Department of Epileptology, University of Bonn, Bonn, Germany.
PLoS One. 2011;6(8):e22826. doi: 10.1371/journal.pone.0022826. Epub 2011 Aug 5.
We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erdös-Rényi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures--known for their complex spatial and temporal dynamics--we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.
我们研究了从多元时间序列中得出的相互作用网络，这些方法经常被应用于生物学、定量金融、物理、地球和气候科学以及神经科学等不同科学领域。为了模拟实验情况，我们生成了具有有限长度和变化频率内容的时间序列，但这些时间序列来自独立的随机过程。我们使用相关系数和最大互相关来估计这些时间序列之间的相关性。通过聚类系数和平均最短路径长度，我们观察到无权重相互作用网络，通过对相关性值进行阈值处理，可以得到与 Erdös-Rényi 网络相比具有非平凡拓扑的网络，这表明具有小世界特征。这些拓扑结构反映了数据不可避免的有限性，这限制了通常用于信号相关性估计的可靠性。我们提出了随机网络，这些网络是根据从经验数据中得出相互作用网络的方式量身定制的。通过对癫痫发作的多通道脑电图记录的示例研究——这些记录以其复杂的时空动态而闻名——我们表明，这种随机网络有助于区分与癫痫发作动力学相关的相互依赖结构的网络特性，以及由分析方法的应用引起的虚假特性。
