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:
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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.
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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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