay variables of the state space.Then,the conditional entropy criterion is used to determine the embedding dimension.The proposed method has high calculation accuracy and efficiency.The reconstructed state space can not only recover the dynamic characteristics of the original system,but also effectively remove the redundant information.(2)Aiming at the problem of causality analysis of multivariate time series,a nonlinear Granger causality analysis model based on Hilbert-Schmidt independence criterion(HSIC)-Lasso is proposed.Since the traditional Granger causality model is limited to analyzing the linear causality of bivariate time series,this paper extends it to analyze the nonlinear causality of multivariate time series.First,the method performs stationary test and state space reconstruction on the original time series.Then,the input and output samples are mapped into the reproducing kernel Hilbert space,and the HSIC-Lasso regression model is established.Finally,Granger causality is determined based on the results of significance test.The method proposed in this paper can not only obtain accurate nonlinear causality,but also perform causality analysis from multiple inputs to output at the same time,which has high calculation efficiency and is suitable for solving the problem of causality analysis in high-dimensional systems.(3)For the feature extraction problem of time series,a hybrid feature extraction method is proposed.First,the method extracts features separately according to different types of feature extraction methods,which can comprehensively describe the complex characteristics of time series.Then,a feature selection algorithm based on class separability is designed to select the optimal feature subset for the classification model.In addition,for the problem that classification results of a single extreme learning machine are unstable,an ensemble extreme learning machine model based on linear discriminant analysis is proposed.The model improves the diversity of the base learner from three aspects:data sample perturbation,input attribute perturbation,and algorithm parameter perturbation,thereby improving the generalization performance of the classifier and the stability of the results.The combined method of hybrid feature extraction and ensemble classifier proposed in this paper has high classification accuracy,and has broad prospects in feature extraction and classification of medical signals.