Graph Neural Networks (GNNs) have achieved remarkable success in machine learning tasks by learning the features of graph data. However, experiments show that vanilla GNNs fail to achieve good classification performance in the field of graph anomaly detection. To address this issue, we propose and theoretically prove that the high-Class Homophily Variance (CHV) characteristic is the reason behind the suboptimal performance of GNN models in anomaly detection tasks. Statistical analysis shows that in most standard node classification datasets, homophily levels are similar across all classes, so CHV is low. In contrast, graph anomaly detection datasets have high CHV, as benign nodes are highly homophilic while anomalies are not, leading to a clear separation. To mitigate its impact, we propose a novel GNN model named Homophily Edge Augment Graph Neural Network (HEAug). Different from previous work, our method emphasizes generating new edges with low CHV value, using the original edges as an auxiliary. HEAug samples homophily adjacency matrices from scratch using a self-attention mechanism, and leverages nodes that are relevant in the feature space but not directly connected in the original graph. Additionally, we modify the loss function to punish the generation of unnecessary heterophilic edges by the model. Extensive comparison experiments demonstrate that HEAug achieved the best performance across eight benchmark datasets, including anomaly detection, edgeless node classification and adversarial attack. We also defined a heterophily attack to increase the CHV value in other graphs, demonstrating the effectiveness of our theory and model in various scenarios.

Money laundering is the process of hiding the origin of illicit funds to make them appear legitimate, thereby threatening the integrity of financial systems. To detect money laundering activities, graph neural networks (GNNs) have been widely adopted to model complex relational structures in transaction networks. However, a closer inspection of real-world money laundering cases reveals that launderers deliberately establish connections with multiple licit accounts to mask their illicit attributes. Such disguising behavior introduces network heterogeneity, which contradicts the fundamental assumption of homophily for most GNNs. Additionally, money launderers further conceal their activities by obscuring illicit fund flows through multihop transaction paths. This strategy poses a significant challenge for GNNs, as their limited receptive fields struggle to capture such long-range dependencies. To address these challenges, we propose a dual-view graph representation learning method, named DC-LCG, to detect money laundering. DC-LCG employs complementary local and contextual views to expose disguises and trace illicit flows, respectively. The local view implements a soft-label-guided dynamic grouping and aggregation method that separates nodes into illicit and licit groups, performing probability-weighted aggregations to mitigate network heterogeneity and expose disguises within transaction networks. The contextual view employs a dynamic path pruning method to filter licit nodes and enhance paths relevance, followed by multipath semantic fusion through transformer-based encoding to capture long-range dependencies across multihop transaction paths. A mutual attention mechanism integrates both views to create comprehensive node representations. Experiments on three public transaction datasets show that DC-LCG outperforms state-of-the-art baselines by 2%–10% across evaluation metrics.

Graph neural networks (GNNs) have demonstrated outstanding performance in graph classification tasks. Most existing GNNs designed for graph classification adopt a structure that combines graph convolutional operators with graph pooling operators. However, these methods are often prone to being misled by spurious connections between nodes, which can arise due to noise or inherent data bias. Furthermore, these methods struggle to simultaneously capture the relationships between global and local information, leading to either overly smooth or overly sensitive classifications. To solve the above issues, we introduce a GNN with interaction-aware view fusion (IAVF) for graph classification, which effectively accounts for interactions between nodes to better handle both global and local information while mitigating the impact of misleading connections. Specifically, IAVF first generates multiple views using distinct strategies, ensuring that they can mutually correct each other during the subsequent fusion process. Then, we propose a global-local view interaction module, which captures the relational information between views at both global and local scales to achieve global-local interaction-aware ability. To ensure effective view fusion after interaction, we introduce a dual-supervision mechanism as a constraint to align features across views while preventing excessive alignment that may lead to an overly smooth model. On established and competitive benchmarks, even with only a single type of graph convolution, IAVF generally outperforms the strongest baselines. For example, it achieves 78.53% accuracy on NCI109, corresponding to a relative improvement of 1.03%, and 81.88% on Mutagenicity, corresponding to a relative improvement of 0.69%. These results demonstrate that explicit cross-view interaction enhances graph representations.

