  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.
