Matrices spectral structures in graph learning and its applications – MASSILIA

This project aims at tackling current problems related to graph learning and its applications in a unified way centered on the spectral decomposition of the graph Laplacian (and/or adjacency) matrix. The objectives are the following 1) directly control the graph spectral parameters within a robust learning process; 2) meaningfully leverage the spectral components of graphs with different size/topologies; 3) demonstrate the interest of the approach on spectral clustering applications, as well as the development of a framework to transfer signals/filters from one topology to another (e.g., to perform graph signal completion when missing data occurs). We aim to solve the considered problems using tools from statistics (robust costs and priors on structured parameters), optimal transport (defining transport/distances between structured objects), and optimization (solving the corresponding problems).