Hyperbolic Delaunay Geometric Alignment
This provides a tool for researchers in hyperbolic machine learning to analyze hierarchical data representations, though it is incremental as it builds on existing hyperbolic methods.
The paper tackles the problem of evaluating hyperbolic data representations by proposing HyperDGA, a similarity score based on hyperbolic Delaunay graphs, and demonstrates that it outperforms classical hyperbolic distances on synthetic and biological data.
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.