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Uniform Manifold Approximation and Projection

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.

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