Multi-view classification aims at unifying the data from multiple views to complementarily enhance the classification performance. Unfortunately, two major problems in multi-view data are damaging model performance. The first is feature heterogeneity, which makes it hard to fuse features from different views. Considering this, we introduce a multi-scale alignment module, including an instance-scale alignment module and a prototype-scale alignment module to mine the commonality from an inter-view perspective and an inter-class perspective respectively, jointly alleviating feature heterogeneity. The second is information redundancy which easily incurs ambiguous data to blur class boundaries and impair model generalization. Therefore, we propose a novel expanded boundary by extending the original class boundary with fuzzy set theory, which adaptively adjusts the boundary to fit ambiguous data. By integrating the expanded boundary into the prototype-scale alignment module, our model further tightens the produced representations and reduces boundary ambiguity. Additionally, compared with the original class boundary, the expanded boundary preserves more margins for classifying unseen data, which guarantees the model generalization. Extensive experiment results across various real-world datasets demonstrate the superiority of the proposed model against existing state-of-the-art methods.

Graph contrastive learning (GCL) aims at narrowing positives while dispersing negatives, often causing a minority of samples with great similarities to gather as a small group. It results in two latent shortcomings in GCL: 1) local cohesion that a class cluster contains numerous independent small groups, and 2) global sparseness that these small groups (or isolated samples) dispersedly distribute among all clusters. These shortcomings make the learned distribution only focus on local similarities among partial samples, which hinders the ability to capture the ideal global structural properties among real clusters, especially high intra-cluster compactness and inter-cluster separateness. Considering this, we design a novel fuzzy boundary by extending the original cluster boundary with fuzzy set theory, which involves fuzzy boundary construction and fuzzy boundary contraction to address these shortcomings. The fuzzy boundary construction dilates the original boundaries to bridge the local groups, and the fuzzy boundary contraction forces the dispersed samples or groups within the fuzzy boundary to gather tightly, jointly mitigating local cohesion and global sparseness while forming the ideal global structural distribution. Extensive experiments demonstrate that a graph auto-encoder with the fuzzy boundary significantly outperforms current state-of-the-art GCL models in both downstream tasks and quantitative analysis.

Graph contrastive learning (GCL) aims to learn self-supervised representations by distinguishing positive and negative sample pairs generated from multiple augmented graph views. Despite showing promising performance, GCL still suffers from two critical biases: (1) ***Similarity estimation bias*** arises when feature elements that support positive pair alignment are suppressed by conflicting components within the representation, causing truly positive pairs to appear less similar. (2) ***Semantic shift bias*** occurs when random augmentations alter the underlying semantics of samples, leading to incorrect positive or negative assignments and injecting noise into training. To address these issues, we propose CaliGCL, a GCL model for calibrating the biases by integrating an exponential partitioned similarity measure and a semantics-consistency discriminator. The exponential partitioned similarity computes the similarities among fine-grained partitions obtained through splitting representation vectors and uses exponential scaling to emphasize aligned (positive) partitions while reducing the influence of misaligned (negative) ones. The discriminator dynamically identifies whether augmented sample pairs maintain semantic consistency, enabling correction of misleading contrastive supervision signals. These components jointly reduce biases in similarity estimation and sample pairing, guiding the encoder to learn more robust and semantically meaningful representations. Extensive experiments on multiple benchmarks show that CaliGCL effectively mitigates both types of biases and achieves state-of-the-art performance.

Numerous significant temporal graph tasks, such as graph similarity ranking, trend analysis and anomaly detection, necessitate low-dimensional and high-order graph-level embedding in terms of the evolving nodes and topologies over time. However, most existing graph embedding methods focus on extracting node-level embeddings, while ignoring these evolutions. Therefore, these methods inadequately consider the impact of trends on the overall graph. Moreover, there are a large number of nodes in temporal graphs, which make it difficult to generate effective graph embeddings directly by aggregating dynamic node embeddings. In this study, we propose a novel temporal attention network for learning graph-level embedding learning called GraphTAN. Specifically, the proposed model employs pooling attention to select crucial nodes and filter out noisy ones for each snapshot, thereby enhancing the quality of aggregated graph embeddings. Furthermore, we design a graph-level temporal attention mechanism to effectively extract temporal graph embeddings, capturing trends and patterns across snapshots. The proposed model is evaluated on three downstream tasks. Experimental results demonstrate that GraphTAN captures both the topology structure and fine-grained trend effectively, outperforming the state-of-the-art methods with big margins on multiple tasks over several real networks.

