Exploiting Variational Inequalities for Generalized Change Detection on Graphs

This article introduces a unified framework for developing graph-based change detection (CD) algorithms in remote sensing, which is based on signal feasibility problems and variational inequalities. We argue that signal feasibility problems provide a natural way to frame the CD problem, while variational inequalities, core elements of modern data science and signal processing methods, enable us to find efficient, stable, and reliable solutions to the proposed feasibility problems. We demonstrate the design of both semisupervised and unsupervised CD schemes from our perspective, establishing connections with graph Laplacian filtering and graph convolutional networks (GCNs). In contrast to specialized methods that rely on composite objective functions with multiple penalty parameters, our approach greatly simplifies hyperparameter selection, as the hyperparameters are both bounded and can form convex combinations (i.e., they are nonnegative and sum up to one). We evaluate our approach on various real heterogeneous and homogeneous datasets, demonstrating its capabilities compared to traditional and modern CD methods. In addition, our ablation studies confirm the consistency of our solutions under variations in the number of nodes and graph structure learning (GSL) methods. We conclude by discussing the advantages, limitations, and promising future research directions, with connections to graph filtering, sampling set selection, and self-supervised learning. The source code to replicate the experiments and explore the approach further is available on GitHub at https://github.com/jfflorez/Exploiting-variational-inequalities-for-generalized-change-detection-on-graphs.git .