Faes Luca, Nollo Giandomenico, Erla Silvia, Papadelis Christos, Braun Christoph, Porta Alberto
Dept. of Physics and BIOtech, University of Trento, Mattarello (TN), Italy.
Annu Int Conf IEEE Eng Med Biol Soc. 2010;2010:102-5. doi: 10.1109/IEMBS.2010.5626127.
This study introduces a new approach for the detection of nonlinear Granger causality between dynamical systems. The approach is based on embedding the multivariate (MV) time series measured from the systems X and Y by means of a sequential, non-uniform procedure, and on using the corrected conditional entropy (CCE) as unpredictability measure. The causal coupling from X to Y is quantified as the relative decrease of CCE measured after allowing the series of X to enter the embedding procedure for the description of Y. The ability of the approach to quantify nonlinear causality is assessed on MV time series measured from simulated dynamical systems with unidirectional coupling (the Rössler-Lorenz deterministic system) and bidirectional coupling (two coupled stochastic systems). The method is then applied to real magnetoencephalographic data measured during a visuo-tactile cognitive experiment, showing values of causal coupling consistent with the hypothesis of a cross-processing of different sensory modalities.
本研究介绍了一种检测动力系统之间非线性格兰杰因果关系的新方法。该方法基于通过一种顺序的、非均匀的过程对从系统X和Y测量的多元（MV）时间序列进行嵌入，并使用校正条件熵（CCE）作为不可预测性度量。从X到Y的因果耦合被量化为在允许X序列进入嵌入过程以描述Y之后测量的CCE的相对下降。该方法量化非线性因果关系的能力在从具有单向耦合的模拟动力系统（罗斯勒 - 洛伦兹确定性系统）和双向耦合（两个耦合随机系统）测量的MV时间序列上进行了评估。然后将该方法应用于在视觉 - 触觉认知实验期间测量的真实脑磁图数据，显示出因果耦合值与不同感官模态交叉处理的假设一致。
