Research On Nonlinear Times Series Analysis Method Based On Improved Transition Network

After years of research,the complex network has gradually developed into a complete theoretical system and has been widely used in many fields.With the proposed of nonlinear time series to complex network transformation algorithms,complex network theory provides a new research direction for the analysis of nonlinear time series,and complex network becomes a powerful tool for the analysis of nonlinear time series.EEG signals has two typical characteristics of non-stationarity and nonlinearity,which belongs to nonlinear time series.In this paper,the application of complex networks in nonlinear time series is studied by means of epileptic EEG time series.Based on the time series to complex network construction algorithm,this paper mainly studies the transition network construction algorithm.The advantages and disadvantages of transition network algorithm are reviewed in this paper and the shortcomings of the current transition network construction algorithm are improved.This paper proposes multiple improved transition network algorithm and analyzes the statistic characteristics of the network.Combined the extracted classification features with classifier structure epileptic EEG automatic classification algorithm and the algorithm used to distinguish between various classification task of EEG signals.Firstly,an improved transition network algorithm is proposed to improve the node construction method.Because the transition network only uses the sorting information of the data after segmentation and the location information of the starting data when dividing the nodes,it will lose a lot of effective information of the original data in the subsequent network construction.Therefore,by referring to the node construction method of proximity network,the Euclidean distance is calculated after the time series is segmented according to the maximum value.The nodes determined according to the original transition network algorithm will make multiple nodes contain the same data,so the nodes with the same meaning will only appear once in the improved transition network algorithm.The improved transition network uses the same edge weight method as original transition algorithm.The mathematical expectation of node distribution was extracted as the classification feature,and the classifier was used for distinguishing the interictal signals and ictal signals.Classification accuracy can reach 97%.Experimental results show that the classification effect of the transition network based on the improved node construction method is much better than traditional methods.Secondly,based on the correlation between nodes,an improved edge weight method of transition network is proposed.The original transition network determines the edge weight by calculating the number of transitions between nodes and ignores the information contained in the nodes.In the improved method of edge weights,the correlation between coarse graining modes is calculated as another determining condition of edge weights.Because in the transition network of the improved node construction method,the result depends on the data length,we use the embedding theorem to divide the data,calculate the Euclidean distance between the adjacent subsegments and divide the nodes in a coarse-grained way.Then we apply the improved method to the epileptic EEG signals.Using mathematical expectation and global structural entropy as the classification features.the four classification tasks of epileptic EEG signals are realized by combining classification features with the Support Vector Machines(SVM).The experiments show that the improved method can effectively distinguish various epileptic EEG signals and obtain a great performance improvement.Finally,based on the distance between nodes,a new improved edge weight construction algorithm is proposed.the improved edge weight construction method based on node correlation cannot classify group B dataset.To get better classification effect,we use the distance between nodes as one of the edge weights determining condition.The EEG datasets are constructed into complex networks by new construction method,and the sum of the network degree and the sum of the local structural entropy were extracted as the classification features to realize the automatic classification of seven classification tasks in epileptic signals.Experiments found that our approach can achieve high quality of automatic detection classification between normal EEG signal,interictal signals and ictal signals this three kinds of EEG signals.And our approach has an important reference value for clinical medicine,shows that our method can dig out the deeper and broader dynamics characteristics in nonlinear time series,and provides a new research idea for nonlinear time series analysis.