LASAGNE: Locality And Structure Aware Graph Node Embedding

Recent work has attempted to identify structure in social and information graphs by using the following approach: first, use random walk methods to explore the neighborhood of a node; second, use ideas from natural language processing to use this neighborhood information to learn vector representations of these nodes reflecting properties of the graph. Informally, the idea is that if a node is a member of a meaningful cluster or community, then the vector representation should be higher-quality, thereby leading to improved learning. In this paper, we identify and remedy an important shortcoming of this approach. In particular, we show that the performance of existing methodologies depends strongly on the structural properties of the graph, e.g., the size of the graph, whether the graph has a flat or upward-sloping Network Community Profile (NCP), whether the graph is expander-like, whether the classes of interest are more k-core-like or more peripheral, etc. For larger graphs with flat NCPs that are strongly expander-like, existing methods lead to random walks that expand rapidly, touching many dissimilar nodes, thereby leading to lower-quality vector representations that are less useful for downstream tasks. Based on our findings, we propose Lasagne, a methodology to learn locality and structure aware graph node embeddings in an unsupervised way. Rather than relying on global random walks or neighbors within fixed hop distances, Lasagne exploits strongly local Approximate Personalized PageRank stationary distributions to more precisely engineer local information into node embeddings. This leads, in particular, to more meaningful and more useful vector representations of nodes in poorly-structured graphs. We show that Lasagne leads to significant improvement in downstream multi-label classification for larger graphs with flat NCPs, that it is comparable for smaller graphs with upward-sloping NCPs, and that is comparable to existing methods for link prediction tasks.