mlsanityData to 7 Oct 2026

Online Graph Dictionary Learning

arXiv 2102.06555 ↗First posted 12 Feb 2021cs.LGcited by 37

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Abstract (arXiv)

Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). Builds on 30 of its 80 references that are in the map. First posted on arXiv 12 Feb 2021.

Builds on

30 of 80 references.

References · 30

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
  4. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
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  6. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  7. 2018Computational Optimal Transportcited by 765
  8. 2017Wasserstein GANcited by 635
  9. 2016Learning Convolutional Neural Networks for Graphscited by 314
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  11. 2018Optimal Transport for structured data with application on graphscited by 170
  12. 2019Understanding Attention and Generalization in Graph Neural Networkscited by 169
18 more
  1. 2019Gromov-Wasserstein Learning for Graph Matching and Node Embeddingcited by 125
  2. 2019Wasserstein Weisfeiler-Lehman Graph Kernelscited by 104
  3. 2019Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matchingcited by 102
  4. 2018Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical propertiescited by 93
  5. 2014Propagation Kernelscited by 88
  6. 2019GOT: An Optimal Transport framework for Graph comparisoncited by 64
  7. 2020Streaming Graph Neural Networks via Continual Learningcited by 63
  8. 2016Convergence Rate of Frank-Wolfe for Non-Convex Objectivescited by 59
  9. 2018GraKeL: A Graph Kernel Library in Pythoncited by 54
  10. 2017Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networkscited by 40
  11. 2020Generalized Spectral Clustering via Gromov-Wasserstein Learningcited by 37
  12. 2017Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learningcited by 34
  13. 2019Gromov-Wasserstein Factorization Models for Graph Clusteringcited by 25
  14. 2018Recognizing Cuneiform Signs Using Graph Based Methodscited by 14
  15. 2017Concept Drift and Anomaly Detection in Graph Streamscited by 12
  16. 2018Change Detection in Graph Streams by Learning Graph Embeddings on Constant-Curvature Manifoldscited by 8
  17. 2018Change Point Methods on a Sequence of Graphscited by 4
  18. 2016Methods for Sparse and Low-Rank Recovery under Simplex Constraintscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 4; 2023: 13; 2024: 4; 2025: 5; 2026: 8.

37 papers.

Sort:

  1. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  2. 2023Hierarchical Multi-Marginal Optimal Transport for Network Alignmentcited by 24
  3. 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
  4. 2021Semi-relaxed Gromov-Wasserstein divergence with applications on graphscited by 21
  5. 2022Template based Graph Neural Network with Optimal Transport Distancescited by 20
  6. 2022Implicit Graphon Neural Representationcited by 18
  7. 2025Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesicscited by 17
  8. 2023Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transportcited by 15
  9. 2023Fused Gromov-Wasserstein Graph Mixup for Graph-level Classificationscited by 15
  10. 2024Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wassersteincited by 12
  11. 2024Graph Classification via Reference Distribution Learning: Theory and Practicecited by 11
  12. 2021Partition and Code: learning how to compress graphscited by 10
25 more
  1. 2023A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Datacited by 10
  2. 2023Semidefinite Relaxations of the Gromov-Wasserstein Distancecited by 10
  3. 2023Outlier-Robust Gromov-Wasserstein for Graph Datacited by 6
  4. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  5. 2026Structure-Centric Graph Foundation Model via Geometric Basescited by 5
  6. 2021Learning Graphon Autoencoders for Generative Graph Modelingcited by 4
  7. 2024Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networkscited by 4
  8. 2025Topological Dictionary Learningcited by 4
  9. 2023Distances for Markov Chains, and Their Differentiationcited by 2
  10. 2025Gradual Domain Adaptation for Graph Learningcited by 2
  11. 2025GBGC: Efficient and Adaptive Graph Coarsening via Granular-ball Computingcited by 2
  12. 2022Fast and Provably Convergent Algorithms for Gromov-Wasserstein in Graph Datacited by 1
  13. 2023Exploiting Edge Features in Graphs with Fused Network Gromov-Wasserstein Distancecited by 1
  14. 2023A Quasi-Wasserstein Loss for Learning Graph Neural Networkscited by 1
  15. 2025An in depth look at the Procrustes-Wasserstein distance: properties and barycenterscited by 1
  16. 2023Structure-Sensitive Graph Dictionary Embedding for Graph Classificationcited by 0
  17. 2023Interpolating between Clustering and Dimensionality Reduction with Gromov-Wassersteincited by 0
  18. 2024Graph-Dictionary Signal Model for Sparse Representations of Multivariate Datacited by 0
  19. 2026On sparsity, extremal structure, and monotonicity properties of Wasserstein and Gromov-Wasserstein optimal transport planscited by 0
  20. 2026Learning fMRI activations dictionaries across individual geometries via optimal transportcited by 0
  21. 2026Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Modelscited by 0
  22. 2026Network Learning with Semi-relaxed Gromov-Wassersteincited by 0
  23. 2026Towards Faithful Graph Explanations with Synergistic Edge Effects via Granular Ballscited by 0
  24. 2026Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithmscited by 0
  25. 2026A dictionary learning framework for graphs via filters and optimal transportcited by 0