Asymmetric Transitivity Preserving Graph Embedding
Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved. The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs. Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v. Asymmetric transitivity can help in capturing structures of graphs and recovering from partially observed graphs. To tackle this challenge, we propose the idea of preserving asymmetric transitivity by approximating high order proximity which are based on asymmetric transitivity. In particular, we develop a novel graph embedding algorithm, High Order Proximity preserved Embedding (HOPE for short) which is scalable to preserve high order proximities of large scale graphs and capable of capturing the asymmetric transitivity. More specifically, we first derive a general formulation that cover multiple popular high order proximity measurements, then propose a scalable embedding algorithm to approximate the high order proximity measurements based on their general formulation. Moreover, we provide a theoretical upper bound on the RMSE (Root Mean Squared Error) of the approximation. Our empirical experiments on a synthetic dataset and three real world datasets demonstrate that HOPE can approximate the high order proximities significantly better than the state of art algorithms and outperform the state of art algorithms in tasks of reconstruction, link prediction and vertex recommendation.
KDD