Nodes In Graph Research Articles

FlowX: Towards Explainable Graph Neural Networks via Message Flows.

We investigate the explainability of graph neural networks (GNNs) as a step toward elucidating their working mechanisms. While most current methods focus on explaining graph nodes, edges, or features, we argue that, as the inherent functional mechanism of GNNs, message flows are more natural for performing explainability. To this end, we propose a novel method here, known as FlowX, to explain GNNs by identifying important message flows. To quantify the importance of flows, we propose to follow the philosophy of Shapley values from cooperative game theory. To tackle the complexity of computing all coalitions' marginal contributions, we propose a flow sampling scheme to compute Shapley value approximations as initial assessments of further training. We then propose an information-controlled learning algorithm to train flow scores toward diverse explanation targets: necessary or sufficient explanations. Experimental studies on both synthetic and real-world datasets demonstrate that our proposed FlowX and its variants lead to improved explainability of GNNs.

Unraveling Spatial Domain Characterization in Spatially Resolved Transcriptomics with Robust Graph Contrastive Clustering.

Spatial transcriptomics can quantify gene expression and its spatial distribution in tissues, thus revealing molecular mechanisms of cellular interactions underlying tissue heterogeneity, tissue regeneration, and spatially localized disease mechanisms. However, existing spatial clustering methods often fail to exploit the full potential of spatial information, resulting in inaccurate identification of spatial domains. In this paper, we develop a deep graph contrastive clustering framework, stDGCC, that accurately uncovers underlying spatial domains via explicitly modeling spatial information and gene expression profiles from spatial transcriptomics data. The stDGCC framework proposes a spatially informed graph node embedding model to preserve the topological information of spots and to learn the informative and discriminative characterization of spatial transcriptomics data through self-supervised contrastive learning. By simultaneously optimizing the contrastive learning loss, reconstruction loss, and Kullback-Leibler (KL) divergence loss, stDGCC achieves joint optimization of feature learning and topology structure preservation in an end-to-end manner. We validate the effectiveness of stDGCC on various spatial transcriptomics datasets acquired from different platforms, each with varying spatial resolutions. Our extensive experiments demonstrate the superiority of stDGCC over various state-of-the-art clustering methods in accurately identifying cellular-level biological structures. Code and data are available from https://github.com/TimE9527/stDGCC and https://figshare.com/projects/stDGCC/186525. Supplementary data are available at Bioinformatics online.

Drug–target binding affinity prediction model based on multi-scale diffusion and interactive learning

Drug–target interactions (DTIs) play a key role in drug discovery and development as they are critical in understanding the complex mechanisms of underlying drugs and their corresponding targets. Unfortunately, some studies do not fully recognize the significant contribution of graph structure to drug feature extraction, thereby neglecting the extraction of local and global structures inherent in molecular graphs. Furthermore, most existing drug–target binding affinity (DTA) prediction models ignore or simplify complex interaction mechanisms, thus compromising the predictive power of the models. Therefore, this paper proposes a novel DTA prediction model utilizing multi-scale diffusion and interactive learning (MDCT-DTA). To address the limitations of current methods, the multi-scale graph diffusion convolution (MGDC) module is introduced, which can effectively capture the complex interactions between drug molecular graph nodes. Furthermore, a CNN-Transformer Network (CTN) block is proposed to capture the interactions and interdependencies between different amino acids, thereby enhancing the representation and learning capabilities of the model. In addition, a local inter-layer information interaction structure is designed to specifically explore the relationship between drug features and protein features, so as to improve the representativeness and robustness of the model’s structural features. The performance of the proposed model was evaluated using four publicly available benchmark datasets, Davis, KIBA, BindingDB, and Metz. The experimental results confirm that the proposed model can more accurately predict the binding affinity between a drug and its targets. They also provide a new perspective for the prediction task of DTA and contribute to the overall development and improvement of DTA prediction models.

