  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.
