While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally. This graph encodes the data manifold in its original high-dimensional space, before the distortion that UMAP’s 2D projection introduces. We demonstrate the untapped potential of this internal representation, showing how standard graph algorithms applied to this graph enhance data sensemaking: (1) PageRank identifies representative data points, (2) k-core decomposition reveals dense core regions versus sparse periphery, and (3) clustering coefficient detects tight-knit neighborhoods with highly-similar data points. Through quantitative and qualitative evaluation on MNIST and Fashion MNIST, we show that these graph-based analyses are not only practical but also competitive with or complementary to purpose-built methods (e.g., k-medoids for exemplar selection, HDBSCAN for density-based clustering).

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Generative and Contrastive Graph Representation Learning

September 29, 2025research area Methods and Algorithms

Self-supervised learning (SSL) on graphs generates node and graph representations (i.e., embeddings) that can be used for downstream tasks such as node classification, node clustering, and link prediction. Graph SSL is particularly useful in scenarios with limited or no labeled data. Existing SSL methods predominantly follow contrastive or generative paradigms, each excelling in different tasks: contrastive methods typically perform well on…