UMAP, or Uniform Manifold Approximation and Projection, is a non-linear dimensionality reduction technique designed for high-dimensional data. It operates under the assumption that the data is uniformly distributed on a locally connected Riemannian manifold, which allows it to effectively capture the underlying structure of the data.

One of the key advantages of UMAP over other techniques like t-SNE is its ability to preserve both local and global data structures. UMAP uses a different approach to symmetrization and models distance probabilities with a family of curves, which helps in creating more distinct clusters in the low-dimensional space. This makes it particularly useful for tasks such as clustering and visualization of complex datasets, including single-cell RNA sequencing data ¹⁴.

Additionally, UMAP can handle both numeric and categorical data, making it versatile for various applications. It is often validated through downstream tasks, such as classification, to ensure that the reduced dimensions accurately reflect the data’s structure ⁵.