Accessibility setting

Section: New Results

Higher-order Learning with Graphs

Along the thesis of Thomas Ricatte , in [4] and [8] , we propose methods for learning from interactions between groups in networks. We propose a proper extension of graphs, called hypernode graphs as a formal tool able to model group interactions. A hypernode graph is a collection of weighted relations between two groups of distinct nodes. Weights quantify the individual participation of nodes to a given relation. We define Laplacians and kernels for hypernode graphs and and prove that they strictly generalize over graph kernels and hypergraph kernels. We prove that hypernode graphs correspond to signed graphs such that the matrix $D-W$ is positive semidefinite. As a consequence, homophilic relations between groups may lead to non homophilic relations between individuals. We define the notion of connected hypernode graphs and a resistance distance for connected hypernode graphs. We propose spectral learning algorithms on hypernode graphs allowing to infer node ratings or node labelings. As a proof of concept, we model multiple players games with hypernode graphs and we define skill rating algorithms competitive with specialized algorithms.