UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Formulated non-linear dimension reduction using Riemannian geometry and fuzzy simplicial sets, preserving global structure with fast projection.

The dominant manifold visualization and dimension reduction technique in single-cell genomics, NLP embeddings, and cybersecurity analytics.

Assumptions

• Data manifold is locally connected and uniformly distributed with respect to an approximated Riemannian metric

Limitations

• Embeddings depend heavily on n_neighbors and min_dist hyperparameters; distances between distant clusters require cautious interpretation