Hyperbolic Delaunay Geometric Alignment
Aniss Aiman Medbouhi Giovanni Luca Marchetti Vladislav Polianskii Alexander Kravberg Petra Poklukar Anastasia Varava Danica Kragic
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.