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.

翻译：Fused Gromov-Wasserstein (FGW)距离提供了一种通过联合对齐结构与节点特征来比较对象的理论框架。然而，现有FGW公式统一处理所有特征，这在高维场景下（当许多特征可能不相关或含噪声时）限制了可解释性与鲁棒性。我们引入了带特征选择的FGW距离，它将自适应特征抑制权重纳入FGW目标函数中，从而在对齐过程中选择性地降低或抑制区分性特征。我们提出了两种方法：（1）基于Lasso和Ridge惩罚的正则化FGW，（2）带单纯形约束权重的FGW，包括分组扩展方法。我们分析了所得模型并确立了关键理论性质，包括相对于经典FGW和Gromov-Wasserstein距离的界限，以及度量行为。我们开发了一种高效的交替最小化算法。实验表明，特征抑制如何增强可解释性并揭示任务相关结构，并特别应用于计算选区分区领域。