Hyperbolic spaces have been quite popular in the recent past for representing
hierarchically organized data. Further, several classification algorithms for
data in these spaces have been proposed in the literature. These algorithms
mainly use either hyperplanes or geodesics for decision boundaries in a large
margin classifiers setting leading to a non-convex optimization problem. In
this paper, we propose a novel large margin classifier based on horocycle
(horosphere) decision boundaries that leads to a geodesically convex
optimization problem that can be optimized using any Riemannian gradient
descent technique guaranteeing a globally optimal solution. We present several
experiments depicting the performance of our classifier