用几何方法衡量数据集多样性，更准确反映数据结构特征。
Measuring Dataset Diversity from a Geometric Perspective
- 基于拓扑数据分析和持久性景观，从几何角度量化数据多样性。
- 新指标PLDiv在多模态数据上表现可靠，能捕捉深层结构特征。
- 适合关注数据质量、构建与评估的机器学习研究者使用。
多样性可广泛定义为元素间存在的有意义差异，可从统计变异和数据集的几何结构丰富性等多角度理解。现有度量如特征空间分散度和度量空间大小主要捕捉分布变化或熵，却忽略了数据集的几何结构。为弥补这一空白，我们提出一种基于拓扑数据分析（TDA）和持久性景观（PLs）的框架，用于提取并量化数据的几何特征。该方法提供了理论支持，超越熵的范畴，捕获数据集丰富的几何与结构特性。通过在多种模态上的大量实验，我们证明所提出的基于PLs的多样性度量（PLDiv）具有强大性、可靠性与可解释性，直接将数据多样性与其底层几何关联起来，为数据集构建、增强与评估提供基础工具。
原文摘要 · Abstract (English)
Diversity can be broadly defined as the presence of meaningful variation across elements, which can be viewed from multiple perspectives, including statistical variation and geometric structural richness in the dataset. Existing diversity metrics, such as feature-space dispersion and metric-space magnitude, primarily capture distributional variation or entropy, while largely neglecting the geometric structure of datasets. To address this gap, we introduce a framework based on topological data analysis (TDA) and persistence landscapes (PLs) to extract and quantify geometric features from data. This approach provides a theoretically grounded means of measuring diversity beyond entropy, capturing the rich geometric and structural properties of datasets. Through extensive experiments across diverse modalities, we demonstrate that our proposed PLs-based diversity metric (PLDiv) is powerful, reliable, and interpretable, directly linking data diversity to its underlying geometry and offering a foundational tool for dataset construction, augmentation, and evaluation.
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