Zhu Junyao, Chen Mingming, Lu Junfeng, Zhao Kun, Cui Enze, Zhang Zhiheng, Wan Hong
School of Electrical Engineering, Zhengzhou University, Zhengzhou 450001, China.
Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, Zhengzhou 450001, China.
Entropy (Basel). 2022 Aug 13;24(8):1118. doi: 10.3390/e24081118.
The ensemble transfer entropy (TEensemble) refers to the transfer entropy estimated from an ensemble of realizations. Due to its time-resolved analysis, it is adapted to analyze the dynamic interaction between brain regions. However, in the traditional TEensemble, multiple sets of surrogate data should be used to construct the null hypothesis distribution, which dramatically increases the computational complexity. To reduce the computational cost, a fast, efficient TEensemble with a simple statistical test method is proposed here, in which just one set of surrogate data is involved. To validate the improved efficiency, the simulated neural signals are used to compare the characteristics of the novel TEensemble with those of the traditional TEensemble. The results show that the time consumption is reduced by two or three magnitudes in the novel TEensemble. Importantly, the proposed TEensemble could accurately track the dynamic interaction process and detect the strength and the direction of interaction robustly even in the presence of moderate noises. The novel TEensemble reaches its steady state with the increased samples, which is slower than the traditional method. Furthermore, the effectiveness of the novel TEensemble was verified in the actual neural signals. Accordingly, the TEensemble proposed in this work may provide a suitable way to investigate the dynamic interactions between brain regions.
总体转移熵（TEensemble）是指从一组实现中估计出的转移熵。由于其具有时间分辨分析能力，适用于分析脑区之间的动态相互作用。然而，在传统的TEensemble中，需要使用多组替代数据来构建零假设分布，这极大地增加了计算复杂度。为了降低计算成本，本文提出了一种具有简单统计检验方法的快速、高效的TEensemble，其中只涉及一组替代数据。为了验证提高的效率，使用模拟神经信号将新型TEensemble的特征与传统TEensemble的特征进行比较。结果表明，新型TEensemble的时间消耗减少了两到三个数量级。重要的是，即使在存在中等噪声的情况下，所提出的TEensemble也能够准确跟踪动态相互作用过程，并稳健地检测相互作用的强度和方向。新型TEensemble随着样本数量的增加达到稳态，这比传统方法要慢。此外，新型TEensemble在实际神经信号中的有效性得到了验证。因此，本文提出的TEensemble可能为研究脑区之间的动态相互作用提供一种合适的方法。
