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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Accession code at https://tinyurl.com/olssondata.
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Accession code at https://tinyurl.com/pauldata.
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Accession code at https://tinyurl.com/plassdata.
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Acknowledgements
We wish to thank Yoshihiro Nagano for the technical help, and Mohammad Al-Jaff and Michael Welle for their feedback. We are also grateful to the anonymous reviewers for their comments. This work has been supported by the Swedish Research Council, Knut and Alice Wallenberg Foundation, and the European Research Council (ERC AdG BIRD).
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Medbouhi, A.A. et al. (2024). Hyperbolic Delaunay Geometric Alignment. In: Bifet, A., Davis, J., Krilavičius, T., Kull, M., Ntoutsi, E., Žliobaitė, I. (eds) Machine Learning and Knowledge Discovery in Databases. Research Track. ECML PKDD 2024. Lecture Notes in Computer Science(), vol 14943. Springer, Cham. https://doi.org/10.1007/978-3-031-70352-2_7
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