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.