Self-supervised graph representation learning (GRL) has shown great success in scientific research and real-world applications. Nevertheless, one obstacle in GRL is the demand for graph augmentation (GA), which deeply impacts the representation qualities. On the one hand, GA supplements the data amount and enhances the robustness and quality of the representations. On the other hand, collocating appropriate augmentations claims nontrivial attempts. In this article, a new method to free GA is provided building a novel fuzzy view and two crisp views of the original graph. As all the views are transformed from the original graph, they are semantically similar and naturally considered to possess high-quality positive samples. In this way, the data amount is compensated to a degree without changing the raw node attributes or graph topology. Additionally, to ensure the diversity of the positives, asymmetric renormalization and noise perturbation are adopted. Experiments toward node-level tasks on several real-world datasets demonstrate the competition against several state-of-the-art models.

Information aggregation and propagation over networks via graph neural networks (GNNs) plays an important role in node or graph representation learning, which currently depend on the calculation with a fixed adjacency matrix, facing over-smoothing problem, and difficulty to stack multiple layers for high-level representations. In contrast, Transformer calculates an importance score for each node to learn its embedding via the attention mechanism and has achieved great successes in many natural language processing (NLP) and computer vision (CV) tasks. However, Transformer is inflexible to extend to graphs, as its input and output must have the same dimension. It will also become intractable to allocate attention over a large-scale graph due to distractions. Moreover, most graph Transformers are trained in supervised ways, which consume additional resources to annotate samples with potentially wrong labels and have limited generalization of representations. Therefore, this article attempts to build a new Sparse Graph Transformer with Contrastive learning for graph representation learning, called SGTC. Specifically, we first employ centrality measures to remove the redundant topological information from input graph according to the influences of nodes and edges, then disturb the pruned graph to get two different augmentation views, and learn node representations in a contrastive manner. Besides, a novel sparse attention mechanism is also proposed to capture structural features of graphs, which effectively save memory and training time. SGTC can produce low-dimensional and high-order node representations, which have better generalization for multiple tasks. The proposed model is evaluated on three downstream tasks over six networks, and experimental results confirm its superior performance against the state-of-the-art baselines.

Graph representation learning focuses on abstracting critical information from raw graphs. Unfortunately, there always exist various kinds of uncertainties, such as attribute noise and network topology corruption, in raw graphs. Under the message passing mechanism, certainties are likely to spread throughout the whole graph. Matters like these would induce deep graph models into producing uncertain representations and restrict representation expressiveness. Considering this, we propose a pioneering framework to defend graph uncertainties by improving the robustness and capability of graph neural networks (GNNs). In our framework, we consider that weights and biases are all fuzzy numbers, thus generating representations to assimilate graph uncertainties, which are finally released by defuzzification. To describe the process of the framework, in this article, a graph convolutional network (GCN) is employed to construct a robust graph model, called FuzzyGCN. To verify the effectiveness of FuzzyGCN, it is trained in both supervised and unsupervised ways. In the supervised setting, we find that FuzzyGCN has stronger power and is more immune to data uncertainties when compared with various classical and robust GNNs. In the unsupervised setting, FuzzyGCN surpasses many state-of-the-art models in node classification and community detection over several real-world datasets.

Recent years have witnessed a drastic surge in graph representation learning, which usually produces low-dimensional and crisp representations from graph topology and high-dimensional node attributes. Nevertheless, a crisp representation of a node or graph actually conceals the uncertainty and interpretability of features. In citation networks, for example, the reference between the two papers is always involved with fuzziness denoting the correlation degrees, that is, one connection may simultaneously belong to strong and weak references in different beliefs. The uncertainty in node connections and attributes inspires us to delve into fuzzy representations. This article, for the first time, proposes an unsupervised fuzzy representation learning model for graphs and networks to improve their expressiveness by making crisp representations fuzzy. Specifically, we develop a fuzzy graph convolution neural network (FGCNN), which could aggregate high-level fuzzy features, leveraging fuzzy logic to fully excavate feature-level uncertainties, and finally generate fuzzy representations. The corresponding hierarchical model composed of multiple FGCNNs, called deep fuzzy graph convolution neural network (DFGCNN), is able to generate fuzzy node representations which are more expressive than crisp ones. Experimental results of multiple network analysis tasks validate that the proposed fuzzy representation models have strong competitiveness against the state-of-the-art baselines over several real-world datasets.