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：双曲空间近年来在表示层次化组织数据方面非常流行。此外，文献中提出了多种针对这些空间中数据的分类算法。这些算法主要在大间隔分类器设置中利用超平面或测地线作为决策边界，导致非凸优化问题。在本文中，我们提出了一种基于霍罗球决策边界的新型大间隔分类器，该分类器导致一个测地凸优化问题，可以使用任何黎曼梯度下降技术进行优化，保证全局最优解。我们进行了多项实验，展示了我们的分类器与现有最先进技术相比的竞争性能。