Scaling attributed network embedding to massive graphs

Given a graph G where each node is associated with a set of attributes, attributed network embedding (ANE) maps each node v ∈ G to a compact vector X v , which can be used in downstream machine learning tasks. Ideally, X v should capture node v 's affinity to each attribute, which considers not only v 's own attribute associations, but also those of its connected nodes along edges in G . It is challenging to obtain high-utility embeddings that enable accurate predictions; scaling effective ANE computation to massive graphs with millions of nodes pushes the difficulty of the problem to a whole new level. Existing solutions largely fail on such graphs, leading to prohibitive costs, low-quality embeddings, or both. This paper proposes PANE, an effective and scalable approach to ANE computation for massive graphs that achieves state-of-the-art result quality on multiple benchmark datasets, measured by the accuracy of three common prediction tasks: attribute inference, link prediction, and node classification. In particular, for the large MAG data with over 59 million nodes, 0.98 billion edges, and 2000 attributes, PANE is the only known viable solution that obtains effective embeddings on a single server, within 12 hours. PANE obtains high scalability and effectiveness through three main algorithmic designs. First, it formulates the learning objective based on a novel random walk model for attributed networks. The resulting optimization task is still challenging on large graphs. Second, PANE includes a highly efficient solver for the above optimization problem, whose key module is a carefully designed initialization of the embeddings, which drastically reduces the number of iterations required to converge. Finally, PANE utilizes multi-core CPUs through non-trivial parallelization of the above solver, which achieves scalability while retaining the high quality of the resulting embeddings. Extensive experiments, comparing 10 existing approaches on 8 real datasets, demonstrate that PANE consistently outperforms all existing methods in terms of result quality, while being orders of magnitude faster.