Hyperbolic Delaunay Geometric Alignment
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.
Cite
Text
Medbouhi et al. "Hyperbolic Delaunay Geometric Alignment." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2024. doi:10.1007/978-3-031-70352-2_7Markdown
[Medbouhi et al. "Hyperbolic Delaunay Geometric Alignment." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2024.](https://mlanthology.org/ecmlpkdd/2024/medbouhi2024ecmlpkdd-hyperbolic/) doi:10.1007/978-3-031-70352-2_7BibTeX
@inproceedings{medbouhi2024ecmlpkdd-hyperbolic,
title = {{Hyperbolic Delaunay Geometric Alignment}},
author = {Medbouhi, Aniss Aiman and Marchetti, Giovanni Luca and Polianskii, Vladislav and Kravberg, Alexander and Poklukar, Petra and Varava, Anastasia and Kragic, Danica},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2024},
pages = {111-126},
doi = {10.1007/978-3-031-70352-2_7},
url = {https://mlanthology.org/ecmlpkdd/2024/medbouhi2024ecmlpkdd-hyperbolic/}
}