通过自适应筛选特征，提升结构对齐的可解释性与鲁棒性。
Fused Gromov-Wasserstein Distance with Feature Selection
- 在FGW距离中引入可学习的特征抑制权重，动态忽略无关特征。
- 两种方法分别用Lasso/Ridge正则和单纯形约束实现特征选择，提升稳定性。
- 适用于高维数据中的结构对比，尤其适合红区划分等任务分析。
融合式格罗莫夫-沃瑟斯坦（FGW）距离提供了一种联合对齐结构与节点特征的框架。然而，现有方法对所有特征一视同仁，在高维场景下因冗余或噪声特征导致可解释性差、鲁棒性下降。本文提出带特征选择的FGW距离，将自适应特征抑制权重融入目标函数，实现对差异特征的动态降权或屏蔽。提出两种方法：(1) 带有Lasso与Ridge正则的修正型FGW；(2) 单纯形约束权重的FGW，含分组扩展形式。理论分析揭示其相对于经典FGW与格罗莫夫-沃瑟斯坦距离的界关系及度量性质。设计了高效的交替优化算法。实验表明，特征抑制显著提升可解释性并揭示任务相关结构，特别应用于计算红区划分任务。
原文摘要 · Abstract (English)
Fused Gromov-Wasserstein (FGW) distances provide a principled framework for comparing objects by jointly aligning structure and node features. However, existing FGW formulations treat all features uniformly, which limits interpretability and robustness in high-dimensional settings where many features may be irrelevant or noisy. We introduce FGW distances with feature selection, which incorporate adaptive feature suppression weights into the FGW objective to selectively downweight or suppress differentiating features during alignment. We propose two approaches: (1) regularized FGW with Lasso and Ridge penalties, and (2) FGW with simplex-constrained weights, including groupwise extensions. We analyze the resulting models and establish their key theoretical properties, including bounds relative to classical FGW and Gromov-Wasserstein distances, and metric behavior. An efficient alternating minimization algorithm is developed. Experiments illustrate how feature suppression enhances interpretability and reveals task-relevant structure, with a special application to computational redistricting.
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