Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a wide spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and information systems. With the continuous penetration of artificial intelligence technologies, graph learning (i.e., machine learning on graphs) has been gaining rapidly increasing attention from both researchers and practitioners. Graph learning has proved to be effective for many tasks, such as classification, link prediction, matching, and anomaly detection. Generally, graph learning methods extract relevant features of graphs by taking advantage of machine learning algorithms. In this survey, we present a comprehensive overview on the state of the art of graph learning. Special attention is paid to four categories of existing graph learning methods, including graph signal processing, matrix factorization, random walk, and deep learning. Major models and algorithms under these categories are reviewed respectively. Graph learning applications are examined. In addition, we discuss several promising research directions in this field.

Network representation learning (NRL) is an effective graph analytics technique and promotes users to deeply understand the hidden characteristics of graph data. It has been successfully applied in many real-world tasks related to network science, such as social network data processing, biological information processing, and recommender systems. Deep Learning is a powerful tool to learn data features. However, it is non-trivial to generalize deep learning to graph-structured data since it is different from the regular data such as pictures having spatial information and sounds having temporal information. Recently, researchers proposed many deep learning-based methods in the area of NRL. In this survey, we investigate classical NRL from traditional feature learning method to the deep learning-based model, analyze relationships between them, and summarize the latest progress. Finally, we discuss open issues considering NRL and point out the future directions in this field.

Graph neural networks (GNNs) have demonstrated a remarkable ability in the task of semi-supervised node classification. However, most existing GNNs suffer from the nonrobustness issues, which poses a great challenge for applying GNNs into sensitive scenarios. Some researchers concentrate on constructing an ensemble model to mitigate the nonrobustness issues. Nevertheless, these methods ignore the interaction among base models, leading to similar graph representations. Moreover, due to the deterministic propagation applied in most existing GNNs, each node highly relies on its neighbors, leaving the nodes to be sensitive to perturbations. Therefore, in this paper, we propose a novel framework of graph ensemble learning based on knowledge passing (called GEL) to address the above issues. In order to achieve interaction, we consider the predictions of prior models as knowledge to obtain more reliable predictions. Moreover, we design a multilayer DropNode propagation strategy to reduce each node’s dependence on particular neighbors. This strategy also empowers each node to aggregate information from diverse neighbors, alleviating oversmoothing issues. We conduct experiments on three benchmark datasets, including Cora, Citeseer, and Pubmed. GEL outperforms GCN by more than 5% in terms of accuracy across all three datasets and also performs better than other state-of-the-art baselines. Extensive experimental results also show that the GEL alleviates the nonrobustness and oversmoothing issues.

Brain networks are built according to the structures or neural activities of different brain regions, which can be modeled as complex networks. Many studies exploit brains from the perspective of graph learning to diagnose the nerve diseases of brains. However, many of these algorithms are unable to automatically construct brain function topology based on electroencephalogram (EEG) and fail to capture the global features of multi-channel EEG signals for whole-graph embedding. To address these challenging issues, we propose an attention-based whole-graph learning model for the diagnosis of brain diseases, namely MAINS, which can adaptively construct brain functional topology from EEG signals and effectively embed multiple node features and the global structural features of brain networks into the whole-graph representations. We validated the model by conducting classification (diagnosis) experiments on real EEG datasets. Comprehensive experimental results demonstrate the superiority of the proposed approach over state-of-the-art methods.

Graph-learning methods, especially graph neural networks (GNNs), have shown remarkable effectiveness in handling non-Euclidean data and have achieved great success in various scenarios. Existing GNNs are primarily based on message-passing schemes, that is, aggregating information from neighboring nodes. However, the diversity and complexity of complex systems from real-world circumstances are not sufficiently taken into account. In these cases, the individual should be treated as an agent, with the ability to perceive their surroundings and interact with other individuals, rather than just be viewed as nodes in existing graph approaches. Additionally, the pairwise interactions used in existing methods also lack the expressiveness for the higher-order complex relations among multiple agents, thus limiting the performance in various tasks. In this work, we propose a Multiagent Hypergraph Force-learning method dubbed MHGForce. First, we formalize the multiagent system (MAS) and illustrate its connection to graph learning. Then, we propose a generalized multiagent hypergraph-learning framework. In this framework, we integrate message-passing and force-based interactions to devise a pluggable method. The method empowers graph approaches to excel in downstream tasks while effectively maintaining structural information in the representations. Experimental results on the Cora, Citeseer, Cora-CA, Zoo, and NTU2012 datasets in node classification demonstrate the effectiveness and generality of our proposed method. We also discuss the characteristics of the MHGForce and explore its role through parametric analysis and visualization. Finally, we give a discussion, conclude our work, and propose future directions.

Relations in knowledge graphs have rich relational structures and various binary relational patterns. Various relation modelling strategies are proposed for embedding knowledge graphs, but they fail to fully capture both features of relations, rich relational structures and various binary relational patterns. To address the problem of insufficient embedding due to the complexity of the relations, we propose a novel knowledge graph representation model in complex space, namely MARS, to exploit complex relations to embed knowledge graphs. MARS takes the mechanisms of complex numbers and message-passing and then embeds triplets into relation-specific complex hyperplanes. Thus, MARS can well preserve various relation patterns, as well as structural information in knowledge graphs. In addition, we find that the scores generated from the score function approximate a Gaussian distribution. The scores in the tail cannot effectively represent triplets. To address this particular issue and improve the precision of embeddings, we use the standard deviation to limit the dispersion of the score distribution, resulting in more accurate embeddings of triplets. Comprehensive experiments on multiple benchmarks demonstrate that our model significantly outperforms existing state-of-the-art models for link prediction and triple classification.