Polynomial-based learnable spectral graph neural networks (GNNs) utilize polynomial to approximate graph convolutions and have achieved impressive performance on graphs. Nevertheless, there are three progressive problems to be solved. Some models use polynomials with better approximation for approximating filters, yet perform worse on real-world graphs. Carefully crafted graph learning methods, sophisticated polynomial approximations, and refined coefficient constraints leaded to overfitting, which diminishes the generalization of the models. How to design a model that retains the ability of polynomial-based spectral GNNs to approximate filters while it possesses higher generalization and performance? In this paper, we propose a spectral GNN with triple filter ensemble (TFE-GNN), which extracts homophily and heterophily from graphs with different levels of homophily adaptively while utilizing the initial features. Specifically, the first and second ensembles are combinations of a set of base low-pass and high-pass filters, respectively, after which the third ensemble combines them with two learnable coefficients and yield a graph convolution (TFE-Conv). Theoretical analysis shows that the approximation ability of TFE-GNN is consistent with that of ChebNet under certain conditions, namely it can learn arbitrary filters. TFE-GNN can be viewed as a reasonable combination of two unfolded and integrated excellent spectral GNNs, which motivates it to perform well. Experiments show that TFE-GNN achieves high generalization and new state-of-the-art performance on various real-world datasets.

Graph convolutional networks (GCNs) can quickly and accurately learn graph representations and have shown powerful performance in many graph learning domains. Despite their effectiveness, neighborhood awareness remains essential and challenging for GCNs. Existing methods usually perform neighborhood-aware steps only from the node or hop level, which leads to a lack of capability to learn the neighborhood information of nodes from both global and local perspectives. Moreover, most methods learn the nodes' neighborhood information from a single view, ignoring the importance of multiple views. To address the above issues, we propose a multi-view adaptive neighborhood-aware approach to learn graph representations efficiently. Specifically, we propose three random feature masking variants to perturb some neighbors' information to promote the robustness of graph convolution operators at node-level neighborhood awareness and exploit the attention mechanism to select important neighbors from the hop level adaptively. We also utilize the multi-channel technique and introduce a proposed multi-view loss to perceive neighborhood information from multiple perspectives. Extensive experiments show that our method can better obtain graph representation and has high accuracy.

Many studies have achieved excellent performance in analyzing graph-structured data. However, learning graph-level representations for graph classification is still a challenging task. Existing graph classification methods usually pay less attention to the fusion of node features and ignore the effects of different-hop neighborhoods on nodes in the graph convolution process. Moreover, they discard some nodes directly during the graph pooling process, resulting in the loss of graph information. To tackle these issues, we propose a new Graph Multi-Convolution and Attention Pooling based graph classification method (GMCAP). Specifically, the designed Graph Multi-Convolution (GMConv) layer explicitly fuses node features learned from different perspectives. The proposed weight-based aggregation module combines the outputs of all GMConv layers, for adaptively exploiting the information over different-hop neighborhoods to generate informative node representations. Furthermore, the designed Local information and Global Attention based Pooling (LGAPool) utilizes the local information of a graph to select several important nodes and aggregates the information of unselected nodes to the selected ones by a global attention mechanism when reconstructing a pooled graph, thus effectively reducing the loss of graph information. Extensive experiments show that GMCAP outperforms the state-of-the-art methods on graph classification tasks, demonstrating that GMCAP can learn graph-level representations effectively.

Unbounded Petri nets (UPNs) can describe and analyze discrete event systems with infinite states (DESIS). Due to the infinite state space and the combination explosion problem, the reachability analysis of UPNs is an NP-Hard problem. The existing reachability analysis methods cannot achieve an accurate result at reasonable costs (computational time and space) due to the finite reachability tree with$\omega$-numbers. Based on the idea of approximating infinite space with finite states, given some limited reachable markings of a UPN, we propose a method that can quantitatively solve the UPN’s reachability problem with machine learning. Firstly, we define the probabilistic reachability of markings and transform the UPN’s reachability problem into the prediction problem of markings. The proposed method based on positive and unlabeled learning (PUL) and bagging trains a classifier to predict the probabilistic reachability of unknown markings. Finally, to predict the markings outside the positive sample set and unlabeled sample set, an iterative strategy is designed to update the classifier. Based on seven general UPNs, the results of the experiments show that the proposed method has a good performance in the accuracy and time consumption for the UPN’s reachability problem.Note to Practitioners—In discrete event systems, the reachability problem mainly studies reachable states of the system and the relationship between states, which is the basis of the system’s states, behaviors, attributes and performance analysis. For discrete event systems with infinite states, it is hard to analyze the reachable relationship between states within a finite time due to the infinite state space and the combination explosion problem. The main motivation of the paper is to propose a method that can predict the reachable relationship between the states with a probability value within a finite time. By machine learning algorithms, the method learns the feature information of the known reachable states. The reachability of unknown states in the infinite state space can be predicted approximately. The proposed approximation method can be applied to analyze the reachability properties of general discrete event systems with infinite states, such as checking whether a fault occurs in operating systems, whether a message is delivered in communication and so on.

