In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and established, the field of dynamic network embedding is comparatively in its infancy. We propose that a wide class of established static network embedding methods can be used to produce interpretable and powerful dynamic network embeddings when they are applied to the dilated unfolded adjacency matrix. We provide a theoretical guarantee that, regardless of embedding dimension, these unfolded methods will produce stable embeddings, meaning that nodes with identical latent behaviour will be exchangeable, regardless of their position in time or space. We additionally define a hypothesis testing framework which can be used to evaluate the quality of a dynamic network embedding by testing for planted structure in simulated networks. Using this, we demonstrate that, even in trivial cases, unstable methods are often either conservative or encode incorrect structure. In contrast, we demonstrate that our suite of stable unfolded methods are not only more interpretable but also more powerful in comparison to their unstable counterparts.

翻译：本文研究了动态网络嵌入问题，即将动态网络中的节点表示为低维空间中的演化向量。尽管静态网络嵌入领域已发展成熟且应用广泛，但动态网络嵌入领域仍处于相对初期阶段。我们提出，将时间膨胀展开邻接矩阵应用于一类广泛的成熟静态网络嵌入方法，可生成可解释且强大的动态网络嵌入。我们提供了理论保证：无论嵌入维度如何，这些展开方法均能产生稳定嵌入，即具有相同潜在行为的节点在时间或空间位置上具有可交换性。此外，我们建立了一个假设检验框架，通过模拟网络中植入结构检验动态网络嵌入的质量。实验表明，即使在简单案例中，不稳定的方法往往存在保守性或编码错误结构的问题。相比之下，我们的稳定展开方法套件不仅更具可解释性，在性能上也显著优于其不稳定对应方法。