Some recent trends in embeddings of time series and dynamic networks

TL;DR

This paper reviews recent advances in embedding techniques for time series and dynamic networks, highlighting neural network approaches, topological data analysis, and identifying gaps between theory and real-world applications.

Contribution

It provides a comprehensive overview of current embedding methods for dynamic data, emphasizing neural networks and topological analysis, and discusses open problems in the field.

Findings

Neural network-based embeddings perform well in forecasting competitions.

Sparse literature exists on nonlinear time-varying embeddings.

There is a gap between theory and real-world network behavior.

Abstract

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.