Abstract
UMAP is widely used for exploring high-dimensional data, but typical workflows primarily 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:
- PageRank identifies representative data points;
- k-core decomposition reveals dense core regions versus sparse periphery;
- 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).
Blogger's Review: This study profoundly reveals the value of UMAP's internal structure, emphasizing the importance of leveraging graph algorithms for data analysis. This approach not only deepens the understanding of data but also provides data scientists with new tools to tackle the complexities of high-dimensional data.