The Gromov-Wasserstein distance between networks and stable network invariants

Chowdhury, S.; Mémoli, Facundo

doi:10.48550/arxiv.1808.04337

Cited by 7 publications

(14 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The GW discrepancy is suitable for solving matching problems like shape and object matching (Mémoli, 2009;2011). Besides graphics and computer vision, recently its potential for other applica-tions has been investigated, e.g., matching vocabulary sets between different languages (Alvarez-Melis & Jaakkola, 2018) and matching weighted directed networks (Chowdhury & Mémoli, 2018). The work in (Peyré et al, 2016) considers the Gromov-Wasserstein barycenter and proposes a fast Sinkhorn projection-based algorithm to compute GW discrepancy (Cuturi, 2013).…”

Section: Related Workmentioning

confidence: 99%

Gromov-Wasserstein Learning for Graph Matching and Node Embedding

Xu,

Luo,

Zha

et al. 2019

Preprint

View full text Add to dashboard Cite

A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node embeddings associated with the two graphs are learned under the guidance of the optimal transport, the distance of which not only reflects the topological structure of each graph but also yields the correspondence across the graphs. These two learning steps are mutually-beneficial, and are unified here by minimizing the Gromov-Wasserstein discrepancy with structural regularizers. This framework leads to an optimization problem that is solved by a proximal point method. We apply the proposed method to matching problems in real-world networks, and demonstrate its superior performance compared to alternative approaches.

show abstract

Section: Related Workmentioning

confidence: 99%

Gromov-Wasserstein Learning for Graph Matching and Node Embedding

Xu,

Luo,

Zha

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Gromov-Wasserstein distance The GW distance has been used as a metric for shape registration (Mémoli, 2009;2011), vocabulary set alignment (Alvarez-Melis & Jaakkola, 2018), and graph matching (Chowdhury & Mémoli, 2018;Vayer et al, 2018b;Xu et al, 2019b). The work in (Peyré et al, 2016) proposes an entropy-regularized GW distance and calculates it based on Sinkhorn iterations (Cuturi, 2013).…”

Section: Related Workmentioning

confidence: 99%

Learning Autoencoders with Relational Regularization

Xu,

Luo,

Henao

et al. 2020

Preprint

View full text Add to dashboard Cite

A new algorithmic framework is proposed for learning autoencoders of data distributions. We minimize the discrepancy between the model and target distributions, with a relational regularization on the learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the latent prior and its corresponding posterior, allowing one to flexibly learn a structured prior distribution associated with the generative model. Moreover, it helps co-training of multiple autoencoders even if they have heterogeneous architectures and incomparable latent spaces. We implement the framework with two scalable algorithms, making it applicable for both probabilistic and deterministic autoencoders. Our relational regularized autoencoder (RAE) outperforms existing methods, e.g., the variational autoencoder, Wasserstein autoencoder, and their variants, on generating images. Additionally, our relational co-training strategy for autoencoders achieves encouraging results in both synthesis and real-world multi-view learning tasks.

show abstract

“…The collection of equivalence of classes of networks will be denoted [N ]. See also [CM18] for more details on weak isomorphism.…”

Section: Weak Isomorphism: From Transport Plans To Transport Maps Via...mentioning

confidence: 99%

Gromov-Wasserstein Averaging in a Riemannian Framework

Chowdhury¹,

Needham²

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We introduce a theoretical framework for performing statistical tasks-including, but not limited to, averaging and principal component analysis-on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is carried out under the lens of the Gromov-Wasserstein (GW) distance, and our methods translate the Riemannian framework of GW distances developed by Sturm into practical, implementable tools for network data analysis. Our methods are illustrated on datasets of asymmetric stochastic blockmodel networks and planar shapes viewed as metric spaces. On the theoretical front, we supplement the work of Sturm by producing additional results on the tangent structure of this "space of spaces", as well as on the gradient flow of the Fréchet functional on this space.

show abstract

The Gromov-Wasserstein distance between networks and stable network invariants

Cited by 7 publications

References 7 publications

Gromov-Wasserstein Learning for Graph Matching and Node Embedding

Gromov-Wasserstein Learning for Graph Matching and Node Embedding

Learning Autoencoders with Relational Regularization

Gromov-Wasserstein Averaging in a Riemannian Framework

Contact Info

Product

Resources

About