Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics.
Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics.
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DOI：
10.3390/e23020221
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发表时间：
2021-02-11
期刊：
影响因子：
--
通讯作者：
Ruiz Marín M
中科院分区：
文献类型：
--
作者：
Matilla-García M;Morales I;Rodríguez JM;Ruiz Marín M
混沌时间序列的建模和预测需要从已有的数据中适当地重构状态空间，以便成功地估计嵌入吸引子的不变性质。因此，对于相空间重构，必须选择合适的时间延迟和嵌入维度p。可以根据互信息估计的值，但这种方法计算起来相当繁琐。此外，一些研究人员建议，应该通过适当的时延取值来选择依赖于嵌入维度p的时延，这是时间序列独立性的最佳时延。基于相关积分的C-C方法是一种比互信息更简单的方法，已被提出用来进行最优选择。本文提出了一种基于符号分析和符号熵的简单估计方法。在C-C方法中，被估计为第一个局部最优时滞，并被估计为时间序列独立的时延。将该方法应用于几个混沌时间序列，作为几种方法比较的基础。对这些系统的数值仿真表明，基于符号的方法对实践者是有用的，并且根据所研究的模型，在时延和嵌入维度的选择上比C-C方法具有更好的性能。此外，将该方法应用于脑电信号数据，以研究和比较癫痫发作时的一些脑活动的动态特征
The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay and embedding dimension p for phase space reconstruction. The value of can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay , which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally and . In this paper, we suggest a simple method for estimating and based on symbolic analysis and symbolic entropy. As in the C-C method, is estimated as the first local optimal time delay and as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes
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