We pursue the problem of modelling and analysing latent space dynamics in collections of networks. Towards this end, we pose and study latent space generative models for signed networks that are amenable to inference via spectral methods. Permitting signs, rather than restricting to unsigned networks, enables richer latent space structure and permissible dynamic mechanisms that can be provably inferred via low rank truncations of observed adjacency matrices. Our treatment of and ability to recover latent space dynamics holds across different levels of granularity, namely, at the overall graph level, for communities of nodes, and even at the individual node level. We provide synthetic and real data examples to illustrate the effectiveness of methodologies and to corroborate accompanying theory. The contributions set forth in this paper complement an emerging statistical paradigm for random graph inference encompassing random dot product graphs and generalizations thereof.

中文翻译：

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具有潜在空间动力学和符号的网络的频谱分析

我们致力于对网络集合中的潜在空间动态进行建模和分析。为此，我们提出并研究了可通过谱方法进行推理的有符号网络的潜在空间生成模型。允许符号，而不是仅限于无符号网络，可以实现更丰富的潜在空间结构和允许的动态机制，这些机制可以通过观察到的邻接矩阵的低秩截断来证明。我们对潜在空间动态的处理和恢复能力适用于不同的粒度级别，即在整体图级别、节点社区，甚至在单个节点级别。我们提供合成和真实数据示例来说明方法论的有效性并证实伴随的理论。