GraphMriNet: a few-shot brain tumor MRI image classification model based on Prewitt operator and graph isomorphic network

Brain tumors are regarded as one of the most lethal forms of cancer, primarily due to their heterogeneity and low survival rates. To tackle the challenge posed by brain tumor diagnostic models, which typically require extensive data for training and are often confined to a single dataset, we propose a diagnostic model based on the Prewitt operator and a graph isomorphic network. Firstly, during the graph construction stage, edge information is extracted from MRI (magnetic resonance imaging) images using the Prewitt filtering algorithm. Pixel points with a gray value intensity greater than 128 are designated as graph nodes, while the remaining pixel points are treated as edges of the graph. Secondly, the graph data is inputted into the GIN model for training, with model parameters optimized to enhance performance. Compared with existing work using small sample sizes, the GraphMriNet model has achieved classification accuracies of 100%, 100%, 100%, and 99.68% on the BMIBTD, CE-MRI, BTC-MRI, and FSB open datasets, respectively. The diagnostic accuracy has improved by 0.8% to 5.3% compared to existing research. In a few-shot scenario, GraphMriNet can accurately diagnose various types of brain tumors, providing crucial clinical guidance to assist doctors in making correct medical decisions. Additionally, the source code is available at this link: https://github.com/keepgoingzhx/GraphMriNet.

ОПТИМИЗАЦИЯ ПОСЛЕДОВАТЕЛЬНОСТИ ВЫПОЛНЕНИЯ ЗАКАЗОВ ПРЕДПРИЯТИЯ ЭВРИСТИЧЕСКИМИ АЛГОРИТМАМИ

The production process of fulfilling orders with parameters that require equipment readjustment is considered. The problem of determining the optimal strategy for the production equipment changeover is an optimization problem, which is formulated as a travelling salesman problem. When solving such a task, the graph nodes are orders, the arcs are changeovers with a known cost when moving from one order to another. The optimization criterion is the minimum total cost of equipment changeovers. Based on the cost matrix of equipment changeovers when executing orders with the known parameters, research is carried out to solve the problem using the 2-opt local search algorithm and the genetic algorithm. Examples are given for estimating the total cost of changeovers for orders that have several parameters with different levels. The steps for implementing heuristic algorithms to solve the problem are presented, and the results of experiments are shown.

Mathematical models for determining the optimum cyber security strategy of intelligent computer networks of railway electrical supply distances

A study of the problem of the security of information resources of intelligent computer networks for power supply management in railway power generation was conducted. The logical structure of an intelligent computer network is presented, reflecting the topological characteristics of the power supply distance, in the form of a graph. A conceptual approach to the organization of an optimal cyber security strategy is proposed. On the based of Pukhov's differential transformations, differential mathematical models are proposed for determining, in analytical form, the state probabilities of graph nodes. Based on the minimax principle, methods have been developed to determine the optimal cyber security strategy, which allows to achieve the specified security indicators. A criterion for ensuring information security is formulated, which allows determining the state of cyber security of each graph node and the probability of this node being in this state.

Urban micro-scale street thermal comfort prediction using a ‘graph attention network’ model

Outdoor thermal comfort (OTC) directly affects human behavior and building operations. It is also a key factor in the achievement of smart living. When modeling OTC, existing studies tend to reduce the computational burden by conceptualizing urban spatial elements (e.g., buildings, streets) as static entities without considering the intricate dynamics of their synergistic influence. This research presents an innovative network-based framework for urban micro-scale street OTC prediction. The proposed graph attention network (GAT), in conjunction with building energy modeling (BEM), treating building clusters as graph nodes and streets as edges, capturing the interrelations between urban spatial elements, and modeling the street's universal thermal climate index (UTCI) at different time periods. The GAT model is trained and tested using simulated data from representative high-density residential areas in Hong Kong. Its performance is evaluated against an artificial neural network (ANN) model that disregards interrelations among urban spatial elements. Results demonstrate that, compared to the ANN model, the GAT model achieves an improvement in overall mean absolute error (MAE) of 37.5 %, root mean square error (RMSE) of 36.07 %, and correlation coefficient (r) of 10.58 %. Furthermore, the GAT model can better predict situations with significant amplitude changes and rapid frequency variations.

STAD-GCN: Spatial–Temporal Attention-based Dynamic Graph Convolutional Network for retail market price prediction

As technology advances, competition among market players intensifies, highlighting the importance of comprehending both one’s own and competitors’ pricing strategies. Traditional approaches often rely on static factors for price forecasting, disregarding the dynamic nature of market competition. In contrast to methods utilizing a static graph structure and uniform weights for predictions, we introduce STAD-GCN (Spatial–Temporal Attention-based Dynamic Graph Convolutional Network). This innovative model dynamically incorporates competitive factors into price prediction by employing attention mechanisms and graph convolution operations. Such an approach allows for the adaptation of graph structures and node relationships in response to temporal and spatial changes, offering a more nuanced understanding of market dynamics. To test STAD-GCN, we utilized international and domestic oil price data alongside specific gas station details from the South Korea National Oil Corporation, focusing on Seoul and Busan. The model presents remarkable performance, achieving mean absolute errors of 12.648 in Seoul and 11.242 in Busan, surpassing state-of-the-art models. Based on the findings of our research, we present some academic and practical implications, as well as several future research directions.

