用流形优化追踪动态网络中的社区演化，统一了多种谱方法。
A Spectral Framework for Tracking Communities in Evolving Networks
- 将静态谱聚类视为高维节点嵌入的低秩近似，构建动态追踪框架。
- 在合成与真实时间网络上表现优异，涵盖加权、有向、混合成员等复杂结构。
- 适用于多视图、层次化、共社区等复杂网络，适合研究动态关系的学者。
在随时间变化的网络中发现并追踪社区是网络科学的重要任务，应用场景涵盖神经科学到社会学。本文从高维节点嵌入的低秩近似角度重新诠释经典谱聚类方法，并将其自然拓展为在Grassmann流形上的子空间追踪问题。尽管优化问题非凸，我们采用块极大极小黎曼优化方案，学习拟合数据的最佳格拉斯曼测地线。该框架可泛化任意静态谱社区检测方法，在合成与真实时间网络（包括加权、符号、有向、混合成员、多视图、层次化、共社区结构、二分网络或其组合）上均取得优异性能。文中展示了如何将多种方法纳入本框架，并在所有情形下显著提升动态社区检测效果。
原文摘要 · Abstract (English)
Discovering and tracking communities in time-varying networks is an important task in network science, motivated by applications in fields ranging from neuroscience to sociology. In this work, we characterize the celebrated family of spectral methods for static clustering in terms of the low-rank approximation of high-dimensional node embeddings. From this perspective, it becomes natural to view the evolving community detection problem as one of subspace tracking on the Grassmann manifold. While the resulting optimization problem is nonconvex, we adopt a block majorize-minimize Riemannian optimization scheme to learn the Grassmann geodesic which best fits the data. Our framework generalizes any static spectral community detection approach and leads to algorithms achieving favorable performance on synthetic and real temporal networks, including those that are weighted, signed, directed, mixed-membership, multiview, hierarchical, cocommunity-structured, bipartite, or some combination thereof. We demonstrate how to specifically cast a wide variety of methods into our framework, and demonstrate greatly improved dynamic community detection results in all cases.
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