This repository contains the code for the paper called "Hyperbolic Delaunay Geometric Alignment".
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.
Our main codes are in the jupyter notebooks: HyperDGA_notebook_Experiment1.ipynb, HyperDGA_notebook_Experiment2.ipynb and HyperDGA_notebook_Experiment3.ipynb.
To get started, create a conda environment from the yaml file: HyperDGA_environment.yml
For the experiments 1 and 2, one needs to first train a Hyperbolic VAE with synthetic dataset using the code at: https://github.com/pfnet-research/hyperbolic_wrapped_distribution
For the experiment 3, one needs to first get the Poincaré embeddings of Olsson, Paul and Planaria datasets using the code from: https://github.com/facebookresearch/PoincareMaps/tree/main
For convenience we put these embeddings as pickle files called "dict_data_xxx.pkl" in the current folder.
Part of our code for the Voronoi diagram is from Devert Alexandre: https://gist.github.com/marmakoide/45d5389252683ae09c2df49d0548a627#file-laguerre-voronoi-2d-py
Part of our code for the synthetic dataset and the Hyperbolic VAE is from https://github.com/pfnet-research/hyperbolic_wrapped_distribution
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