Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction

technique that can be used for visualisation similarly to t-SNE, but also for

general non-linear dimension reduction. The algorithm is founded on three assumptions

about the data:

1. The data is uniformly distributed on a Riemannian manifold;

2. The Riemannian metric is locally constant (or can be approximated as such);

3. The manifold is locally connected.

From these assumptions it is possible to model the manifold with a fuzzy topological

structure. The embedding is found by searching for a low dimensional projection

of the data that has the closest possible equivalent fuzzy topological structure.