Title: Geometry-Aware Metric for Dataset Diversity via Persistence Landscapes
Primary area: learning on graphs and other geometries & topologies
Keywords: dataset diversity, topological data analysis, text and image temebdding, metric space

Abstract: Diversity can be broadly defined as the presence of meaningful variation across elements, which may 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 metric (PLDiv) is powerful, flexible, and interpretable, directly linking data diversity to its underlying geometry and offering new insights for dataset construction, augmentation, and evaluation.