Learning Time-Varying Graph Signals via Koopman

TL;DR

This paper introduces a Koopman autoencoder framework for modeling and predicting the evolution of time-varying graph signals by capturing their underlying non-linear dynamics in a latent space.

Contribution

It proposes a novel approach combining graph embedding and Koopman autoencoders to analyze dynamic graph data and predict their evolution.

Findings

Effective modeling of time-varying graph signals.

Improved prediction and reconstruction of dynamic graphs.

Framework applicable to real-world sensor and UAV data.

Abstract

A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting non-Euclidean structures. These graph representations may evolve over time, forming time-varying graphs. Effectively modeling and analyzing such dynamic graph data is critical for tasks like predicting graph evolution and reconstructing missing graph data. In this paper, we propose a framework based on the Koopman autoencoder (KAE) to handle time-varying graph data. Specifically, we assume the existence of a hidden non-linear dynamical system, where the state vector corresponds to the graph embedding of the time-varying graph signals. To capture the evolving graph structures, the graph data is first converted into a vector time series through graph embedding, representing the structural information in a finite-dimensional latent space. In this latent space, the KAE is applied to learn the underlying non-linear dynamics governing the temporal evolution of graph features, enabling both prediction and reconstruction tasks.