一种异质图的Lorentz嵌入模型

异质图嵌入的目标是用低维稠密向量表示原网络的拓扑结构和节点属性信息。为提高异质图嵌入质量、减少失真，提出了一种将异质图嵌入到基于Lorentz模型的双曲空间中的方法。该方法采用元路径约束的随机游走进行节点关系和语义的发现，模型基于负采样的极大似然为目标函数，使目标节点与邻居更相近，而远离非邻居节点，优化方法不同于欧式空间的黎曼梯度下降；在引文网上将所提算法与4种基准图嵌入算法进行比较，实验证明该方法不但获得了优于其他基准算法的预测精度，而且还保留了可解释的图的层次结构。双曲嵌入为异质图的研究提供了一种新的思路，能够为异质图的下游任务提供更高质量的嵌入结果。

A Lorentz Embedding Model for Heterogeneous Graphs

Heterogeneous graph (HG) embedding method has been proposed as a new learning paradigm that embeds vertices into a low-dimensional dense vector space, by preserving Heterogeneous graph topology structure and vertex attributes information. In order to improve the quality of HG embedding and reduce distortion, a method for embedding HGs into hyperbolic space based on Lorentz model is proposed. This method employ the meta-path guided random walk to capture the structure and semantic relations between nodes. Specifically, the maximum likelihood estimate based on negative sampling is used as the objective function to achieve binary classification: making the target node more similar to its neighbor and farther away from non-neighbor nodes. Then, the Riemann gradient descent, which is different from the Euclidean space, is used to optimize the model parameters. Experiments on PubMed dataset demonstrate that our proposed model not only has superior performance on link prediction tasks than 4 baseline methods but also show its ability of capture graph’s hierarchy structure. Hyperbolic space provides a new idea for analyzing structure of heterogeneous graphs and can provide higher-quality embedding results for downstream tasks of heterogeneous graphs.