UMAP is a nonlinear dimensionality-reduction technique for projecting high-dimensional data into a lower-dimensional space while preserving local and global relationships. It assumes that high-dimensional data lies on an embedded lower-dimensional manifold, making the resulting representation useful for visualization and analysis. section 6.5
UMAP constructs an embedding through the following ideas:
- Build a weighted nearest-neighbor graph, generally using Euclidean distance, to represent relationships in the original space. section 6.5.1
- Represent distances with fuzzy simplicial sets that capture probability distributions and underlying manifold structure. section 6.5.1
- Optimize a lower-dimensional graph by minimizing cross-entropy between the original and projected relationships with stochastic gradient descent. section 6.5.1
- Tune n_neighbors to balance local and global structure, and min_dist to control how tightly points cluster. section 6.5.1
Use UMAP to visualize complex datasets, reduce dimensions before modeling, inspect hidden groupings, or combine lower-dimensional representations with clustering algorithms such as k-means and DBSCAN. The umap-learn library provides a direct Python implementation. section 6.5.2
Gene-expression visualization
Project a high-dimensional gene dataset with UMAP to inspect clusters and relationships associated with cell types, developmental stages, and gene-expression patterns. section 6.5.2
