ELTRA: An Embedding Method based on Learning-to-Rank to Preserve Asymmetric Information in Directed Graphs

Abstract

Double-vector embedding methods capture the asymmetric information in directed graphs first, and then preserve them in the embedding space by providing two latent vectors, i.e., source and target, per node. Although these methods are known to be superior to the single-vector ones (i.e., providing a single latent vector per node), we point out their three drawbacks as inability to preserve asymmetry on NU-paths, inability to preserve global nodes similarity, and impairing in/out-degree distributions. To address these, we first propose CRW, a novel similarity measure for graphs that considers contributions of both in-links and out-links in similarity computation, without ignoring their directions. Then, we propose ELTRA, an effective double-vector embedding method to preserve asymmetric information in directed graphs. ELTRA computes asymmetry preserving proximity scores (AP-scores) by employing CRW in which the contribution of out-links and in-links in similarity computation is upgraded and downgraded, respectively. Then, for every node u, ELTRA selects its top-t closest nodes based on AP-scores and conforms the ranks of their corresponding target vectors w.r.t u's source vector in the embedding space to their original ranks. Our extensive experimental results with seven real-world datasets and sixteen embedding methods show that (1) CRW significantly outperforms Katz and RWR in computing nodes similarity in graphs, (2) ELTRA outperforms the existing state-of-the-art methods in graph reconstruction, link prediction, and node classification tasks.