新方法让异质数据匹配更准，自动学习距离规则。
Structured Matching via Cost-Regularized Unbalanced Optimal Transport
- 让运输成本可学习，自动适应不同数据几何结构
- 在无直接对应关系的单细胞组学数据上对齐效果提升
- 适合处理跨空间、不均衡的复杂生物数据匹配
非平衡最优传输（UOT）为比较非负有限Radon测度提供了灵活方式。但传统UOT依赖预设的基底传输成本，可能无法准确反映数据内在几何结构。当数据分布在异构空间时，这一问题尤为突出，常促使研究者采用格罗莫夫-沃瑟斯坦（Gromov-Wasserstein）形式。为此，我们提出成本正则化非平衡最优传输（CR-UOT），允许基底成本动态变化，同时支持质量的生成与移除。我们证明，通过由线性变换参数化的内积成本族，CR-UOT可包含非平衡格罗莫夫-沃瑟斯坦类问题，从而实现欧氏空间间测度或点云的匹配。我们基于熵正则化开发了相应算法，并验证该方法显著提升了异质单细胞组学数据的对齐效果，尤其在大量细胞无直接对应关系时表现更优。
原文摘要 · Abstract (English)
Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such a cost is particularly challenging when datasets live in heterogeneous spaces, often motivating practitioners to adopt Gromov-Wasserstein formulations. To address this challenge, we introduce cost-regularized unbalanced optimal transport (CR-UOT), a framework that allows the ground cost to vary while allowing mass creation and removal. We show that CR-UOT incorporates unbalanced Gromov-Wasserstein type problems through families of inner-product costs parameterized by linear transformations, enabling the matching of measures or point clouds across Euclidean spaces. We develop algorithms for such CR-UOT problems using entropic regularization and demonstrate that this approach improves the alignment of heterogeneous single-cell omics profiles, especially when many cells lack direct matches.
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