Graph convolutional networks (GCNs) have shown superior performance on graph classification tasks, and their structure can be considered as an encoder-decoder pair. However, most existing methods lack the comprehensive consideration of global and local in decoding, resulting in the loss of global information or ignoring some local information of large graphs. And the commonly used cross-entropy loss is essentially an encoder-decoder global loss, which cannot supervise the training states of the two local components (encoder and decoder). We propose a multichannel convolutional decoding network (MCCD) to solve the above-mentioned problems. MCCD first adopts a multichannel GCN encoder, which has better generalization than a single-channel GCN encoder since different channels can extract graph information from different perspectives. Then, we propose a novel decoder with a global-to-local learning pattern to decode graph information, and this decoder can better extract global and local information. We also introduce a balanced regularization loss to supervise the training states of the encoder and decoder so that they are sufficiently trained. Experiments on standard datasets demonstrate the effectiveness of our MCCD in terms of accuracy, runtime, and computational complexity.

Graph neural networks (GNNs) have achieved effective performance in many graph-related tasks involving recommendation systems, social networks, and bioinformatics. Recent studies have proposed several graph pooling operators to obtain graph-level representations from node representations. Nevertheless, they usually adopt a single strategy to evaluate the importance of nodes, which may generate node rankings with weak robustness. Also, they cannot capture the different substructures of a graph since they shrink the graph layer by layer. To solve the above problems, this article proposes a Multistructure graph classification method with Attention mechanism and Convolutional neural network (CNN), called MAC. In particular, we propose a novel pooling operator, which adopts multiple strategies to evaluate the importance of nodes and updates node representations through an attention mechanism. Also, we design a hierarchical architecture for MAC to capture multiple different substructures of a graph. To further reduce the loss of graph information, we utilize 2-D CNN to generate a graph-level representation. Comparative experiments are performed on public benchmark datasets deriving from social systems, and the experimental results indicate that our method outperforms a range of state-of-the-art graph classification methods.

Graph neural networks, which generalize deep learning to graph-structured data, have achieved significant improvements in numerous graph-related tasks. Petri nets (PNs), on the other hand, are mainly used for the modeling and analysis of various event-driven systems from the perspective of prior knowledge, mechanisms, and tasks. Compared with graph data, net data can simulate the dynamic behavioral features of systems and are more suitable for representing real-world problems. However, the problem of large-scale data analysis has been puzzling the PN field for decades, and thus, limited its universal applicability. In this article, a framework of net learning (NL) is proposed. NL contains the advantages of PN modeling and analysis with the advantages of graph learning computation. Then, two kinds of NL algorithms are designed for performance analysis of stochastic PNs, and more specifically, the hidden feature information of the PN is obtained by mapping net information to the low-dimensional feature space. Experiments demonstrate the effectiveness of the proposed model and algorithms on the performance analysis of stochastic PNs.

The existing Stochastic Petri Net (SPN) analysis methods are based on a series of steps, including generating the reachable graph, solving the state equation, etc. Unfortunately, these methods cannot perform performance analysis when the state equation has no unique solution. The end-to-end deep learning methods can build a mapping relationship from SPN to performance indicators, which avoids solving the state equation. However, there is a lack of benchmark datasets for SPN learning and training. This paper proposes an automatic generation method of SPN datasets, including SPN random generation, data labeling, data enhancement, and filtering. To relieve the local aggregation problem of random-based organization, a grid-based data organization method is proposed to ensure the diversity of the datasets. In the experimental section, the generated datasets are trained and tested on three types of neural networks. The results show that the generated benchmark datasets are useful, and the increase of dataset size will significantly improve the learning performance.