We give a review of some recent developments in embeddings of time series and dynamic networks. We start out with traditional principal components and then look at extensions to dynamic factor models for time series. Unlike principal components for time series, the literature on time-varying nonlinear embedding is rather sparse. The most promising approaches in the literature is neural network based, and has recently performed well in forecasting competitions. We also touch upon different forms of dynamics in topological data analysis. The last part of the paper deals with embedding of dynamic networks where we believe there is a gap between available theory and the behavior of most real world networks. We illustrate our review with two simulated examples. Throughout the review, we highlight differences between the static and dynamic case, and point to several open problems in the dynamic case.
翻译:我们审视了在嵌入时间序列和动态网络方面的一些最新动态。 我们先从传统的主要组成部分开始, 然后再研究时间序列动态要素模型的扩展。 与时间序列的主要组成部分不同, 时间变化的非线性嵌入文献相当稀少。 文献中最有希望的方法是以神经网络为基础, 最近在预测竞争方面表现良好 。 我们还在地貌数据分析中触及不同形式的动态。 论文最后一部分涉及嵌入动态网络, 我们认为在其中现有理论与最真实世界网络的行为之间存在差距。 我们用两个模拟的例子来说明我们的审查。 在整个审查过程中, 我们强调静态和动态案例之间的差异, 并指出动态案例中存在的几个尚未解决的问题 。