I am a mathematician who works mostly with the tools of category theory and algebraic topology to study geometry, so when I open up a paper and see adjunctions and simplicial sets and geometric realisation and Riemannian metrics, I feel pretty happy. One of the infinitely many things I am not is a data scientist, so when I am asked about dimension-reduction methods, I cannot give a meaningful or confident answer. This blog post arises from an odd middle ground, where I hope I can say something useful by being on this side of the fence.
This is a companion discussion topic for the original entry at https://topos.site/blog/2024-04-05-understanding-umap/