On Uniform Manifold Approximation and Projection (UMAP):
"Analytical properties of UMAP dimensionality reductions", Levernier and Rouault, 2023.
https://hal.science/hal-04046849/document
"Here we give analytical prediction for the UMAP projection of well defined datasets including pure noise, binary data and one-dimensional signal. For the latter, we uncover a phase transition in the lateral spreading of the projected points."