Research area: ML Authors: Duen Horng Chau, Donghao Ren, Fred Hohman Published: 2025-07-12 arXiv: 2507.08728
Summary
While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally. This graph encodes the data manifold in its original high-dimensional space, before the distortion that UMAP's 2D projection introduces.
The authors demonstrate the untapped potential of this internal representation, showing how standard graph algorithms applied to this graph enhance data sensemaking:
1. PageRank identifies representative data points. 2. k-core decomposition reveals dense core regions versus sparse periphery. 3. Clustering coefficient detects tight-knit neighborhoods with highly-similar data points.
Through quantitative and qualitative evaluation on MNIST and Fashion MNIST, they show that these graph-based analyses are not only practical, but competitive with or complementary to purpose-built methods, such as k-medoids for exemplar selection and HDBSCAN for density-based clustering.
Key points
- UMAP's internal kNN graph captures the original high-dimensional data manifold without 2D projection distortion.
- Off-the-shelf network science algorithms (PageRank, k-core, clustering coefficient) provide useful data insights for free.
- Results are validated on MNIST and Fashion MNIST against established baselines (k-medoids, HDBSCAN).