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.
@article{arxiv.2404.08608,
title = {Hyperbolic Delaunay Geometric Alignment},
author = {Aniss Aiman Medbouhi and Giovanni Luca Marchetti and Vladislav Polianskii and Alexander Kravberg and Petra Poklukar and Anastasia Varava and Danica Kragic},
journal= {arXiv preprint arXiv:2404.08608},
year = {2024}
}