Abstract: Graph convolutional autoencoders emerged as powerful graph representation learning methods with promising performance on link prediction. However, existing methods typically rely on graph convolutional network to encode adjacency matrix and attribute matrix. This strategy ignores high-order features such as second-order information. This paper proposes a new SeVGAE model based on second-order graph convolutional autoencoders to tackle this problem. Firstly, graph convolutional network and second-order graph convolutional network are used to generate the mean and variance of the variational autoencoders. Then, the embeddings are learned to represent the mixed probability distribution of the original graph. Finally, the topology is recovered by the inner product decoder. SeVGAE performs better than the baselines in the link prediction. AUC and AP are raised by 3.26% and 2.56% respectively compared to the original VGAE on Citeseer dataset. The results show that the second-order information can retain richer graph information in low-dimensional embeddings. Besides, the proposed method has obvious advantages in insufficient attribute and inaccurate topology. In the extreme case where both edges and attributes are missing up to 40%, SeVGAE still improves AUC and AP by 4.79% and 3.47%respectively compared to VGAE.

Key words: graph representation learning, second-order graph convolutional network, link prediction

摘要： 图卷积自编码器是一类高效的图表示学习模型，在链路预测等任务中具有出色性能。然而现有模型大多依赖图卷积网络对邻接矩阵和属性矩阵进行编码，未充分利用二阶信息等高阶结构特征。针对上述问题，提出了基于二阶信息的图卷积自编码器模型SeVGAE。首先使用图卷积和二阶图卷积生成变分自编码器的均值和方差，然后学习嵌入向量表示原始图的混合概率分布，最后使用内积解码器恢复拓扑结构。在链接预测任务中，SeGVAE表现优于基线模型，Citeseer数据集上的AUC和AP相较原始的VGAE分别提升了3.26%和2.56%。实验结果表明，二阶信息的引入能够在低维嵌入中保留更丰富的图信息，提升模型性能。模型在处理属性信息不足、拓扑信息不准确的图数据时具有较为明显的优势，在边缘和属性均缺失40%的极端情况下，SeVGAE的AUC和AP相较VGAE提升4.79%和3.47%。

关键词: 图表示学习, 二阶图卷积网络, 链接预测