Measuring Dataset Diversity from a Geometric Perspective
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917263169290240 |
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| author | Ba, Yang Abolhasani, Mohammad Sadeq Mancenido, Michelle V Pan, Rong |
| author_facet | Ba, Yang Abolhasani, Mohammad Sadeq Mancenido, Michelle V Pan, Rong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_09340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Measuring Dataset Diversity from a Geometric Perspective Ba, Yang Abolhasani, Mohammad Sadeq Mancenido, Michelle V Pan, Rong Artificial Intelligence 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. |
| title | Measuring Dataset Diversity from a Geometric Perspective |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2602.09340 |