Wasserstein-based Graph Alignment

A novel method for comparing non-aligned graphs of various sizes is proposed, based on the Wasserstein distance between graph signal distributions induced by respective Laplacian matrices. Specifically, a new formulation one-to-many alignment problem casted, which aims at matching node in smaller with one or more nodes larger graph. By incorporating optimal transport into our comparison framework, structurally-meaningful distance, and transportation plan that models structure data are generated. The resulting solved stochastic gradient descent, where Dykstra operator used to ensure solution (soft) assignment matrix. performance framework demonstrated alignment, classification transportation. Our shown lead significant improvements respect state-of-the-art algorithms each ofthese tasks.