Gromov-Wasserstein Averaging of Kernel and Distance Matrices

By G. Peyr'e, Marco Cuturi, Justin M. Solomon. 2016

505 citations recorded by the source corpus.

How researchers see this paper

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1. Zhe Gan
2. Chunyuan Li
3. Linjie Li
4. Wojciech Samek
5. Yoshua Bengio
6. Yu Cheng
7. Grgoire Montavon
8. Dacheng Tao

Citations in the corpus

• Computational Optimal Transport (2018, methodology): “A heuristic approach is used in [Peyré et al., 2016] to define geodesics and barycenters of metric measure spaces while imposing the cardinality of the involved spaces and making use of the entropic smoothing (10.”
• Robust Wasserstein profile inference and applications to machine learning (2016, background): “ntly, optimal transport metrics and Wasserstein distances are being actively investigated for RWPI AND APPLICATIONS TO MACHINE LEARNING 9 its use in various machine learning applications as well (see [34,28,32,37,14,39] and references therein for a growing list of new applications). Throughout this ”
• Analyzing ImageNet with Spectral Relevance Analysis: Towards ImageNet un-Hans'ed (2019, methodology): “In order to further expand the scope of SpRAy, we consider the Gromov-Wasserstein distance (GWD) [28], as an additional distance measure.”
• Space-Time Correspondence as a Contrastive Random Walk (2020, background): “A key challenge is inferring correspondence between graphs, which has been approached in prior work [115, 86] with efficient optimal transport algorithms [91, 18, 81].”
• Gromov-Wasserstein Learning for Graph Matching and Node Embedding (2019, methodology): “Note that besides our proximal point method, another method for solving (5) involves replacing the KL-divergence KL(T ‖T (n)) in (6) with an entropy regularizer H(T ) and minimizing an entropic GW discrepancy via iterative Sinkhorn projection (Peyré et al., 2016).”
• Optimal Transport for structured data with application on graphs (2018, methodology): “4 in (Peyré et al., 2016)) : C ← 1 hhT ∑ k λkπ T k Ckπk where h is the histogram of the barycenter as discussed in section 3.2.”
• Graph Optimal Transport for Cross-Domain Alignment (2020, methodology): “Gromov-Wasserstein Distance Instead of directly calculating distances between two sets of nodes as in WD, Gromov-Wasserstein distance (GWD) (Peyr´e et al., 2016; Chowdhury & M ´ emoli, 2019) can be used to calculate distances between pairs of nodes within each domain, as well as measuring how these…”
• Inferring spatial and signaling relationships between cells from single cell transcriptomic data (2020, background): “(3) The Gromov-Wasserstein (GW) distance measures difference between metric spaces.[16] In other words, it focuses on how well the intra-dataset relationship is preserved by the mapping.”
• Gromov-Wasserstein Alignment of Word Embedding Spaces (2018, methodology): “Furthermore, for suitable choices of loss function L , Peyr´e et al. (2016) show that instead of the O ( N 21 N 22 ) complexity implied by naive fourth-order tensor product, this computation reduces to Their approach consists of solving (5) by projected gradient descent, which yields iterations…”