FOBE and HOBE: First- and High-Order Bipartite Embeddings

Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better served with specialized embedding techniques. We propose two embeddings for bipartite graphs that decompose edges into sets of indirect relationships between node neighborhoods. When sampling higher-order relationships, we reinforce similarities through algebraic distance on graphs. We also introduce ensemble embeddings to combine both into a "best of both worlds" embedding. The proposed methods are evaluated on link prediction and recommendation tasks and compared with other state-of-the-art embeddings. While being all highly beneficial in applications, we demonstrate that none of the considered embeddings is clearly superior (in contrast to what is claimed in many papers), and discuss the trade offs present among them. Reproducibility: Our code, data sets, and results are all publicly available online at: http://bit.ly/fobe_hobe_code.