A modeling framework for detecting and leveraging node-level information in Bayesian network inference.

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

A binary-domain recurrent-like architecture-based dynamic graph neural network

The integration of Dynamic Graph Neural Networks (DGNNs) with Smart Manufacturing is crucial as it enables real-time, adaptive analysis of complex data, leading to enhanced predictive accuracy and operational efficiency in industrial environments. To address the problem of poor combination effect and low prediction accuracy of current dynamic graph neural networks in spatial and temporal domains, and over-smoothing caused by traditional graph neural networks, a dynamic graph prediction method based on spatiotemporal binary-domain recurrent-like architecture is proposed: Binary Domain Graph Neural Network (BDGNN). The proposed model begins by utilizing a modified Graph Convolutional Network (GCN) without an activation function to extract meaningful graph topology information, ensuring non-redundant embeddings. In the temporal domain, Recurrent Neural Network (RNN) and residual systems are employed to facilitate the transfer of dynamic graph node information between learner weights, aiming to mitigate the impact of noise within the graph sequence. In the spatial domain, the AdaBoost (Adaptive Boosting) algorithm is applied to replace the traditional approach of stacking layers in a graph neural network. This allows for the utilization of multiple independent graph learners, enabling the extraction of higher-order neighborhood information and alleviating the issue of over-smoothing. The efficacy of BDGNN is evaluated through a series of experiments, with performance metrics including Mean Average Precision (MAP) and Mean Reciprocal Rank (MRR) for link prediction tasks, as well as metrics for traffic speed regression tasks across diverse test sets. Compared with other models, the better experiments results demonstrate that BDGNN model can not only better integrate the connection between time and space information, but also extract higher-order neighbor information to alleviate the over-smoothing phenomenon of the original GCN.

Spatiotemporal Variations in Co-Occurrence Patterns of Planktonic Prokaryotic Microorganisms along the Yangtze River.

Bacteria and archaea are foundational life forms on Earth and play crucial roles in the development of our planet's biological hierarchy. Their interactions influence various aspects of life, including eukaryotic cell biology, molecular biology, and ecological dynamics. However, the coexistence network patterns of these microorganisms within natural river ecosystems, vital for nutrient cycling and environmental health, are not well understood. To address this knowledge gap, we systematically explored the non-random coexistence patterns of planktonic bacteria and archaea in the 6000-km stretch of the Yangtze River by using high-throughput sequencing technology. By analyzing the O/R ratio, representing the divergence between observed (O%) and random (R%) co-existence incidences, and the module composition, we found a preference of both bacteria and archaea for intradomain associations over interdomain associations. Seasons notably influenced the co-existence of bacteria and archaea, and archaea played a more crucial role in spring as evidenced by their predominant presence of interphyla co-existence and more species as keystone ones. The autumn network was characterized by a higher node or edge number, greater graph density, node degree, degree centralization, and nearest neighbor degree, indicating a more complex and interconnected structure. Landforms markedly affected microbial associations, with more complex networks and more core species found in plain and non-source areas. Distance-decay analysis suggested the importance of geographical distance in shaping bacteria and archaea co-existence patterns (more pronounced in spring). Natural, nutrient, and metal factors, including water temperature, NH4+-N, Fe, Al, and Ni were identified as crucial determinants shaping the co-occurrence patterns. Overall, these findings revealed the dynamics of prokaryotic taxa coexistence patterns in response to varying environmental conditions and further contributed to a broader understanding of microbial ecology in freshwater biogeochemical cycling.

Global-local graph neural networks for node-classification

The task of graph node classification is often approached by utilizing a local Graph Neural Network (GNN), that learns only local information from the node input features and their adjacency. In this paper, we propose to improve the performance of node classification GNNs by utilizing both global and local information, specifically by learning label- and node- features. We therefore call our method Global-Local-GNN (GLGNN). To learn proper label features, for each label, we maximize the similarity between its features and nodes features that belong to the label, while maximizing the distance between nodes that do not belong to the considered label. We then use the learnt label features to predict the node classification map. We demonstrate our GLGNN using three different GNN backbones, and show that our approach improves baseline performance, revealing the importance of global information utilization for node classification.

