Node representation learning in a network is an important machine learning technique for encoding relational information in a continuous vector space while preserving the inherent properties and structures of the network. Recently, \textit{unsupervised} node embedding methods such as DeepWalk \citep{deepwalk}, LINE \citep{line}, struc2vec \citep{struc2vec}, PTE \citep{pte}, UserItem2vec \citep{wu2020multi}, and RWJBG \citep{li2021random} have emerged from the Skip-gram model \citep{word2vec} and perform better performance in several downstream tasks such as node classification and link prediction than the existing relational models. However, providing post-hoc explanations of Skip-gram-based embeddings remains a challenging problem because of the lack of explanation methods and theoretical studies applicable for embeddings. In this paper, we first show that global explanations to the Skip-gram-based embeddings can be found by computing \textit{bridgeness} under a spectral cluster-aware local perturbation. Moreover, a novel gradient-based explanation method, which we call GRAPH-wGD, is proposed that allows the top-$q$ global explanations about learned graph embedding vectors more efficiently. Experiments show that the ranking of nodes by scores using GRAPH-wGD is highly correlated with true \textit{bridgeness} scores. We also observe that the top-$q$ node-level explanations selected by GRAPH-wGD have higher importance scores and produce more changes in class label prediction when perturbed, compared with the nodes selected by recent alternatives, using five real-world graphs.

翻译：网络中的节点表示学习是一项重要的机器学习技术，旨在将关系信息编码到连续向量空间中，同时保留网络的内在属性和结构。近年来，受Skip-gram模型启发的无监督节点嵌入方法（如DeepWalk、LINE、struc2vec、PTE、UserItem2vec和RWJBG）在节点分类和链路预测等多个下游任务中表现出优于现有关系模型的性能。然而，由于缺乏适用于嵌入的事后解释方法和理论研究，为基于Skip-gram的嵌入提供事后解释仍然是一个具有挑战性的问题。本文首先证明，通过计算谱聚类感知的局部扰动下的桥接性，可以找到基于Skip-gram嵌入的全局解释。此外，我们提出了一种新的基于梯度的解释方法——GRAPH-wGD，该方法能够更高效地获取学习到的图嵌入向量的top-q全局解释。实验表明，使用GRAPH-wGD得到的节点评分排序与真实的桥接性评分高度相关。我们还观察到，在五个真实世界图的实验中，与近期替代方法选择的节点相比，GRAPH-wGD选择的top-q节点级解释具有更高的重要性评分，并且在受到扰动时会导致类别标签预测产生更大变化。