用UMAP内部的kNN图做数据分析，发现新方法能更好识别关键数据点。
Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph
- 利用UMAP生成的kNN图，不用降维直接分析高维数据结构
- 通过图算法识别出核心数据点、密集区和相似小团体
- 适合想深入理解数据分布的研究者，尤其在图像数据上效果好
尽管UMAP广泛用于高维数据探索，但常规流程只关注其低维嵌入，忽视了其内部构建的k近邻(kNN)图。该图在降维前保留了原始高维空间中的数据流形信息。我们展示这一内部表示的未被发掘潜力：应用标准图算法于该图可增强数据洞察力——(1) PageRank识别代表性数据点，(2) k-core分解揭示密集核心与稀疏边缘区域，(3) 聚类系数检测高度相似的数据紧密邻域。在MNIST和Fashion MNIST上的定量与定性评估表明，这些基于图的分析不仅实用，且在性能上可媲美或补充专门设计的方法（如使用k-medoids进行示例选择，HDBSCAN进行密度聚类）。
原文摘要 · Abstract (English)
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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