Hyperbolic Delaunay Geometric Alignment
<|reference_start|>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 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.<|reference_end|>
@article{medbouhi2024hyperbolic,
    title={Hyperbolic Delaunay Geometric Alignment},
    author={Aniss Aiman Medbouhi, Giovanni Luca Marchetti, Vladislav Polianskii,
  Alexander Kravberg, Petra Poklukar, Anastasia Varava, and Danica Kragic},
    journal={arXiv preprint arXiv:2404.08608},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.08608},
    primaryClass={cs.LG}
}