Multivariate Time Series Classification Based On Granger Causality

Multivariate time series,which is a family of ordered observations for multiple variables.As a kind of complex structured data,multivariate time series has the charac-teristics of high dimension,varying lengths and dependency among variables.Typical state space models that are commonly used for processing time series data,e.g.Recur-rent Neural Network,usually considers multiple variables as a unit for each frame.This strategy is limited in taking advantage of the inter-relationship between multiple vari-ables.The intrinsic relationship between variables may help reveal the characteristics of multivariate time series and benefit the classification performance.To mitigate the above problems,this paper proposes an algorithm to learn the causality between multiple variables by the non-linear dynamical mappings of Echo State Network,based on a non-linear state space model,i.e.Echo State Network com-bined with Granger causality mechanism.We learn a model for each multivariate time series and evaluate the distance of the original multivariate time series by the distance of their models in the model space.We further constrain the sparsity of the learned time series models to find the Focal Series,which is a subset of variables playing the most important role in the generating mechanism of a multivariate time series.Exper-iments on benchmark datasets demonstrate the superior classification performance of the proposed method and the ability to catch the relationship among multiple variables according to Granger causality.It is demonstrated that the parameters of the learned model are more sparse and have more interpretability.The main work of this paper is summarized as follows:(1)We propose an algorithm to learn the causality between multiple variables by the non-linear dynamical mappings of Echo State Network.The algorithm is able to utilize the relationship between multiple variables to learn faithful representations for the original multivariate time series.(2)The proposed method is endowed with better sparity and interpretation by de?signing an algorithm to exploit the Focal Sereis.(3)For classification tasks,the similarity between the original multivariate time series is evaluated by calculating the distance in the model space.The paramater-free distance between models is beneficial to avoiding problems caused by the different lengths of multivariate time series effectively.(4)Experiments on benchmark datasets demonstrate the classification accuracy and the robustness of the proposed method.