Dimensionality Reduction Meets Network Science: Making Sense of UMAP's kNN Graph

Although UMAP is widely used to explore high-dimensional data, common workflows focus on its low-dimensional embeddings, focusing mainly on the rich k-nearest-neighbor (kNN) graph that UMAP builds internally. This graph encodes the frequency of the data in its original high-dimensional space, before the distortion introduced by the 2D UMAP display. We demonstrate the untapped potential of this internal representation, showing how common graph algorithms applied to this graph improve data visualization: (1) PageRank identifies representative data points, (2) k-core decomposition reveals dense core regions compared to the core region, and (3) clustering coefficient finds the closest regions with neighboring data. Through quantitative and qualitative tests on MNIST and Fashion MNIST, we show that this graph-based analysis is not only effective but also competitive with purpose-built methods (eg, medoid for instance selection, HDBSCAN for density-based clustering).