Knowledge graph (KG) embedding is a fundamental problem in data mining research with many real-world applications. It aims to encode the entities and relations in the graph into low dimensional vector space, which can be used for subsequent algorithms. Negative sampling, which samples negative triplets from non-observed ones in the training data, is an important step in KG embedding. Recently, generative adversarial network (GAN), has been introduced in negative sampling. By sampling negative triplets with large scores, these methods avoid the problem of vanishing gradient and thus obtain better performance. However, using GAN makes the original model more complex and hard to train, where reinforcement learning must be used. In this paper, motivated by the observation that negative triplets with large scores are important but rare, we propose to directly keep track of them with cache. However, how to sample from and update the cache are two important questions. We carefully design the solutions, which are not only efficient but also achieve good balance between exploration and exploitation. In this way, our method acts as a "distilled" version of previous GANbased methods, which does not waste training time on additional parameters to fit the full distribution of negative triplets. The extensive experiments show that our method can gain significant improvement on various KG embedding models, and outperform the state-of-the-arts negative sampling methods based on GAN.

SimRank is an important measure of vertex-pair similarity according to the structure of graphs. The similarity search based on Sim-Rank is an important operation for identifying similar vertices in a graph and has been employed in many data analysis applications. Nowadays, graphs in the real world become much larger and more dynamic. The existing solutions for similarity search are expensive in terms of time and space cost. None of them can efficiently support similarity search over large dynamic graphs. In this paper, we propose a novel two-stage random-walk sampling framework (TSF) for SimRank-based similarity search (e.g., top-k search). In the preprocessing stage, TSF samples a set of one-way graphs to index raw random walks in a novel manner within O(N Rg) time and space, where N is the number of vertices and Rg is the number of one-way graphs. The one-way graph can be efficiently updated in accordance with the graph modification, thus TSF is well suited to dynamic graphs. During the query stage, TSF can search similar vertices fast by naturally pruning unqualified vertices based on the connectivity of one-way graphs. Furthermore, with additional Rq samples, TSF can estimate the SimRank score with probability 1 − 2e −2ǫ 2 Rg Rq (1−c) 2 if the error of approximation is bounded by 1 − ǫ. Finally, to guarantee the scalability of TSF, the one-way graphs can also be compactly stored on the disk when the memory is limited. Extensive experiments have demonstrated that TSF can handle dynamic billion-edge graphs with high performance.

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