Apple researchers show that UMAP's internal k-nearest-neighbor graph—the high-dimensional structure typically hidden behind its 2D projection—can be analyzed using standard graph algorithms to identify representative data points, dense regions, and tight-knit neighborhoods.
Testing on MNIST and Fashion MNIST, they found these graph-based methods are competitive with or complementary to purpose-built methods like k-medoids and HDBSCAN, suggesting practitioners can gain richer insights by analyzing the graph directly rather than relying only on the 2D visualization.
What happened
Apple researchers demonstrate that UMAP's internal k-nearest-neighbor graph—typically ignored in practice—can be analyzed using standard graph algorithms (PageRank, k-core decomposition, clustering coefficient) to extract patterns from high-dimensional data. Testing on MNIST and Fashion MNIST, they show these graph-based methods match or outperform purpose-built alternatives like k-medoids and HDBSCAN.
Why it matters
UMAP is widely used to explore high-dimensional data by projecting it into 2D, but that projection distorts the original structure. The kNN graph captures the true manifold before distortion, so applying graph algorithms to it reveals representative points, dense regions, and tight-knit neighborhoods—giving practitioners a richer, complementary view without building new tools.
What to watch
The research points to untapped potential in UMAP workflows; practitioners may benefit from combining traditional 2D visualization with direct kNN graph analysis for more comprehensive data sensemaking.
Researchers at Apple have identified an overlooked resource in one of machine learning's most popular data exploration tools: UMAP's internal k-nearest-neighbor graph. While UMAP is widely used to project high-dimensional data into 2D for visualization, the algorithm constructs a kNN graph as an intermediate step to encode the data's manifold structure before distortion occurs. This graph remains largely invisible in typical workflows, where attention focuses on the final 2D embedding.
The team, led by authors Duen Horng (Polo) Chau, Donghao Ren, Fred Hohman, and Dominik Moritz, demonstrated how to extract value from this hidden layer by applying three standard graph algorithms: PageRank identifies representative data points by ranking nodes based on neighborhood connectivity, k-core decomposition partitions the graph into core (dense) and periphery (sparse) regions, and clustering coefficient measures the degree to which neighboring nodes form tight-knit communities with highly similar data.
They evaluated these graph-based approaches on two benchmark datasets—MNIST (handwritten digits) and Fashion MNIST (clothing images)—comparing results against purpose-built methods: k-medoids for selecting exemplar points and HDBSCAN for density-aware clustering. The quantitative and qualitative analysis showed that the graph algorithms were not only practical but also competitive with or complementary to these specialized alternatives. This finding suggests that the untapped potential of UMAP's kNN graph offers practitioners a powerful, low-cost way to enhance data sensemaking without adopting new tools or methods.
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.
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