Online Graph Dictionary Learning

Cédric Vincent-Cuaz, Titouan Vayer, Rémi Flamary, Marco Corneli, Nicolas Courty
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:10564-10574, 2021.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-vincent-cuaz21a, title = {Online Graph Dictionary Learning}, author = {Vincent-Cuaz, C{\'e}dric and Vayer, Titouan and Flamary, R{\'e}mi and Corneli, Marco and Courty, Nicolas}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {10564--10574}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/vincent-cuaz21a/vincent-cuaz21a.pdf}, url = {https://proceedings.mlr.press/v139/vincent-cuaz21a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Online Graph Dictionary Learning %A Cédric Vincent-Cuaz %A Titouan Vayer %A Rémi Flamary %A Marco Corneli %A Nicolas Courty %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-vincent-cuaz21a %I PMLR %P 10564--10574 %U https://proceedings.mlr.press/v139/vincent-cuaz21a.html %V 139 %X 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.
APA
Vincent-Cuaz, C., Vayer, T., Flamary, R., Corneli, M. & Courty, N.. (2021). Online Graph Dictionary Learning. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:10564-10574 Available from https://proceedings.mlr.press/v139/vincent-cuaz21a.html.

Related Material