An Optimal Transport-based Undersampling Technique for Handling Imbalanced Datasets

This paper investigates a novel undersampling technique based on optimal transport for managing imbalanced datasets in classification tasks. Undersampling is crucial for reducing dataset size while preserving essential statistical properties, thereby improving both classification performance and computational efficiency. Existing methods, such as random undersampling, NearMiss, Tomek Links, and Edited Nearest Neighbor, often fail to optimally preserve data distribution. To address this, we propose a Wasserstein distance-based undersampling method that formulates an optimization problem to minimize distributional distortion. By leveraging the Wasserstein distance to measure dissimilarity between probability distributions, the proposed approach ensures that the reduced dataset retains key structural information. Additionally, we analyze the method's computational complexity and its impact on geodesic structures in Wasserstein space, highlighting its theoretical advantages over conventional techniques. Simulation results on synthetically generated imbalanced datasets demonstrate that the proposed method preserves the statistical structure of the original data more effectively than existing resampling techniques and achieves balanced classification performance for both the majority class and minority class, offering an effective and scalable solution to class imbalance in classification problems.