cjnolet
commented
4 years ago Looking through more recent umap changes, i don’t believe this should be too hard to implement, as it seems to have the most effect on the SGD stage.
I believe a first pass for this could support hard-coded distance metrics and future iterations could use something like NVRTC to compile custom functions in real-time and pass them to the optimizer.
I suppose Haversine metric would even be a good starting point for a proof-of-concept.
Thank you, @vals, for bringing this feature to our attention!
github-actions[bot]
A recent new feature in the UMAP package is the ability to use alternative metrics for the embedding space: https://umap-learn.readthedocs.io/en/latest/embedding_space.html
This has the effect of embedding the data on a different manifold than the Euclidean plane as is commonly done. This way e.g. more interpretable embeddings can be made. I find the embedding using the Haversine metric particularly interesting since it allows you to make more use of the plotting window with less white space when converting the coordinates to latitudes and longitudes.
I believe the same concept would work for TSNE as well. When calculating the q_ij's in the embedding space some other norm could be used instead of Euclidean norm.
Describe the solution you'd like
It would be great if a reasonable number of metrics for 1- and 2-dimensional manifolds could be implemented and a user could pick an output metric when calling UMAP or TSNE.