Title: Large-Margin Classification in Hyperbolic Space,
Abstract: Representing data in hyperbolic space can effectively capture latent
hierarchical relationships. With the goal of enabling accurate classification
of points in hyperbolic space while respecting their hyperbolic geometry, we
introduce hyperbolic SVM, a hyperbolic formulation of support vector machine
classifiers, and elucidate through new theoretical work its connection to the
Euclidean counterpart. We demonstrate the performance improvement of hyperbolic
SVM for multi-class prediction tasks on real-world complex networks as well as
simulated datasets. Our work allows analytic pipelines that take the inherent
hyperbolic geometry of the data into account in an end-to-end fashion without
resorting to ill-fitting tools developed for Euclidean space.