Measuring Dataset Diversity from a Geometric Perspective

• URL: http://arxiv.org/abs/2602.09340v1
• Date: Tue, 10 Feb 2026 02:17:16 GMT
• Title: Measuring Dataset Diversity from a Geometric Perspective
• Abstract summary: We introduce a framework based on topological data analysis (TDA) and persistence landscapes (PLs) to extract and quantify geometric features from data.<n>Our proposed PLs-based diversity metric (PLDiv) is powerful, reliable, and interpretable, directly linking data diversity to its underlying geometry.
• Score: 6.87941190955006
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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