动态多层图的双重展开邻接谱嵌入
Doubly unfolded adjacency spectral embedding of dynamic multiplex graphs
AI总结：
本文提出动态多层随机点积图模型，结合双重展开邻接谱嵌入方法，用于估计参数并捕捉网络复杂行为，应用于地缘政治和金融新闻分析。
摘要：
许多现实网络随时间动态演变，呈现不同类型的节点连接，称为层。本文提出动态多层随机点积图（DMPRDPG）模型，利用层特定和时间特定的节点潜在表示内积获得边概率。进一步引入计算高效的谱嵌入方法，称为双重展开邻接谱嵌入（DUASE），证明其一致性及渐近正态性。方法的关键在于将时间特定节点表示和层特定效应编码在独立潜在空间中，允许模型捕捉复杂行为同时保持低维性。所提嵌入方法也可高效用于后续推断任务。特别强调ISOMAP算法与DUASE结合以高效捕捉网络趋势和全局变化点，以及DUASE用于图聚类。在描述国家地缘政治互动和金融新闻报道的现实网络上的应用展示了方法的实用性。
英文摘要：
Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this work, we propose a latent position model for these objects, called the dynamic multiplex random dot product graph (DMPRDPG), which uses an inner product between layer-specific and time-specific latent representations of the nodes to obtain edge probabilities. We further introduce a computationally efficient spectral embedding method for estimation of DMPRDPG parameters, called doubly unfolded adjacency spectral embedding (DUASE). The DUASE estimates are proved to be both consistent and asymptotically normally distributed. A key strength of our method is the encoding of time-specific node representations and layer-specific effects in separate latent spaces, which allows the model to capture complex behaviors while maintaining relatively low dimensionality. The embedding method we propose can also be efficiently used for subsequent inference tasks. In particular, we highlight the use of the ISOMAP algorithm in conjunction with DUASE as a way to efficiently capture trends and global changepoints within a network, and the use of DUASE for graph clustering. Applications on real-world networks describing geopolitical interactions between countries and financial news reporting demonstrate practical uses of our method.
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