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arXiv · 2404.08608

Hyperbolic Delaunay Geometric Alignment

Aniss Aiman Medbouhi·Giovanni Luca Marchetti·Vladislav Polianskii·Alexander Kravberg·Petra Poklukar·Anastasia Varava·Danica Kragic
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Abstract

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.

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Aniss Aiman Medbouhi, Giovanni Luca Marchetti, Vladislav Polianskii, Alexander Kravberg, Petra Poklukar, Anastasia Varava, Danica Kragic. 2024-04-12. Hyperbolic Delaunay Geometric Alignment. https://arxiv.org/abs/2404.08608

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