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 horospherical 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 competitive performance of our classifier in comparison to SOTA.

翻译：双曲空间近年因其对层级组织数据的优越表征能力而备受关注。文献中已提出多种适用于此类空间数据的分类算法，这些算法主要采用超平面或测地线作为大间隔分类器中的决策边界，但该类方法会导致非凸优化问题。本文提出一种基于轨道球面决策边界的新型大间隔分类器，该分类器可转化为测地凸优化问题，可通过任意黎曼梯度下降技术优化，并保证获得全局最优解。我们通过多项实验表明，该分类器的性能与当前最优方法相比具有竞争力。