用曲率分析数据降维效果，能估计数据真实维度。
Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension
- 基于点间度量关系构建曲率几何谱
- 可量化评估降维方法效果并估计内在维度
- 适合研究高维数据几何结构的学者
利用近期发展的截面曲率抽象概念，我们提出一种构建离散度量空间曲率几何谱的方法。该曲率概念捕捉三元组点与其他点之间的度量关系。更重要的是，基于此曲率谱，我们引入了一种定量指标，用于评估数据表示的有效性，如降维技术生成的结果。实验表明，这种基于曲率的分析可用于估计数据集的内在维度。我们将其应用于探索经验网络的大尺度几何结构，并评估降维技术的有效性。
原文摘要 · Abstract (English)
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations between triples of points and other points. More significantly, based on this curvature profile, we introduce a quantitative measure to evaluate the effectiveness of data representations, such as those produced by dimensionality reduction techniques. Furthermore, Our experiments demonstrate that this curvature-based analysis can be employed to estimate the intrinsic dimensionality of datasets. We use this to explore the large-scale geometry of empirical networks and to evaluate the effectiveness of dimensionality reduction techniques.
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