Apple researchers show UMAP's hidden kNN graph beats standard methods for data analysis

UMAP has become a standard tool for exploring high-dimensional datasets by projecting them into two dimensions for visual interpretation. However, this projection inherently distorts the original structure of the data—a well-known limitation in dimensionality reduction. The researchers recognized that UMAP constructs a k-nearest-neighbor graph during its algorithm, which preserves the manifold structure in the original high-dimensional space before any 2D distortion occurs. By applying established graph algorithms to this internal representation—rather than discarding it in favor of the 2D visualization—they unlock a complementary lens for data analysis.

The three graph algorithms they tested each serve a different analytical purpose: PageRank identifies which points are most representative or central within the data's neighborhood structure, k-core decomposition segments the graph into regions of varying density, and clustering coefficient captures local cohesion. The key finding is that these off-the-shelf methods match or exceed the performance of specialized tools like k-medoids and HDBSCAN when applied to UMAP's kNN graph. This suggests that practitioners may not need to adopt new methods—they can instead leverage the graph information already embedded in UMAP's computation to gain deeper understanding of their data.