基于网络模体与簇结构的非线性时间序列预测方法研究

In recent years with the method to transform a time series into a complex network, a natural bridge between complex networks theory and nonlinear time series analysis has now been built. The nonlinear time series analysis method based on complex network has become an important research focus. However, The research on the nonlinear time series prediction method based on complex network has not been reported at home and abroad. Based on the overembedding method, the method to transform a time series into a complex network for nonstationary time series will be proposed. To improve the nonlinear models' generalization capability and to solve the nonlinear models' overfitting problem, based on the spatial information and the hierarchical structure of the constructed complex network from a time series, we will propose the nonlinear time series prediction methods based on the complex network motif and based on the complex network cluster structure, which improve the nonlinear models' prediction accuracy and reduce the nonlinear models' complexity. Based on the complex network statistical measures and based on the nonlinear models' prediction error, the feature extraction methods for EEG signals will be proposed and applied to analyze various EEG signals' pattern (epileptic ictal EEG, interictal EEG, preictal EEG), which improve the accuracy of the seizure detection and the seizure prediction. The project construct the platform for the nonlinear time series prediction methods based on complex network and its application. The project research results are important for the study on the nonlinear time series analysis methods based on complex network and the nonlinear dynamical analyse of EEG signals.

近年来把时间序列构造为复杂网络的方法在非线性时间序列分析与复杂网络之间架起了桥梁，基于复杂网络的非线性时间序列分析方法成为一个重要的研究热点。但是基于复杂网络的非线性时间序列预测方法的研究国内外未见有报道。基于过嵌入法，提出适用于非平稳时间序列的复杂网络构造法；针对非线性模型泛化推广能力差和存在过拟合等问题，利用构造的复杂网络的空间信息与分层结构，重点提出基于复杂网络模体和网络簇结构的非线性时间序列预测方法，提高模型预测精度并降低模型复杂度；基于复杂网络统计量与模型预测误差，提出脑电信号特征提取方法，并应用于分析不同模式脑电信号（癫痫脑电、发作间歇期脑电、发作前期脑电）的动力学状态，提高癫痫检测和癫痫发作预测的精度；构建基于复杂网络的非线性时间序列预测方法及其应用平台。本项目研究成果在基于复杂网络的非线性时间序列分析方法研究与脑电信号非线性动力学分析方面都具有重要意义。

近年来把时间序列构造为复杂网络的方法在非线性时间序列分析与复杂网络之间架起了桥梁，基于复杂网络的非线性时间序列分析方法成为一个重要的研究热点。基于非线性时间序列局域预测法与相关向量机回归模型，提出了局域相关向量机预测方法，并应用于预测实际的小尺度网路流量序列。应用基于信息准则的局域预测法邻近点的选取方法来选取局域相关向量机回归模型的邻近点个数。基于递归图的递归量化分析重现了非线性时间序列的动力学行为，分析了其递归特性，提出了基于递归量化分析的癫痫脑电信号特征提取方法。在把脑电信号构造为复杂网络的基础上，提出了基于复杂网络度分布的香农熵的脑电信号特征提取方法。加权复杂网络是一种重要的复杂网络，其优点是避免了选取转换阈值所带来的信息丢失。本项目组研究了加权复杂网络顶点强度分布，并提出了基于加权复杂网络顶点强度分布的癫痫脑电特征提取方法。加权复杂网络权值差异可以从统计角度研究复杂网络中各个节点之间的权值不同，即从权值角度分析了加权网络拓扑结构的稀疏程度。本项目组研究了癫痫脑电序列加权复杂网络权值差异分布，并提出了基于加权复杂网络权值差异分布的特征提取方法。本项目组提出了一种基于LZ复杂度和时间序列分解的心室纤颤和心动过速心电信号特征提取的新方法。本项目研究成果在基于复杂网络的非线性时间序列分析方法研究与脑电信号非线性动力学分析方面都具有重要意义。