  Problems involving multiple networks are prevalent in many scientific and
other domains. In particular, network alignment, or the task of identifying
corresponding nodes in different networks, has applications across the social
and natural sciences. Motivated by recent advancements in node representation
learning for single-graph tasks, we propose REGAL (REpresentation
learning-based Graph ALignment), a framework that leverages the power of
automatically-learned node representations to match nodes across different
graphs. Within REGAL we devise xNetMF, an elegant and principled node embedding
formulation that uniquely generalizes to multi-network problems. Our results
demonstrate the utility and promise of unsupervised representation
learning-based network alignment in terms of both speed and accuracy. REGAL
runs up to 30x faster in the representation learning stage than comparable
methods, outperforms existing network alignment methods by 20 to 30% accuracy
on average, and scales to networks with millions of nodes each.
