提出热扩散条件熵,用于分析动态网络的演化规律。
Conditional Entropy of Heat Diffusion on Temporal Networks

- 用热扩散条件熵衡量连续时间动态网络的信息演化。
- 该熵随时间单调递增,类比热力学第二定律。
- 可检测网络结构突变点,提升社区发现效果。
基于扩散的信息论方法为复杂网络研究提供了新的理论与实践工具。然而,这些方法尚未推广到时序网络。本文指出,传统基于图扩散的熵度量(如熵率和谱熵)无法直接适用于时序网络,因其过程非平稳且存在时间不对称性。为此,我们提出连续时间时序网络的热扩散条件熵作为信息度量,并研究其性质。该量随时间单调递增,为非均匀扩散过程提供信息论意义上的热力学第二定律类比。我们给出其演化的上界,并提出下界,解释因时间路径不对称导致的偏差。进一步引入局部版本的条件熵,用于探测有限时间窗口内的扩散变化,有效识别时序网络中的突变点。我们在合成基准数据集上进行对比实验(与现有非参数基线在快照设置下比较),并应用于真实世界时序接触网络。最后展示如何利用检测到的突变点指导子区间上的社区发现,显著提升聚类结果的质量与可解释性。
原文摘要 · Abstract (English)
Diffusion-based information-theoretic approaches provide new theoretical and practical tools to study complex networks. So far, they have not been generalized to temporal networks. In this work, we show that common entropic measures based on modeling diffusion on graphs, such as the entropy rate and the spectral entropy, do not generalize straightforwardly to temporal networks due to the process's non-stationarity and temporal asymmetries. Instead, we propose the conditional entropy of heat diffusion as an entropic measure for continuous-time temporal networks and study its properties. We show that this quantity is monotone in time, yielding an information-theoretic analog of the second law of thermodynamics for inhomogeneous diffusion on temporal networks. We provide an upper bound and suggest a lower bound on its evolution and explain how discrepancies from it arise due to asymmetric temporal paths. We then introduce a local version of conditional entropy, designed to probe diffusion over finite temporal windows, and show that it provides an informative signal for change-point detection in continuous-time temporal networks. We evaluate the proposed methodology on synthetic benchmarks, including comparative experiments with existing nonparametric baselines in the snapshot setting, and then apply it to a real-world temporal contact network. Finally, we show how to use detected change points to guide community detection on targeted sub-intervals, improving the quality and interpretability of the clustering results.
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