Adaptive multi-scale Graph Neural Architecture Search framework

Graph neural networks (GNNs) have gained significant attention for their ability to learn representations from graph-structured data, in which message passing and feature fusion strategies play an essential role. However, traditional Graph Neural Architecture Search (GNAS) mainly focuses on optimization with a static perceptive field to ease the search process. To efficiently utilize latent relationships between non-adjacent nodes as well as edge features, this work proposes a novel two-stage approach that is able to optimize GNN structures more effectively by adaptively aggregating neighborhood features in multiple scales. This adaptive multi-scale GNAS is able to assign optimal weights for different neighbors in different graphs and learning tasks. In addition, it takes latent relationships and edge features into message passing into account, and can incorporate different feature fusion strategies. Compared with traditional ones, our proposed approach can explore a much larger and more diversified search space efficiently. We also prove that traditional multi-hop GNNs are low-pass filters, which can lead to the removal of important low-frequency components of signals from remote neighbors in a graph, and they are not even expressive enough to distinguish some simple regular graphs, justifying the superiority of our approach. Experiments with seven datasets across three graph learning tasks, including graph regression, node classification, and graph classification, demonstrate that our method yields significant improvement compared with state-of-the-art GNAS approaches and human-designed GNN approaches. Specifically, for example, with our framework, the MAE of the 12-layer AM-GNAS was 0.102 for the ZINC dataset, yielding over 25% improvement.

Detection of autism spectrum disorder using multi‐scale enhanced graph convolutional network

AbstractMagnetic Resonance Imaging (MRI) based Autism Spectrum Disorder (ASD) detection approaches face various challenges due to variations in brain connectivity patterns, limited sample sizes, and heterogeneity of available data. These challenges make it hard to find consistent imaging markers. To address these issues, researchers have focused on advanced analysis methods, such as multi‐modal imaging techniques and graph‐based approaches to gain a comprehensive understanding of ASD neurobiology. However, existing graph‐based approaches for ASD detection have primarily focused on pairwise similarities between individuals, neglecting individual characteristics and features. A novel framework to detect ASD using a Multi‐Scale Enhanced Graph Convolutional Network (MSE‐GCN). The framework combines the functional connectivity of resting‐state functional MRI (rs‐fMRI) with non‐imaging phenotype data from Autism Brain Imaging Data Exchange‐I (ABIDE‐I). The framework uses MSE‐GCN to represent individuals as node in a population graph. Each node corresponds to an individual and connects to feature vectors from imaging data. Edge weights between nodes are assigned to integrate phenotypic information. Then, the multiple parallel GCN layers are designed using random walk embedding. The output of these GCN layers is then combined in the fully connected layer to detect ASD effectively. The performance of the framework is evaluated using the ABIDE‐I dataset. In addition, Recursive Feature Elimination and Multilayer Perceptron are utilised for feature selection. The outcome of this approach shows more than 10% advancement in accuracy, achieving an accuracy of 83% by incorporating phenotypic data in conjunction with MRI data within a GCN.

Inter-structure and intra-semantics graph contrastive learning for disease prediction

Ever-evolving healthcare applications have witnessed a surge in the utilization of electronic health records (EHR) for predicting future patient diagnoses. While Graph Neural Networks have demonstrated that promise in modeling disease-patient relationships, challenges arise from the sparsity and imbalance of patient and diagnostic data. Moreover, the existing models face difficulties in learning the unique disease combination features of patients. To address these challenges, we proposed a novel disease. prediction architecture based on Contrastive Learning (CL) from interstructural and intrasemantic perspectives, rather than traditional CL methods. We generated an initial global static disease graph to directly represent the relationships. among all diseases and a local dynamic disease graph to capture the indirect latent disease relationships among different patients. Multiple CL tasks were designed to learn sparse and imbalanced potentials. Relationships Between Diseases. Interstructure graph CL was first proposed to sample a graph enhancement, based on the distribution of nodes in the global disease graph. To further explore the deep embedding space of the disease, an intra-view graph CL was introduced by injecting noise at the semantic level for robust graph comparison. Experimental validation on two real EHR datasets demonstrates the superior performance of the approach by comparing it with state-of-the-art models.

