Graph Signal Reconstruction via Koopman Autoencoder

Abstract

Real-world graph signals are inherently time-varying and evolve smoothly, making the characterization of such data challenging. We propose a novel approach for reconstructing missing time-varying graph data by leveraging the assumption that the latent variable responsible for generating this data evolves according to nonlinear dynamics. To learn these dynamics, we employ a Koopman autoencoder, and apply graph embedding techniques to map the graph data into a latent space. While existing approaches require known time-invariant Laplacian matrices, our proposed approach can perform reconstruction without needing these matrices, which can also be time-varying. Simulation results show that our method surpasses baseline approaches, achieving a reduction in reconstruction error by 47% to 61% compared to alternative methods, while effectively reconstructing time-varying graphs with dynamic structures.