Directed graphs have been widely used in Community Question Answering services (CQAs) to model asymmetric relationships among different types of nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is an essential property of directed graphs, since it can play an important role in downstream graph inference and analysis. Question difficulty and user expertise follow the characteristic of asymmetric transitivity. Maintaining such properties, while reducing the graph to a lower dimensional vector embedding space, has been the focus of much recent research. In this paper, we tackle the challenge of directed graph embedding with asymmetric transitivity preservation and then leverage the proposed embedding method to solve a fundamental task in CQAs: how to appropriately route and assign newly posted questions to users with the suitable expertise and interest in CQAs. The technique incorporates graph hierarchy and reachability information naturally by relying on a non-linear transformation that operates on the core reachability and implicit hierarchy within such graphs. Subsequently, the methodology levers a factorization-based approach to generate two embedding vectors for each node within the graph, to capture the asymmetric transitivity. Extensive experiments show that our framework consistently and significantly outperforms the state-of-the-art baselines on two diverse real-world tasks: link prediction, and question difficulty estimation and expert finding in online forums like Stack Exchange. Particularly, our framework can support inductive embedding learning for newly posted questions (unseen nodes during training), and therefore can properly route and assign these kinds of questions to experts in CQAs.
Graph Embedding methods are aimed at mapping each vertex into a low dimensional vector space, which preserves certain structural relationships among the vertices in the original graph. Recently, several works have been proposed to learn embeddings based on sampled paths from the graph, e.g., DeepWalk, Line, Node2Vec. However, their methods only preserve symmetric proximities, which could be insufficient in many applications, even the underlying graph is undirected. Besides, they lack of theoretical analysis of what exactly the relationships they preserve in their embedding space. In this paper, we propose an asymmetric proximity preserving (APP) graph embedding method via random walk with restart, which captures both asymmetric and high-order similarities between node pairs. We give theoretical analysis that our method implicitly preserves the Rooted PageRank score for any two vertices. We conduct extensive experiments on tasks of link prediction and node recommendation on open source datasets, as well as online recommendation services in Alibaba Group, in which the training graph has over 290 million vertices and 18 billion edges, showing our method to be highly scalable and effective. 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.