Department of Physics, University of California, Santa Barbara, California 93106, USA.
Chaos. 2013 Mar;23(1):013142. doi: 10.1063/1.4790830.
We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations ("optimization variance") and over randomizations of network structure ("randomization variance"). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.
我们描述了在某些类的时变网络中稳健检测社区结构的技术。具体来说，我们考虑使用统计空模型来促进半可分解系统中结构模块的原则性识别。空模型在优化质量函数（如模块性）和随后评估识别的社区结构的统计有效性方面都起着重要作用。我们检查了这些方法对模型参数的敏感性，并展示了如何将其与空模型进行比较以帮助识别系统规模。通过考虑大量优化，我们量化了网络诊断在优化（“优化方差”）和网络结构随机化（“随机化方差”）中的方差。由于使用真实数据构建的网络的模块化质量函数通常具有大量几乎退化的局部最优解，因此我们开发了一种使用空模型来校正分区集合中的统计噪声的方法来构建代表性分区。为了说明我们的结果，我们使用了从非线性振荡器和经验神经科学数据中提取的时变网络的集合。
