Fused Gromov-Wasserstein Distance for Structured Objects

Vayer, Titouan; Chapel, Laëtitia; Flamary, Rémi; Tavenard, Romain; Courty, Nicolas

doi:10.3390/a13090212

Cited by 56 publications

(57 citation statements)

References 41 publications

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“…The high computational complexity limits the applications of GW discrepancy. These years, many variants of GW discrepancy have been proposed, e.g., the recursive GW discrepancy , and the sliced GW discrepancy (Vayer et al 2019b). Although these works have achieved encouraging results in many tasks, none of them consider building Gromov-Wasserstein factorization models as we do.…”

Section: Gw Discrepancy and Its Applicationsmentioning

confidence: 99%

Gromov-Wasserstein Factorization Models for Graph Clustering

2020

AAAI

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We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters constructed by a set of atoms with different weights. By minimizing the GW discrepancy between each observed graph and its GW barycenter-based estimation, we learn the atoms and their weights associated with the observed graphs. The model achieves a novel and flexible factorization mechanism under GW discrepancy, in which both the observed graphs and the learnable atoms can be unaligned and with different sizes. We design an effective approximate algorithm for learning this Gromov-Wasserstein factorization (GWF) model, unrolling loopy computations as stacked modules and computing gradients with backpropagation. The stacked modules can be with two different architectures, which correspond to the proximal point algorithm (PPA) and Bregman alternating direction method of multipliers (BADMM), respectively. Experiments show that our model obtains encouraging results on clustering graphs.

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Section: Gw Discrepancy and Its Applicationsmentioning

confidence: 99%

Gromov-Wasserstein Factorization Models for Graph Clustering

2020

AAAI

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“…FG-W, unlike the G-W, combines both feature and structural information and shows its advantage in graph classification. 23 , 44 Consider two sets of tuples

in space

and

, in space

, here,

and

are the data points,

and

are their corresponding features, which are both in space

and share the same dimension. With a slight abuse of notation, we will use the same symbol as Eq.…”

Section: Domain Adaptation For Fnirsmentioning

confidence: 99%

“…FG-W, unlike the G-W, combines both feature and structural information and shows its advantage in graph classification. 23,44 Consider two sets of tuples With a slight abuse of notation, we will use the same symbol as Eq. (1) to denote their empirical distribution E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 8 ; 1 1 6 ; 2 2 9…”

Section: Fused Gromov-wasserstein Barycentermentioning

confidence: 99%

Domain adaptation for robust workload level alignment between sessions and subjects using fNIRS

et al. 2021

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We demonstrated the potential of using domain adaptation on functional Near-Infrared Spectroscopy (fNIRS) data to detect and discriminate different levels of n-back tasks that involve working memory across different experiment sessions and subjects. Aim: To address the domain shift in fNIRS data across sessions and subjects for task label alignment, we exploited two domain adaptation approaches -Gromov-Wasserstein (G-W) and Fused Gromov-Wasserstein (FG-W). Approach: We applied G-W for session-by-session alignment and FG-W for subject-by-subject alignment with Hellinger distance as underlying metric to fNIRS data acquired during different n-back task levels. We also compared with a supervised method -Convolutional Neural Network (CNN). Results: For session-by-session alignment, using G-W resulted in alignment accuracy of 70 ± 4 % (weighted mean ± standard error), whereas using CNN resulted in classification accuracy of 58 ± 5 % across five subjects. For subject-by-subject alignment, using FG-W resulted in alignment accuracy of 55 ± 3 %, whereas using CNN resulted in classification accuracy of 45 ± 1 %. Where in both cases 25 % represents chance. We also showed that removal of motion artifacts from the fNIRS data plays an important role in improving alignment performance. Conclusions: Domain adaptation is potential for session-by-session and subject-by-subject alignment using fNIRS data.

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“…Similar to the drug networks, some of the protein networks are highly dense. Implementation Details and Competing Algorithms: To measure the Gromov Wassertein Discrepancy (GWD) among layers of multiplex networks, we build our Python code on the implementation provided by [24]. We use this tool with σ = 100 to compute w ij 's for all multiplex networks.…”

Section: Drug-target Interaction Predictionmentioning

confidence: 99%

Multiplex Embedding of Biological Networks Using Topological Similarity of Different Layers

Coşkun

Koyutürk

2021

Preprint

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Network embedding techniques, which provide low dimensional representations of the nodes in a network, have been commonly applied to many machine learning problems in computational biology. In most of these applications, multiple networks (e.g., different types of interactions/associations or semantically identical networks that come from different sources) are available. Multiplex network embedding aims to derive strength from these data sources by integrating multiple networks with a common set of nodes. Existing approaches to this problem treat all layers of the multiplex network equally while performing integration, ignoring the differences in the topology and sparsity patterns of different networks. Here, we formulate an optimization problem that accounts for inner-network smoothness, intra-network smoothness, and topological similarity of networks to compute diffusion states for each network. To quantify the topological similarity of pairs of networks, we use Gromov-Wasserteins discrepancy. Finally, we integrate the resulting diffusion states and apply dimensionality reduction (singular value decomposition after log-transformation) to compute node embeddings. Our experimental results in the context of drug repositioning and drug-target prediction show that the embeddings computed by the resulting algorithm, Hattusha, consistently improve predictive accuracy over algorithms that do not take into account the topological similarity of different networks.

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Fused Gromov-Wasserstein Distance for Structured Objects

Cited by 56 publications

References 41 publications

Gromov-Wasserstein Factorization Models for Graph Clustering

Gromov-Wasserstein Factorization Models for Graph Clustering

Domain adaptation for robust workload level alignment between sessions and subjects using fNIRS

Multiplex Embedding of Biological Networks Using Topological Similarity of Different Layers

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