Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph

论文概要

研究领域: 数据科学
作者: Duen Horng Chau, Donghao Ren, Fred Hohman
发布时间: 2025-07-12
arXiv: 2507.08728

中文摘要

虽然UMAP被广泛用于探索高维数据，但典型工作流程专注于其低维嵌入，很大程度上忽略了UMAP内部构建的丰富的k近邻（kNN）图。该图在UMAP的2D投影引入失真之前，编码了原始高维空间中的数据流形。我们展示了这种内部表示的未开发潜力：PageRank识别代表性数据点，k-core分解揭示密集核心区域与稀疏外围，聚类系数检测具有高度相似数据点的紧密邻里。在MNIST和Fashion MNIST上的评估表明，这些基于图的分析与专门构建的方法具有竞争力或互补性。

原文摘要

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 Fas...

自动采集于 2025-07-13

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