Graph Learning Based on Total Variation Minimization

We consider the problem of learning the topology of a graph from a given set of smooth graph signals. We construct a weighted adjacency matrix that best explains the data in the sense of achieving the smallest graph total variation. For the case of noisy measurements of the graph signals we propose a scheme that simultaneously denoises the signals and learns the graph adjacency matrix. Our method allows for a direct control of the number of edges and of the weighted node degree. Numerical experiments demonstrate that our graph learning scheme is well suited for community detection.