Time-Varying Graph Learning with Constraints on Graph Temporal Variation

TL;DR

This paper introduces a convex optimization framework with regularization for learning sparse, time-varying graphs from limited spatiotemporal data, improving accuracy over existing methods.

Contribution

It presents a novel regularization-based approach and scalable algorithm for estimating dynamic graphs with constrained temporal variation.

Findings

Outperforms state-of-the-art methods on synthetic data.

Effective on real datasets like point clouds and temperature measurements.

Demonstrates robustness with limited measurements.

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.