Supervised UMAP using already projected points as regression

Hey Leland,

Thanks for this great library, and for being so responsive with issues.

Question: Is it possible to train a (semi-)supervised UMAP model where some of the projections are already known/provided, as a regression task? This is contrast to using labels for supervision, which are categorical.

To provide an example, imagine I had a set of 100 embeddings. 50 of those embeddings have 2d coordinates associated with them; the other 50 do not. I want to be able to train a UMAP model on the 50 embeddings with 2d coordinates, and then run inference on the other 50 (or do a semi-supervised training and run on all of them at the same time).

If this isn't feasible with UMAP, do you know of any other algos/models that might be a good fit for what I'm suggesting (besides deep learning of course)?

Thanks! Amol

No files, tests, or implementation entry points are named. First review how supervised UMAP training and inference currently handle categorical labels, then clarify the expected behavior for provided coordinates, including whether prediction should cover only unprojected points or all points. Done requires an agreed design and validation for this regression-style workflow.

Written by the indexing model from the issue text.