Where Dimensionality Reduction Meets Network Science: Understanding Data Using UMAP's kNN Graph

Most UMAP usage workflows focus solely on visualizing the low-dimensional embedding, but the potential of the rich k-nearest-neighbor (kNN) graph that UMAP builds internally is often overlooked. This graph retains the high-dimensional data manifold information without the distortions that arise during low-dimensional projection.

This study presents methods for applying standard graph algorithms to this internal kNN graph to enhance data sensemaking.

• PageRank: identifies core data points that are representative of the data.
• k-core decomposition: distinguishes densely packed core regions of the data from sparse peripheral regions.
• Clustering coefficient: detects tight-knit neighborhoods where highly similar data points are clustered together.

Quantitative and qualitative evaluations using the MNIST and Fashion MNIST datasets confirmed that this graph-based analysis is not only practical but also a powerful tool that is competitive with, or complementary to, purpose-driven methodologies such as k-medoids and HDBSCAN.