Two Separation Axioms in L-Fuzzy Topological Spaces

Cheng, Jieren

doi:10.1109/icmlc.2006.258976

Cited by 7 publications

(1 citation statement)

References 11 publications

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“…To date, a multitude of pairwise network alignment methods have been developed based on the consistency principle (Singh, Xu, and Berger 2008;Koutra, Tong, and Lubensky 2013;Zhang and Tong 2016), node embedding (Li et al 2019;Chu et al 2019;Zhang et al 2021), and optimal transport (OT) (Maretic et al 2019(Maretic et al , 2022Chen et al 2020;Zeng et al 2023a) with superior performance, but this is not the case for the multi-network setting due to two fundamental challenges. First (discrepancy measure), most existing pairwise methods essentially optimize the pairwise discrepancy (e.g., Frobenius norm (Zhang and Tong 2016), contrastive loss (Chu et al 2019), and Wasserstein distance (Maretic et al 2020)) between one network and its aligned counterpart, but a similar discrepancy measure for multi-network is lacking.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Multi-Marginal Optimal Transport for Network Alignment

Zeng,

Du,

Zhang

et al. 2024

AAAI

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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.

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