IEEE Trans Cybern. 2019 May;49(5):1885-1895. doi: 10.1109/TCYB.2018.2816657. Epub 2018 Apr 10.
State space reconstruction is the foundation of chaotic system modeling. Selection of reconstructed variables is essential to the analysis and prediction of multivariate chaotic time series. As most existing state space reconstruction theorems deal with univariate time series, we have presented a novel nonuniform state space reconstruction method using information criterion for multivariate chaotic time series. We derived a new criterion based on low dimensional approximation of joint mutual information for time delay selection, which can be solved efficiently through the use of an intelligent optimization algorithm with low computation complexity. The embedding dimension is determined by conditional entropy, after which the reconstructed variables have relatively strong independence and low redundancy. The scheme, which integrates nonuniform embedding and feature selection, results in better reconstructions for multivariate chaotic systems. Moreover, the proposed nonuniform state space reconstruction method shows good performance in forecasting benchmark and actual multivariate chaotic time series.
状态空间重构是混沌系统建模的基础。对于多变量混沌时间序列的分析和预测，重构变量的选择至关重要。由于大多数现有的状态空间重构定理都处理单变量时间序列，因此我们提出了一种使用信息准则的新的非均匀状态空间重构方法，用于多变量混沌时间序列。我们推导了一种新的基于联合互信息低维近似的时滞选择准则，该准则可以通过使用具有低计算复杂度的智能优化算法来有效地解决。嵌入维度由条件熵确定，然后重构变量具有相对较强的独立性和较低的冗余度。该方案集成了非均匀嵌入和特征选择，可为多变量混沌系统提供更好的重建。此外，所提出的非均匀状态空间重构方法在预测基准和实际多变量混沌时间序列方面表现出良好的性能。
