Department of Physics, University of Michigan, Ann Arbor, USA.
Department of Statistics and the Informatics Institute, University of Florida, Gainesville, USA.
Sci Rep. 2018 Aug 28;8(1):12938. doi: 10.1038/s41598-018-29964-9.
Community detection in time series networks represents a timely and significant research topic due to its applications in a broad range of scientific fields, including biology, social sciences and engineering. In this work, we introduce methodology to address this problem, based on a decomposition of the network adjacency matrices into low-rank components that capture the community structure and sparse & dense noise perturbation components. It is further assumed that the low-rank structure exhibits sharp changes (phase transitions) at certain epochs that our methodology successfully detects and identifies. The latter is achieved by averaging the low-rank component over time windows, which in turn enables us to precisely select the correct rank and monitor its evolution over time and thus identify the phase transition epochs. The methodology is illustrated on both synthetic networks generated by various network formation models, as well as the Kuramoto model of coupled oscillators and on real data reflecting the US Senate's voting record from 1979-2014. In the latter application, we identify that party polarization exhibited a sharp change and increased after 1993, a finding broadly concordant with the political science literature on the subject.
由于在生物学、社会科学和工程等广泛科学领域中的应用，时间序列网络中的社区检测是一个及时且重要的研究课题。在这项工作中，我们提出了一种基于将网络邻接矩阵分解为低秩分量（捕获社区结构和稀疏和密集噪声扰动分量）的方法来解决这个问题。进一步假设低秩结构在某些时段表现出明显的变化（相变），我们的方法成功地检测和识别了这些变化。后者是通过在时间窗口上对低秩分量进行平均来实现的，这反过来使我们能够精确地选择正确的秩，并监测其随时间的演变，从而识别相变时段。该方法在各种网络形成模型生成的合成网络以及耦合振荡器的 Kuramoto 模型上进行了说明，并在反映 1979-2014 年美国参议院投票记录的真实数据上进行了说明。在后一种应用中，我们发现党派极化在 1993 年后发生了明显变化并加剧，这一发现与该主题的政治学文献广泛一致。
