Uniform Manifold Approximation and Projection (UMAP)
- is a dimension reduction technique similarly to t-SNE
- is also a general non-linear dimension reduction
- introduced in 2018
UMAP - Assumptions
The algorithm is founded on three assumptions about the data:
- the data is uniformly distributed on Riemannian manifold
- the Riemannian metric is locally constant (or can be approximated as such)
- 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.