基于近邻轨道平均长度的混沌时间序列分类方法

Classification of chaotic time series data based on the average length of close orbits

在混沌时间序列的复原图 (recurrenceplot,RP)基础上 ,提出了两混沌时间序列的相干复原图 (crossrecurrenceplot,CRP)的定义 ,并在CRP上提取出两时间序列在同一重构相空间中演化趋势接近的轨道的平均长度 (近邻轨道平均长度 ) ,最终实现对混沌时间序列的分类 .通过对Lorenz信号的分析 ,得出两时间序列的近邻轨道平均长度随着它们的重构轨道在相空间中的演化相似性的减小而减短 ;通过本方法与Schreiber提出的相干预测误差分类方法对心电信号 (ECG)的节律变化的检测实验 ,得出 :对波形差异较大的不同节律ECG信号 ,两种方法都能有效地进行分类 ;而对波形差异较小的不同节律ECG信号 ,近邻轨道平均长度分类方法更有效 .

Based on recurrence plot (RP) of chaotic time series, this paper develops the definition of cross recurrence plot (CRP) and the average length of close orbits, which reflects the similarity of two time series and is used to classify time series. By analysing the Lorenz signals, we conclude that the average length is decreased with the decrease of the similarity of two orbits. We have used our method and the cross-prediction error in the detection of ECG rhythm. The results show that both methods work for rhythm with different waveforms, but our method works better for rhythms with similar waveforms than the method of cross-prediction error.