Graph Alignment: Wasserstein-based

This lecture covers the challenges in comparing non-Euclidean data such as social, functional, and economic networks, emphasizing the importance of topology. The instructor proposes a solution using Laplacian matrices for graph alignment, discussing the limitations of existing methods. The lecture explores optimal transport for graph distance computation, graph signal prediction, and the GOT algorithm for graph alignment optimization. It delves into the optimization difficulties and stochastic exploration techniques, concluding with experiments on graph classification and the significance of optimal transport in capturing structural information and transferring signals between graphs.