Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph

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

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.