Learning graph connectivity has broad-ranging applications from 3D reconstruction to unsupervised learning. In this talk I will introduce a new method to learn the graph structure underlying noisy point set observations assumed to lie near a complex manifold. Rather than assuming regularity of the manifold itself, as customary, we assume regularity of the geodesic flow through the boundary of arbitrary regions on the graph. The idea is to exploit this more flexible notion of regularity, captured by the discrete equivalent of the isoperimetric inequality for closed manifolds, to infer the graph structure.
In a broader perspective, when studying the topology of the graph networks, we would like to learn new representations that capture not only local connectivity, i.e., nodes that belong to the same local structure, but also similarity which is based on their structural role in the graph. I will discuss a new approach and vision towards learning a good trade-off between these local and structural types of similarities that includes diverse possible applications including point clouds, biological networks and social networks.
Shay Deutsch received a B.Sc. in Mathematics from the Technion—Israel Institute of Technology in 2007, an M.Sc. in Applied Mathematics from Tel Aviv University in 2010, and a Ph.D. in Computer Science from the University of Southern California (USC) in 2016. He is currently an Assistant Adjunct Professor in the Mathematics Department at the University of California, Los Angeles (UCLA). His research work is in the union of transfer learning, graph signal processing and graph networks, where his research is dedicated to developing robust methods for unsupervised learning. His most recent research efforts focus on developing cohesive relations between embedding topology and graph networks using uncertainty principles on graphs.