Graph representation learning often faces knowledge scarcity in real-world applications, including limited labels and sparse relationships. Although a range of methods have been proposed to address these problems, such as graph few-shot learning, they mainly rely on inadequate knowledge within the task graph, which would limit their effectiveness. Moreover, they fail to consider other potentially useful task-related graphs. To overcome these limitations, domain adaptation for graph representation learning has emerged as an effective paradigm for transferring knowledge across graphs. It is also recognized as graph domain adaptation (GDA). In particular, to enhance model performance on target graphs with specific tasks, GDA introduces a bunch of task-related graphs as source graphs and adapts the knowledge learnt from source graphs to the target graphs. Since GDA combines the advantages of graph representation learning and domain adaptation, it has become a promising direction of transfer learning on graphs and has attracted an increasing amount of research interest in recent years. In this paper, we comprehensively overview the studies of GDA and present a detailed survey of recent advances. Specifically, we outline the current research status, analyze key challenges, propose a taxonomy, introduce representative work and practical applications, and discuss future prospects. To the best of our knowledge, this paper is the first survey for graph domain adaptation.

Network embedding, as an approach to learning low-dimensional representations of nodes, has been proved extremely useful in many applications, e.g., node classification and link prediction. Unfortunately, existing network embedding models are vulnerable to random or adversarial perturbations, which may degrade the performance of network embedding when being applied to downstream tasks. To achieve robust network embedding, researchers introduce adversarial training to regularize the embedding learning process by training on a mixture of adversarial examples and original examples. However, existing methods generate adversarial examples heuristically, failing to guarantee the imperceptibility of generated adversarial examples, and thus limit the power of adversarial training. In this paper, we propose a novel method Identity-Preserving Adversarial Training (IPAT) for network embedding, which generates imperceptible adversarial examples with explicit identity-preserving regularization. We formalize such identity-preserving regularization as a multi-class classification problem where each node represents a class, and we encourage each adversarial example to be discriminated as the class of its original node. Extensive experimental results on real-world datasets demonstrate that our proposed IPAT method significantly improves the robustness of network embedding models and the generalization of the learned node representations on various downstream tasks.

Knowledge graph embedding, which maps the entities and relations into low-dimensional vector spaces, has demonstrated its effectiveness in many tasks such as link prediction and relation extraction. Typical methods include TransE, TransH, and TransR. All these methods map different relations into the vector space separately and the intrinsic correlations of these relations are ignored. It is obvious that there exist some correlations among relations because different relations may connect to a common entity. For example, the triples (Steve Jobs, PlaceOfBrith, California) and (Apple Inc., Location, California) share the same entity California as their tail entity. We analyze the embedded relation matrices learned by TransE/TransH/TransR, and find that the correlations of relations do exist and they are showed as low-rank structure over the embedded relation matrix. It is natural to ask whether we can leverage these correlations to learn better embeddings for the entities and relations in a knowledge graph. In this paper, we propose to learn the embedded relation matrix by decomposing it as a product of two low-dimensional matrices, for characterizing the low-rank structure. The proposed method, called TransCoRe (Translation-Based Method via Modeling the Correlations of Relations), learns the embeddings of entities and relations with translation-based framework. Experimental results based on the benchmark datasets of WordNet and Freebase demonstrate that our method outperforms the typical baselines on link prediction and triple classification tasks.