Discrete Curvature and Applications in Graph Machine Learning
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of Representation Learning. In this talk, we study this problem from the perspective of Discrete Geometry. We start by reviewing discrete notions of curvature with a focus on discrete Ricci curvature. Then we discuss how curvature is linked to mesoscale structure in graphs, which gives rise to applications in graph machine learning, such as (unsupervised) node clustering. For downstream machine learning and data science applications, it is often beneficial to represent graph-structured data in a continuous space, which may be Euclidean or Non-Euclidean. We show that discrete curvature allows for characterizing the geometry of a suitable embedding space both locally and in the sense of global curvature bounds and discuss implications of those results in graph machine learning.