Finding node correspondence across networks, namely multi-network alignment,
is an essential prerequisite for joint learning on multiple networks. Despite
great success in aligning networks in pairs, the literature on multi-network
alignment is sparse due to the exponentially growing solution space and lack of
high-order discrepancy measures. To fill this gap, we propose a hierarchical
multi-marginal optimal transport framework named HOT for multi-network
alignment. To handle the large solution space, multiple networks are decomposed
into smaller aligned clusters via the fused Gromov-Wasserstein (FGW)
barycenter. To depict high-order relationships across multiple networks, the
FGW distance is generalized to the multi-marginal setting, based on which
networks can be aligned jointly. A fast proximal point method is further
developed with guaranteed convergence to a local optimum. Extensive experiments
and analysis show that our proposed HOT achieves significant improvements over
the state-of-the-art in both effectiveness and scalability.

多网络对齐的多层次多边界优化传输框架（HOT）通过分解网络，使用融合的 Gromov-Wasserstein（FGW）质心来处理大规模的解空间，并基于多边界设置将 FGW 距离推广到多网络对齐中，进而开发了一种快速的邻近点方法以获得局部最优解，通过广泛的实验证明了 HOT 在效果和可扩展性方面都明显优于现有技术的成果。

网络对齐的分层多边际最优输运

Hierarchical Multi-Marginal Optimal Transport for Network Alignment

Graph data augmentation has proven to be effective in enhancing the
generalizability and robustness of graph neural networks (GNNs) for graph-level
classifications. However, existing methods mainly focus on augmenting the graph
signal space and the graph structure space independently, overlooking their
joint interaction. This paper addresses this limitation by formulating the
problem as an optimal transport problem that aims to find an optimal strategy
for matching nodes between graphs considering the interactions between graph
structures and signals. To tackle this problem, we propose a novel graph mixup
algorithm dubbed FGWMixup, which leverages the Fused Gromov-Wasserstein (FGW)
metric space to identify a "midpoint" of the source graphs. To improve the
scalability of our approach, we introduce a relaxed FGW solver that accelerates
FGWMixup by enhancing the convergence rate from $\mathcal{O}(t^{-1})$ to
$\mathcal{O}(t^{-2})$. Extensive experiments conducted on five datasets,
utilizing both classic (MPNNs) and advanced (Graphormers) GNN backbones,
demonstrate the effectiveness of FGWMixup in improving the generalizability and
robustness of GNNs.

本文提出了一种基于 Fused Gromov-Wasserstein 度量空间的 FGWMixup，旨在通过匹配图之间的节点来找到一种匹配策略，以提高图神经网络的泛化性和鲁棒性。