Shay Deutsch: Robust Methods for Topology Estimation in Unsupervised Learning

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. This regularization alone, paired with the simplest
baseline model, outperforms the state-of-the-art among fully automated
methods in zero-shot learning benchmarks such as AwA and CUB. This
improvement is achieved solely by learning the structure of the
underlying spaces by imposing regularity.

In a broader perspective, when studying the topology of the graph
networks, we would like to design a representation of the graph that
can capture both the local similarity between adjacent nodes, as well
as the non-local similarity of distant nodes based on their structural
properties. I will discuss a new unsupervised learning approach
to learn an embedding function associated at each node, that trades
off local and structural similarity.  Such a representation would
empower network topology analysis in fields as diverse as material
science, social science, biology and commerce.