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Large-Margin Classification in Hyperbolic Space.

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.

SUBMITTER: Cho H

PROVIDER: S-EPMC7434093 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature

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Large-Margin Classification in Hyperbolic Space.

Cho Hyunghoon H DeMeo Benjamin B Peng Jian J Berger Bonnie B

Proceedings of machine learning research 20190401

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 geome ...[more]

PMID: 32832915

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