提出新方法,让动态网络随时间变化的轨迹更准确、可解释。
Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points

- 基于二阶矩几何构造多尺度时间轨迹,消除原有表示的模糊性。
- 能准确检测网络中关键时间节点的变化,性能优于现有方法。
- 适合研究网络演化、节点贡献和结构突变的学者使用。
动态网络分析的核心挑战是如何以几何有意义且统计可识别的方式表征随时间演变的结构。现有方法将网络快照序列嵌入欧几里得空间形成轨迹,但多层与展开谱构造中的节点嵌入及其潜在位置仅在一般线性变换下可识别。这种模糊性虽保留边概率,却会扭曲几何结构,导致基于距离的时间比较在轨迹与节点层面失效。本文提出多尺度欧几里得网络轨迹(MENT),基于二阶矩几何构建多尺度时间轨迹。通过施加各向同性归一化于锚点潜在位置,将模糊性缩减至正交变换,防止二阶矩几何失真。在此标准表示中,定义迹变异性距离与沿正交方向的模式变异性距离,并利用多维标度获得全局与模式级的低维时间点轨迹。所得轨迹支持解释与推断:具备模式分解能力,可归因全局与模式级的时序变化至具体节点,并通过一维轨迹实现变化点检测。我们证明了所提展开谱嵌入及诱导时间轨迹的一致性。在两个合成数据集与两个真实动态网络上的实验表明,该方法能稳定、可解释地恢复时序结构,且在变化点检测上显著优于现有基线方法。
原文摘要 · Abstract (English)
A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.
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