监督的格罗莫夫-瓦瑟斯坦最佳运输与米度保护限制
Zixuan Cang1, Yaqi Wu2, Yanxiang Zhao2
1Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695 USA.
SIAM journal on mathematics of data science
|September 2, 2025
概括
我们推出监督格罗莫夫-瓦瑟斯坦 (sGW), 这是一种新的最佳运输方法, 这种方法增强了数据对齐,特别是对于部分重叠的数据集,如单细胞RNA测序数据.
科学领域:
- 最佳运输理论
- 计算几何学
- 数据科学
背景情况:
- 格罗莫夫-瓦瑟斯坦 (GW) 是一个比较尺度空间的强大工具.
- 在某些约束条件下,现有的GW方法可能无法充分保持对距离.
- 调整数据集,特别是单细胞RNA测序数据,通常需要强大的距离保护.
研究的目的:
- 引入监督的格罗莫夫-瓦瑟斯坦 (sGW) 最佳运输.
- 在成本张量中包含无限条目以强制执行距离保存约束.
- 为sGW问题开发和验证一个数值解法.
主要方法:
- 通过将潜在的无限项纳入成本张量来扩展格罗莫夫-瓦瑟斯坦.
- 通过最小顶点覆盖将高阶约束转换为合矩阵约束.
- 使用镜像C下降代与监督的最佳运输解决方案.
主要成果:
- 通过各种数值实验证明了sGW的有效性.
- 验证了合成数据集和单细胞RNA测序数据的框架.
- 展示了sGW控制距离保护和自动估计数据集重叠的能力.
结论:
- 监督格罗莫夫-瓦瑟斯坦 (sGW) 在最佳运输中提供了对保持距离的增强控制.
- 在数据驱动的应用中,sGW 提高了稳定性和灵活性,包括单单元数据对齐.
- 该方法可自动估计数据集中的重叠部分.
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