Joint Embedding of Graphs

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently accurately learning features multiple graphs has important applications statistical inference on graphs. We propose method to jointly embed undirected Given set graphs, the joint embedding identifies linear subspace spanned by rank one symmetric matrices projects adjacency into this subspace. The projection coefficients can be treated as while components represent vertex features. also random graph model that generalizes other classical models show through theory numerical experiments under model, produces estimates parameters with small errors. Via simulation experiments, we demonstrate which lead state art performance classifying Applying human brain find it extracts interpretable good prediction accuracy different tasks.