Gromov-Wasserstein Learning for Graph Matching and Node Embedding

Xu, Hongteng; Luo, Dixin; Zha, Hongyuan; Carin, Lawrence

doi:10.48550/arxiv.1901.06003

Cited by 8 publications

(22 citation statements)

References 36 publications

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“…Although it is an unsupervised method, it has achieved successes in multi-modal learning [9], neural language processing [52], and 3D shape correspondence [17,30]. Among graph matching approaches, it is common to perform alignment by Wasserstein distance (WD) [37], Gromov-Wasserstein distance [38], and them both [9,51]. Recent graph-matching studies combine WD and GWD, and learn the shared correspondence between WD and GWD, for improving effectiveness [9,51].…”

Section: Related Workmentioning

confidence: 99%

“…Among graph matching approaches, it is common to perform alignment by Wasserstein distance (WD) [37], Gromov-Wasserstein distance [38], and them both [9,51]. Recent graph-matching studies combine WD and GWD, and learn the shared correspondence between WD and GWD, for improving effectiveness [9,51]. However, these methods have a relatively high computational complexity of 𝑂 (𝑛 3 ), and they are not scalable for large graphs.…”

Section: Related Workmentioning

confidence: 99%

“…First, besides sharing models, node alignment between graphs is necessary because of differences in data distribution or feature spaces. Since no fine-grained correspondence is provided in each category, unsupervised alignment is required, which is well formulated and handled by graph matching approaches [9,51,53]. These approaches can align nodes based on consistency between node representations and node-node matching relationships.…”

Section: Introductionmentioning

confidence: 99%

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Incentive Compatible Pareto Alignment for Multi-Source Large Graphs

Liang¹,

Lv²,

Liu³

et al. 2021

Preprint

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In this paper, we focus on learning effective entity matching models over multi-source large-scale data. For real applications, we relax typical assumptions that data distributions/spaces, or entity identities are shared between sources, and propose a Relaxed Multi-source Large-scale Entity-matching (RMLE) problem. Challenges of the problem include 1) how to align large-scale entities between sources to share information and 2) how to mitigate negative transfer from joint learning multi-source data. What's worse, one practical issue is the entanglement between both challenges. Specifically, incorrect alignments may increase negative transfer; while mitigating negative transfer for one source may result in poorly learned representations for other sources and then decrease alignment accuracy. To handle the entangled challenges, we point out that the key is to optimize information sharing first based on Pareto front optimization, by showing that information sharing significantly influences the Pareto front which depicts lower bounds of negative transfer. Consequently, we proposed an Incentive Compatible Pareto Alignment (ICPA) method to first optimize cross-source alignments based on Pareto front optimization, then mitigate negative transfer constrained on the optimized alignments. This mechanism renders each source can learn based on its true preference without worrying about deteriorating representations of other sources. Specifically, the Pareto front optimization encourages minimizing lower bounds of negative transfer, which optimizes whether and which to align. In detail, we adopt graph neural networks to handle data sparsity in each source and a scalable alignment based on sliced graph matching. Comprehensive empirical evaluation results on four large-scale datasets are provided to demonstrate the effectiveness and superiority of ICPA. Online A/B test results at a search advertising platform also demonstrate the effectiveness of ICPA in production environments. We also release an International Entity Graph (IEG) 1 dataset to facilitate future research.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Incentive Compatible Pareto Alignment for Multi-Source Large Graphs

Liang¹,

Lv²,

Liu³

et al. 2021

Preprint

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“…A (T ) are calculated based on the updated base intensities and infectivity matrices. Inspired by the work in [6,10], we apply a proximal gradient method to solve (6) iteratively. Given current optimal transport T (n) , we add a proximal term as the regularizer of ( 6):…”

Section: Updating Hawkes Processesmentioning

confidence: 99%

Fused Gromov-Wasserstein Alignment for Hawkes Processes

Luo,

Xu,

Carin

2019

Preprint

Self Cite

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We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure their dissimilarity, which considers both the Wasserstein discrepancy based on their base intensities and the Gromov-Wasserstein discrepancy based on their infectivity matrices. Accordingly, the learned optimal transport reflects the correspondence between the event types of these two Hawkes processes. The Hawkes processes and their optimal transport are learned jointly via maximum likelihood estimation, with a fused Gromov-Wasserstein regularizer. Experimental results show that the proposed method works well on synthetic and real-world data.

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“…In particular, improvements of the computational strategies to efficiently obtain Wasserstein distances [1,8] have led to many applications in machine learning that use it for various purposes, ranging from generative models [2] to new loss functions [14]. For applications to graphs, notions from optimal transport were used to tackle the graph alignment problem [44]. In this work, we provide the theoretical foundations of our method, then define a new graph kernel formulation and finally present successful experimental results.…”

Section: Introductionmentioning

confidence: 99%

Wasserstein Weisfeiler-Lehman Graph Kernels

Togninalli,

Ghisu,

Llinares-López

et al. 2019

Preprint

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Graph kernels are an instance of the class of R-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially discarding valuable information about the distribution of individual components. Furthermore, only a limited instance of these approaches can be extended to continuously attributed graphs. We propose a novel method that relies on the Wasserstein distance between the node feature vector distributions of two graphs, which allows to find subtler differences in data sets by considering graphs as high-dimensional objects, rather than simple means. We further propose a Weisfeiler-Lehman inspired embedding scheme for graphs with continuous node attributes and weighted edges, enhance it with the computed Wasserstein distance, and thus improve the state-of-the-art prediction performance on several graph classification tasks.Preprint. Under review.

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Gromov-Wasserstein Learning for Graph Matching and Node Embedding

Cited by 8 publications

References 36 publications

Incentive Compatible Pareto Alignment for Multi-Source Large Graphs

Incentive Compatible Pareto Alignment for Multi-Source Large Graphs

Fused Gromov-Wasserstein Alignment for Hawkes Processes

Wasserstein Weisfeiler-Lehman Graph Kernels

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