Contrastive learning on graphs aims at extracting distinguishable high-level representations of nodes. In this paper, we theoretically illustrate that the entropy of a dataset can be approximated by maximizing the lower bound of the mutual information across different views of a graph, \ie, entropy is estimated by a neural network. Based on this finding, we propose a simple yet effective subset sampling strategy to contrast pairwise representations between views of a dataset. In particular, we randomly sample nodes and edges from a given graph to build the input subset for a view. Two views are fed into a parameter-shared Siamese network to extract the high-dimensional embeddings and estimate the information entropy of the entire graph. For the learning process, we propose to optimize the network using two objectives, simultaneously. Concretely, the input of the contrastive loss function consists of positive and negative pairs. Our selection strategy of pairs is different from previous works and we present a novel strategy to enhance the representation ability of the graph encoder by selecting nodes based on cross-view similarities. We enrich the diversity of the positive and negative pairs by selecting highly similar samples and totally different data with the guidance of cross-view similarity scores, respectively. We also introduce a cross-view consistency constraint on the representations generated from the different views. This objective guarantees the learned representations are consistent across views from the perspective of the entire graph. We conduct extensive experiments on seven graph benchmarks, and the proposed approach achieves competitive performance compared to the current state-of-the-art methods. The source code will be publicly released once this paper is accepted.

翻译：图上的对比学习旨在提取节点可区分的高维表示。本文从理论上证明，数据集的熵可以通过最大化图不同视图间互信息的下界来近似，即通过神经网络估计熵。基于这一发现，我们提出一种简单而有效的子集采样策略，用于对比数据集视图间的成对表示。具体而言，我们从给定图中随机采样节点和边以构建视图的输入子集，并将两个视图输入参数共享的孪生网络，以提取高维嵌入并估计整个图的信息熵。在学习过程中，我们提出同时使用两个目标优化网络。具体地，对比损失函数的输入由正负样本对组成。与以往工作不同，我们提出了基于跨视图相似性选择节点的新策略，以增强图编码器的表示能力。通过跨视图相似性分数的指导，分别选择高度相似的样本和完全不同的数据，从而丰富正负样本对的多样性。此外，我们对不同视图生成的表示引入跨视图一致性约束。该目标从整个图的角度保证了所学表示在不同视图间的一致性。我们在七个图基准上进行了广泛实验，与当前最先进方法相比，所提方法取得了具有竞争力的性能。源代码将在论文接收后公开发布。