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.
Researchers at the Tutte Institute developed both mathematical theory and an efficient software implementation. It is already being used in a variety of fields, including:
- materials science
- Condensed matter physics: Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system
The algorithm itself 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.
The strong mathematical foundations ensure a robust and interpretable algorithm, and are being generalized to broader problems in unsupervised learning.
If you would like to know more, you can contact the Tutte Institute at firstname.lastname@example.org.