Consider using ElMD for the composition-based distance

[sgbaird]

For a "more chemically intuitive" distance metric. Original implementation: ElMD and ElM2D. Lightning-fast version of ElM2D at https://github.com/sparks-baird/chem_wasserstein. $10k \times 10k$ pairwise distances on order of ~10 seconds on CPU.

https://github.com/txie-93/cdvae/blob/f857f598d6f6cca5dc1ea0582d228f12dcc2c2ea/scripts/compute_metrics.py#L17 https://github.com/txie-93/cdvae/blob/f857f598d6f6cca5dc1ea0582d228f12dcc2c2ea/scripts/compute_metrics.py#L92

[sgbaird]

Likewise for CrystalNN an option would be to use Earth Mover's Distance as implemented via dist-matrix, though I'm not sure people have really tested this out to see if it has some favorable properties relative to Euclidean distance.