用张量状态空间建模动态多层网络的时序与跨层演化。
Tensor State Space-based Dynamic Multilayer Network Modeling
- 基于对称的Tucker分解表示节点特征与层间转移模式。
- 固定节点特征，让交互模式随时间演化，捕捉层内与跨层动态。
- 适合研究复杂系统中多层结构随时间变化的科研人员。
理解动态多层网络中的复杂交互对多个科学领域至关重要。现有模型难以捕捉此类网络的时间与跨层动态。本文提出一种基于张量状态空间的动态多层网络建模方法（TSSDMN），采用潜在空间模型框架。TSSDMN利用对称Tucker分解表示潜在节点特征、交互模式及层间转移。通过固定潜在特征并允许交互模式随时间演化，独特地刻画了层内与跨层的时序动态。讨论了模型可辨识性条件。将潜在特征视为变量，使用均值场变分推断近似其后验分布，进而开发了高效的变分期望最大化算法用于模型推断。数值模拟与案例研究验证了TSSDMN在理解动态多层网络方面的有效性。
原文摘要 · Abstract (English)
Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper introduces a novel Tensor State Space Model for Dynamic Multilayer Networks (TSSDMN), utilizing a latent space model framework. TSSDMN employs a symmetric Tucker decomposition to represent latent node features, their interaction patterns, and layer transitions. Then by fixing the latent features and allowing the interaction patterns to evolve over time, TSSDMN uniquely captures both the temporal dynamics within layers and across different layers. The model identifiability conditions are discussed. By treating latent features as variables whose posterior distributions are approximated using a mean-field variational inference approach, a variational Expectation Maximization algorithm is developed for efficient model inference. Numerical simulations and case studies demonstrate the efficacy of TSSDMN for understanding dynamic multilayer networks.
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