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# Large-Margin Classification in Hyperbolic Space

*Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics*, PMLR 89:1832-1840, 2019.

#### Abstract

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. To enable 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 describe its theoretical connection to the Euclidean counterpart. We also generalize Euclidean kernel SVM to hyperbolic space, allowing nonlinear hyperbolic decision boundaries and providing a geometric interpretation for a certain class of indefinite kernels. Hyperbolic SVM improves classification accuracy in simulation and in real-world problems involving complex networks and word embeddings. Our work enables end-to-end analyses based on the inherent hyperbolic geometry of the data without resorting to ill-fitting tools developed for Euclidean space.