Wasserstein Motifs: Optimal Transport for Food Web Alignment

Abstract:

Network alignment is a fundamental problem in various domains, including bioin- formatics, social network analysis, computer vision, and computational ecology. This report investigates the soft network alignment problem from an optimization perspective, proposing an entropically regularized formulation that enables efficient gradient-based optimization. Leveraging primal-dual methods, we derive explicit gradient and Hessian formulations to facilitate scalable and accurate solutions. Through experimental evaluations on both synthetic toy graphs and real-world ecological networks, we demonstrate that soft alignments provide richer structural insights compared to traditional hard alignments. These findings highlight the advantages of soft alignment methods in capturing nuanced structural similarities, making them particularly beneficial when dealing with complex or large-scale network alignment tasks.