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This research elevates UMAP from a simple visualization tool by leveraging its internal kNN graph structure, enabling advanced data sensemaking tasks like identifying representative points and dense clusters using standard algorithms. The study demonstrates that these graph-based approaches are competitive with specialized methods for exemplar selection and density clustering on high-dimensional datasets such as MNIST. By treating the latent manifold directly rather than relying solely on 2D projections, this work offers a more robust framework for interpreting complex machine learning data structures.
Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph
arXiv:2607.08746v3 Announce Type: replace-cross 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).
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).
Accepted to IEEE Workshop on Topology meets Artificial Intelligence (TopoInVis Connect) at IEEE VIS 2026. Code and demo: this https URL
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Data Structures and Algorithms (cs.DS); Human-Computer Interaction (cs.HC)
arXiv:2607.08746 [cs.LG]
(or arXiv:2607.08746v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.08746 Focus to learn more arXiv-issued DOI via DataCite
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