Geometric Median (GM) Matching for Robust k-Subset Selection from Noisy Data

Data pruning -the combinatorial task of selecting a small and representative subset from a large dataset, is crucial for mitigating the enormous computational costs associated with training datahungry modern deep learning models at scale. Since large-scale data collections are invariably noisy, developing data pruning strategies that remain robust even in the presence of corruption is critical in practice. Existing data pruning methods often fail under high corruption rates due to their reliance on empirical mean estimation, which is highly sensitive to outliers. In response, this work proposes Geometric Median (GM) Matching, a novel k-subset selection strategy that leverages the GM, a robust estimator with an optimal breakdown point of 1/2; to enhance resilience against noisy data. Our method iteratively selects a ksubset such that the mean of the subset approximates the GM of the (potentially) noisy dataset, ensuring robustness even under arbitrary corruption. We provide theoretical guarantees, showing that GM MATCHING enjoys an improved O(1/k) convergence rate, outperforming O(1/ √ k) scaling of uniform sampling, even under arbitrary corruption. Extensive experiments across image classification and image generation tasks demonstrate that GM MATCHING consistently outperforms existing pruning approaches, particularly in high-corruption settings; making it a strong baseline for robust data pruning.