Measuring Dataset Diversity from a Geometric Perspective
This provides a foundational tool for dataset construction, augmentation, and evaluation by addressing the gap in existing diversity metrics that neglect geometric structure.
The paper tackled the problem of measuring dataset diversity by introducing a framework based on topological data analysis and persistence landscapes to quantify geometric features, demonstrating that the proposed PLDiv metric is powerful, reliable, and interpretable across diverse modalities.
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.