Multi-scale attributed node embedding

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighbourhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighbourhood relationships over multiple scales is useful for a range of applications, including latent feature identification across disconnected networks with similar features. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are computationally efficient and outperform comparable models on social networks and web graphs.