Apple researchers propose graph-based sensemaking workflows using UMAP’s internal kNN graph

Apple’s Machine Learning Research team argues that UMAP’s lower-dimensional embeddings receive most of the attention, while its internal k-nearest-neighbor (kNN) graph—which encodes the data manifold in the original high-dimensional space—remains underexplored. The researchers propose using standard graph algorithms on this internal graph to improve data sensemaking tasks.

The paper demonstrates three applications: PageRank to identify representative data points, k-core decomposition to distinguish dense core regions from sparse peripheries, and clustering coefficient to detect tight-knit neighborhoods of highly similar points. These methods are applied directly to UMAP’s kNN graph rather than to the final 2D embedding.

The authors evaluate their approach on MNIST and Fashion-MNIST, reporting that graph-based analyses are not only practical but also competitive with or complementary to purpose-built techniques such as k-medoids for exemplar selection and HDBSCAN for density-based clustering. The work suggests that leveraging UMAP’s internal graph structure can yield insights comparable to specialized algorithms without requiring additional model training.

The research is positioned within Apple’s broader focus on methods and algorithms, and the paper is dated July 2026 in the publication listing.