Learning Time-Varying Graph Signals via Koopman

• URL: http://arxiv.org/abs/2511.06493v1
• Date: Sun, 09 Nov 2025 18:33:39 GMT
• Title: Learning Time-Varying Graph Signals via Koopman
• Authors: Sivaram Krishnan, Jinho Choi, Jihong Park,
• Abstract summary: We propose a framework based on the Koopman autoencoder (KAE) to handle time-varying graph data.<n>To capture the evolving graph structures, the graph data is first converted into a vector time series through graph embedding.<n>In this latent space, the KAE is applied to learn the underlying non-linear dynamics governing the temporal evolution of graph features.
• Score: 17.357706885280695
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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