Large-Margin Classification in Hyperbolic Space
This work enables more accurate classification for data with inherent hierarchical structures, such as complex networks, by avoiding the use of ill-fitting Euclidean tools.
The authors tackled the problem of classifying data in hyperbolic space by introducing hyperbolic SVM, a formulation that respects hyperbolic geometry, and demonstrated performance improvements on real-world complex networks and simulated datasets.
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.