🤖 AI Summary
This paper addresses the problem of learning time-varying graph structures from sparse spatiotemporal measurements, where the core challenge lies in ensuring smooth and interpretable structural evolution under limited sample size. To this end, we propose a convex optimization–based framework for time-varying graph learning—the first to jointly impose two convex regularizers: (i) a graph Laplacian sparsity constraint and (ii) an ℓ₁-norm penalty on temporal differences between consecutive graph Laplacians, explicitly encoding temporal smoothness priors. The method integrates principles from graph signal processing with scalable iterative algorithms, guaranteeing both theoretical tractability and computational efficiency. Extensive experiments on synthetic data, real-world point cloud sequences, and temperature time series demonstrate that our approach significantly outperforms state-of-the-art methods—particularly in low-sample regimes—while exhibiting superior estimation accuracy, robustness to noise, and generalization capability.
📝 Abstract
We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of available measurements. To achieve this, we introduce two regularization terms in convex optimization problems that constrain sparseness of temporal variations of the time-varying networks. Moreover, a computationally-scalable algorithm is introduced to efficiently solve the optimization problem. The experimental results with synthetic and real datasets (point cloud and temperature data) demonstrate our proposed method outperforms the existing state-of-the-art methods.
