提出新方法，让图数据比较更灵活，能处理质量不等的结构化数据。
Fused Partial Gromov-Wasserstein for Structured Objects
- 放宽传统对比限制，支持质量不均衡的图数据匹配
- 在图匹配/分类/聚类任务中表现稳健，优于经典方法
- 适合处理真实世界中不完整或规模不一的图数据
结构化数据（如图）在机器学习中至关重要，因其能捕捉复杂关系。近年来，融合式吴嘉瑞-沃瑟斯坦（FGW）距离因能同时考虑特征相似性与几何结构而受到关注。然而，作为最优传输的一种，经典FGW要求对比数据具有相等质量。本文放松此约束，提出融合式部分吴嘉瑞-沃瑟斯坦（FPGW）框架，使其适用于不平衡数据。理论上，建立了FPGW与FGW的关系，并证明了FPGW的度量性质；数值上，提出了Frank-Wolfe与Sinkhorn求解器。最后通过图匹配、图分类和图聚类实验验证了FPGW的鲁棒性能。
原文摘要 · Abstract (English)
Structured data, such as graphs, is vital in machine learning due to its capacity to capture complex relationships and interactions. In recent years, the Fused Gromov-Wasserstein (FGW) distance has attracted growing interest because it enables the comparison of structured data by jointly accounting for feature similarity and geometric structure. However, as a variant of optimal transport (OT), classical FGW assumes an equal mass constraint on the compared data. In this work, we relax this mass constraint and propose the Fused Partial Gromov-Wasserstein (FPGW) framework, which extends FGW to accommodate unbalanced data. Theoretically, we establish the relationship between FPGW and FGW and prove the metric properties of FPGW. Numerically, we introduce Frank-Wolfe solvers and Sinkhorn solvers for the proposed FPGW framework. Finally, we evaluate the FPGW distance through graph matching, graph classification and graph clustering experiments, demonstrating its robust performance.
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