无监督多尺度格罗莫夫-瓦瑟斯坦超图对齐
Unsupervised Multi-Scale Gromov-Wasserstein Hypergraph Alignment
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中文总结 AI 辅助
提出无监督最优传输框架FALCON，通过多尺度GW目标联合对齐超图各层级，在真实超图扰动基准上，其对结构噪声鲁棒且性能优于相关基线。
中文摘要 AI 辅助
我们研究无监督超图对齐问题，其目标是仅利用结构信息推断两个超图之间的节点对应关系，无需节点特征、标签、种子匹配或辅助信息。直接的高阶公式能忠实地表示超边交互，但对于非均匀超图而言，计算量大且繁琐。图约简方法则带来不同挑战：团扩展使对齐问题保持在原始节点集上，但将所有超边证据合并为一个成对图；二部图扩展保留关联结构，但将问题规模从节点扩大到节点加超边。我们提出FALCON（基于滤波的超图对齐跨尺度最优传输框架），这是一个用于超图对齐的无监督最优传输框架。FALCON不将每个超图表示为单个合并团图，而是构造由滤波诱导的基于团的共现不相似度矩阵序列，并通过一个共享的多尺度格罗莫夫-瓦瑟斯坦（GW）目标联合对齐所有层级。共享传输计划在各滤波层级间强制全局一致的节点对应关系，同时避免二部图扩展引入的辅助超边节点。在从真实世界超图衍生的扰动基准上进行的实验表明，FALCON对结构噪声具有鲁棒性，且在几乎所有情况下都优于强大的图对齐和超图对齐基线方法。
英文摘要
We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information, without node features, labels, seed matches, or side information. Direct higher-order formulations can represent hyperedge interactions faithfully, but they can be computationally demanding and cumbersome for non-uniform hypergraphs. Graph-reduction approaches introduce a different challenge: clique expansions keep the alignment problem on the original node set but collapse all hyperedge evidence into one pairwise graph, whereas bipartite expansions preserve incidence structure but enlarge the problem from nodes to nodes plus hyperedges. We introduce FALCON (Filtration-based hypergrAph aLignment via Cross-scale Optimal traNsport), an unsupervised optimal-transport framework for hypergraph alignment. Instead of representing each hypergraph by a single collapsed clique graph, FALCON constructs a filtration-induced sequence of clique-based co-occurrence dissimilarity matrices and jointly aligns all levels through one shared multi-scale Gromov--Wasserstein (GW) objective. The shared transport plan enforces a globally consistent node correspondence across filtration levels while avoiding the auxiliary hyperedge nodes introduced by bipartite expansion. Experiments on perturbation benchmarks derived from real-world hypergraphs show that FALCON is robust to structural noise and in almost all cases outperforms strong graph- and hypergraph-alignment baselines.
发表机构
- University of Liverpool（利物浦大学）
- KTH Royal Institute of Technology（瑞典皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。
