umap

UMAP, or Uniform Manifold Approximation and Projection, is a non-linear dimension reduction method for embedding high-dimensional data into low-dimensional space. It is widely used for data visualization and as a preprocessing step for downstream analyses.

UMAP constructs a graph representing local relationships in the data by building a k-nearest-neighbor graph and converting it into a fuzzy simplicial set. It then searches for a low-dimensional embedding that preserves the high-dimensional fuzzy structure by minimizing a cross-entropy objective between the two graphs, typically via stochastic gradient descent.

Compared with similar methods such as t-SNE, UMAP emphasizes speed and scalability, can preserve more of the global data structure, and often produces more interpretable global arrangements. It supports a supervised variant that uses class labels to optimize the embedding.

Parameters and implementation: common parameters include n_neighbors (controls local vs global balance), min_dist (minimum separation of points in the low-dimensional space), and the distance metric. UMAP is implemented in libraries such as umap-learn for Python and the corresponding packages for R and other languages, and can operate on large datasets with appropriate settings.

Limitations and considerations: results can be sensitive to parameter choices, different runs may yield different embeddings due to stochastic optimization, and the method does not guarantee faithful preservation of all global relationships. It is best used as a visualization or as a preprocessing step to other analyses, with awareness of potential distortions.

History and origins: UMAP was introduced in 2018 by Leland McInnes, John Healy, and James Melville. It drew on ideas from manifold learning and topological data analysis and has since been widely adopted in biology, computer vision, and other fields.