Large-margin classification in hyperbolic space

Hyunghoon Cho, Benjamin DeMeo, Jian Peng, Bonnie Berger

Research output: Contribution to conferencePaperpeer-review

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.

Original languageEnglish (US)
StatePublished - 2020
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: Apr 16 2019Apr 18 2019

Conference

Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
CountryJapan
CityNaha
Period4/16/194/18/19

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

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