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.

超协调机器学习是一个新兴领域，旨在使用分层结构表示数据。然而，目前缺乏用于评估和分析生成的超协调数据表示的工具。为此，我们提出了超协调德劳内几何对齐（HyperDGA）- 一种用于比较超协调空间中数据集的相似度得分。核心思想是计算连接给定集合中数据点的超协调德劳内图的边数。我们对合成和真实生物数据进行了实证研究，并证明了 HyperDGA 在比较数据集之间的性能超过了超协调版本的经典距离。此外，我们展示了 HyperDGA 评估超协调变分自动编码器所推断的潜在表示的潜力。