# Online Graph Dictionary Learning

arXiv: https://arxiv.org/abs/2102.06555 · HTML: https://mlsanity.com/paper/2102.06555/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 80 references that are in the map.
- First posted on arXiv 12 Feb 2021.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Understanding Attention and Generalization in Graph Neural Networks](https://mlsanity.com/paper/1905.02850/) (2019)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Propagation Kernels](https://mlsanity.com/paper/1410.3314/) (2014)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Streaming Graph Neural Networks via Continual Learning](https://mlsanity.com/paper/2009.10951/) (2020)
- [Convergence Rate of Frank-Wolfe for Non-Convex Objectives](https://mlsanity.com/paper/1607.00345/) (2016)
- [GraKeL: A Graph Kernel Library in Python](https://mlsanity.com/paper/1806.02193/) (2018)
- [Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks](https://mlsanity.com/paper/1703.02161/) (2017)
- [Generalized Spectral Clustering via Gromov-Wasserstein Learning](https://mlsanity.com/paper/2006.04163/) (2020)
- [Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning](https://mlsanity.com/paper/1708.01955/) (2017)
- [Gromov-Wasserstein Factorization Models for Graph Clustering](https://mlsanity.com/paper/1911.08530/) (2019)
- [Recognizing Cuneiform Signs Using Graph Based Methods](https://mlsanity.com/paper/1802.05908/) (2018)
- [Concept Drift and Anomaly Detection in Graph Streams](https://mlsanity.com/paper/1706.06941/) (2017)
- [Change Detection in Graph Streams by Learning Graph Embeddings on Constant-Curvature Manifolds](https://mlsanity.com/paper/1805.06299/) (2018)
- [Change Point Methods on a Sequence of Graphs](https://mlsanity.com/paper/1805.07113/) (2018)
- [Methods for Sparse and Low-Rank Recovery under Simplex Constraints](https://mlsanity.com/paper/1605.00507/) (2016)

## Built on by (most cited first, 30 of 37)

- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Hierarchical Multi-Marginal Optimal Transport for Network Alignment](https://mlsanity.com/paper/2310.04470/) (2023)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
- [Semi-relaxed Gromov-Wasserstein divergence with applications on graphs](https://mlsanity.com/paper/2110.02753/) (2021)
- [Template based Graph Neural Network with Optimal Transport Distances](https://mlsanity.com/paper/2205.15733/) (2022)
- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesics](https://mlsanity.com/paper/2505.12709/) (2025)
- [Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport](https://mlsanity.com/paper/2301.12721/) (2023)
- [Fused Gromov-Wasserstein Graph Mixup for Graph-level Classifications](https://mlsanity.com/paper/2306.15963/) (2023)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Data](https://mlsanity.com/paper/2303.06595/) (2023)
- [Graph Classification via Reference Distribution Learning: Theory and Practice](https://mlsanity.com/paper/2408.11370/) (2024)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [Semidefinite Relaxations of the Gromov-Wasserstein Distance](https://mlsanity.com/paper/2312.14572/) (2023)
- [Outlier-Robust Gromov-Wasserstein for Graph Data](https://mlsanity.com/paper/2302.04610/) (2023)
- [Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problem](https://mlsanity.com/paper/2303.05978/) (2023)
- [Learning Graphon Autoencoders for Generative Graph Modeling](https://mlsanity.com/paper/2105.14244/) (2021)
- [Structure-Centric Graph Foundation Model via Geometric Bases](https://mlsanity.com/paper/2605.08689/) (2026)
- [Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networks](https://mlsanity.com/paper/2402.01975/) (2024)
- [Topological Dictionary Learning](https://mlsanity.com/paper/2503.11470/) (2025)
- [Distances for Markov Chains, and Their Differentiation](https://mlsanity.com/paper/2302.08621/) (2023)
- [Gradual Domain Adaptation for Graph Learning](https://mlsanity.com/paper/2501.17443/) (2025)
- [GBGC: Efficient and Adaptive Graph Coarsening via Granular-ball Computing](https://mlsanity.com/paper/2506.19224/) (2025)
- [An in depth look at the Procrustes-Wasserstein distance: properties and barycenters](https://mlsanity.com/paper/2507.00894/) (2025)
- [Fast and Provably Convergent Algorithms for Gromov-Wasserstein in Graph Data](https://mlsanity.com/paper/2205.08115/) (2022)
- [Exploiting Edge Features in Graphs with Fused Network Gromov-Wasserstein Distance](https://mlsanity.com/paper/2309.16604/) (2023)
- [A Quasi-Wasserstein Loss for Learning Graph Neural Networks](https://mlsanity.com/paper/2310.11762/) (2023)
- [Structure-Sensitive Graph Dictionary Embedding for Graph Classification](https://mlsanity.com/paper/2306.10505/) (2023)
- [Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein](https://mlsanity.com/paper/2310.03398/) (2023)
- [Graph-Dictionary Signal Model for Sparse Representations of Multivariate Data](https://mlsanity.com/paper/2411.05729/) (2024)

## 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.