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Sparse Partial Optimal Transport via Quadratic Regularization
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en
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11
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Journal of Computer Science, Volume 21, issue 7, pp. 1677-1687
Abstract
Partial Optimal Transport (POT) has recently emerged as a central tool in various Machine Learning (ML) applications. It lifts the stringent assumption of the conventional Optimal Transport (OT) that input measures are of equal masses, which is often not guaranteed in real-world datasets, and thus offers greater flexibility by permitting transport between unbalanced input measures. Nevertheless, existing major solvers for POT commonly rely on entropic regularization for acceleration and thus return dense transport plans, hindering the adoption of POT in various applications that favor sparsity. In this paper, as an alternative approach to the entropic POT formulation in the literature, we propose a novel formulation of POT with quadratic regularization, hence termed quadratic regularized POT (QPOT), which induces sparsity to the transport plan and consequently facilitates the adoption of POT in many applications with sparsity requirements. Extensive experiments on synthetic and CIFAR-10 datasets, as well as real-world applications such as color transfer and domain adaptations, consistently demonstrate the improved sparsity and favorable performance of our proposed QPOT formulation.
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Publisher Copyright: © 2025 Khang Tran, Khoa Nguyen, Anh Nguyen, Thong Huynh, Son Pham, Sy-Hoang Nguyen-Dang, Manh Pham, Bang Vo, Mai NgocTran and Dung Luong. This open-access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.
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Tran, K, Nguyen, K, Nguyen, A, Huynh, T, Pham, S, Nguyen-Dang, S H, Pham, M, Vo, B, Tran, M N & Luong, D 2025, 'Sparse Partial Optimal Transport via Quadratic Regularization', Journal of Computer Science, vol. 21, no. 7, pp. 1677-1687. https://doi.org/10.3844/jcssp.2025.1677.1687