Graph convolutional networks (GCNs) have achieved great success in graph representation learning by extracting high-level features from nodes and their topology. Since GCNs generally follow a message-passing mechanism, each node aggregates information from its first-order neighbour to update its representation. As a result, the representations of nodes with edges between them should be positively correlated and thus can be considered positive samples. However, there are more non-neighbour nodes in the whole graph, which provide diverse and useful information for the representation update. Two non-adjacent nodes usually have different representations, which can be seen as negative samples. Besides the node representations, the structural information of the graph is also crucial for learning. In this paper, we used quality-diversity decomposition in determinant point processes (DPP) to obtain diverse negative samples. When defining a distribution on diverse subsets of all non-neighbouring nodes, we incorporate both graph structure information and node representations. Since the DPP sampling process requires matrix eigenvalue decomposition, we propose a new shortest-path-base method to improve computational efficiency. Finally, we incorporate the obtained negative samples into the graph convolution operation. The ideas are evaluated empirically in experiments on node classification tasks. These experiments show that the newly proposed methods not only improve the overall performance of standard representation learning but also significantly alleviate over-smoothing problems.

翻译：图卷积网络通过从节点及其拓扑结构中提取高阶特征，在图表示学习领域取得了巨大成功。由于图卷积网络通常遵循消息传递机制，每个节点会聚合其一阶邻居的信息来更新自身表示。因此，存在边连接的节点对之间的表示应呈正相关，可视为正样本。然而，全图中存在更多非邻居节点，它们为表示更新提供了多样且有用的信息。两个非相邻节点通常具有不同的表示，可视为负样本。除了节点表示，图的结构信息对学习也至关重要。本文利用行列式点过程中的质量-多样性分解来获取多样负样本。在定义所有非邻居节点的多样子集分布时，我们同时融合了图结构信息与节点表示。鉴于行列式点过程采样需要矩阵特征值分解，我们提出了一种基于最短路径的新方法以提高计算效率。最终将获取的负样本融入图卷积运算中。该思想在节点分类任务的实验中进行了实证评估。实验表明，新提出的方法不仅提升了标准表示学习的整体性能，还显著缓解了过平滑问题。