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

arXiv: https://arxiv.org/abs/2607.08746 · HTML: https://mlsanity.com/paper/2607.08746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [Embedding Atlas: Low-Friction, Interactive Embedding Visualization](https://mlsanity.com/paper/2505.06386/) (2025)
- [Simple, Scalable and Effective Clustering via One-Dimensional Projections](https://mlsanity.com/paper/2310.16752/) (2023)

## Abstract (arXiv)

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).