Hyperbolic Delaunay Geometric Alignment

Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we propose Hyperbolic Delaunay Geometric Alignment (HyperDGA) -- a s...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Aniss Aiman Medbouhi, Marchetti, Giovanni Luca, Polianskii, Vladislav, Kravberg, Alexander, Poklukar, Petra, Varava, Anastasia, Kragic, Danica
Format: Article
Language:English
Subjects:
Alignment
Empirical analysis
Graph theory
Hyperbolic coordinates
Machine learning
Representations
Online Access:Get full text
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Summary:Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we propose Hyperbolic Delaunay Geometric Alignment (HyperDGA) -- a similarity score for comparing datasets in a hyperbolic space. The core idea is counting the edges of the hyperbolic Delaunay graph connecting datapoints across the given sets. We provide an empirical investigation on synthetic and real-life biological data and demonstrate that HyperDGA outperforms the hyperbolic version of classical distances between sets. Furthermore, we showcase the potential of HyperDGA for evaluating latent representations inferred by a Hyperbolic Variational Auto-Encoder.
ISSN:2331-8422