Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph
2026-07-09 • Machine Learning
Machine LearningArtificial IntelligenceData Structures and AlgorithmsHuman-Computer Interaction
AI summaryⓘ
The authors explain that UMAP, a tool used to visualize complex data, creates a special graph that people usually ignore. This graph shows how data points relate in their original, complex space before being simplified into 2D. They show that using well-known graph methods on this UMAP graph helps find important data points, identify dense clusters, and recognize tight groups of similar points. Their tests on image datasets show these graph-based techniques work well and can add value alongside other common methods.
UMAPk-nearest-neighbor (kNN) graphdata manifoldPageRankk-core decompositionclustering coefficientMNISTFashion MNISTdensity-based clustering
Authors
Duen Horng Chau, Donghao Ren, Fred Hohman, Dominik Moritz
Abstract
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. We 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, and (3) clustering coefficient detects tight-knit neighborhoods with highly-similar data points. Through quantitative and qualitative evaluation on MNIST and Fashion MNIST, we show that these graph-based analyses are not only practical but also competitive with or complementary to purpose-built methods (e.g., k-medoids for exemplar selection, HDBSCAN for density-based clustering).