MCG-SLAM: Tightly coupled SLAM for multi-factor constraint graph optimisation

Simultaneous localization and mapping (SLAM) technology is a core component for achieving high-precision vehicle localization and navigation in the field of autonomous driving. Existing light detection and ranging (LiDAR) SLAM methods typically neglect intersensory constraints when estimating poses based on sensor observations, resulting in reduced accuracy in multi-sensor fusion scenarios. To address this, a tightly coupled SLAM method with multi-factor constraint graph optimisation, referred to as MCG-SLAM, is proposed. The initial odometry information obtained from the extended Kalman filter is used to optimise the state nodes in the multi-factor constraint graph. This is achieved by dynamically adjusting the noise covariance of the odometry factors, global positioning system factors, and loop closure factors, optimising the factor nodes within the multi-factor constraint graph, and continuously updating the multi-factor constraint graph to complete pose optimisation. Furthermore, a loop closure detection method based on the intensity and geometric information of the point cloud is introduced to identify loop closures and incorporate loop closure factors. In this paper, the MCG-SLAM method is comprehensively validated against mainstream LiDAR SLAM methods using the MulRan dataset. The results show that MCG-SLAM outperforms other methods by improving LiDAR SLAM accuracy in localization and mapping.

Ethereum Phishing Scam Detection Based on Data Augmentation Method and Hybrid Graph Neural Network Model.

The rapid advancement of blockchain technology has fueled the prosperity of the cryptocurrency market. Unfortunately, it has also facilitated certain criminal activities, particularly the increasing issue of phishing scams on blockchain platforms such as Ethereum. Consequently, developing an efficient phishing detection system is critical for ensuring the security and reliability of cryptocurrency transactions. However, existing methods have shortcomings in dealing with sample imbalance and effective feature extraction. To address these issues, this study proposes an Ethereum phishing scam detection method based on DA-HGNN (Data Augmentation Method and Hybrid Graph Neural Network Model), validated by real Ethereum datasets to prove its effectiveness. Initially, basic node features consisting of 11 attributes were designed. This study applied a sliding window sampling method based on node transactions for data augmentation. Since phishing nodes often initiate numerous transactions, the augmented samples tended to balance. Subsequently, the Temporal Features Extraction Module employed Conv1D (One-Dimensional Convolutional neural network) and GRU-MHA (GRU-Multi-Head Attention) models to uncover intrinsic relationships between features from the time sequences and to mine adequate local features, culminating in the extraction of temporal features. The GAE (Graph Autoencoder) concept was then leveraged, with SAGEConv (Graph SAGE Convolution) as the encoder. In the SAGEConv reconstruction module, by reconstructing the relationships between transaction graph nodes, the structural features of the nodes were learned, obtaining reconstructed node embedding representations. Ultimately, phishing fraud nodes were further identified by integrating temporal features, basic features, and embedding representations. A real Ethereum dataset was collected for evaluation, and the DA-HGNN model achieved an AUC-ROC (Area Under the Receiver Operating Characteristic Curve) of 0.994, a Recall of 0.995, and an F1-score of 0.994, outperforming existing methods and baseline models.

REFUEL: rule extraction for imbalanced neural node classification

Imbalanced graph node classification is a highly relevant and challenging problem in many real-world applications. The inherent data scarcity, a central characteristic of this task, substantially limits the performance of neural classification models driven solely by data. Given the limited instances of relevant nodes and complex graph structures, current methods fail to capture the distinct characteristics of node attributes and graph patterns within the underrepresented classes. In this article, we propose REFUEL—a novel approach for highly imbalanced node classification problems in graphs. Whereas symbolic and neural methods have complementary strengths and weaknesses when applied to such problems, REFUEL combines the power of symbolic and neural learning in a novel neural rule-extraction architecture. REFUEL captures the class semantics in the automatically extracted rule vectors. Then, REFUEL augments the graph nodes with the extracted rules vectors and adopts a Graph Attention Network-based neural node embedding, enhancing the downstream neural node representation. Our evaluation confirms the effectiveness of the proposed REFUEL approach for three real-world datasets with different minority class sizes. REFUEL achieves at least a 4% point improvement in precision on the minority classes of 1.5–2% compared to the baselines.

On the effectiveness of hybrid pooling in mixup-based graph learning for language processing

Graph neural network (GNN)-based graph learning has been popular in natural language and programming language processing, particularly in text and source code classification. Typically, GNNs are constructed by incorporating alternating layers which learn transformations of graph node features, along with graph pooling layers that use graph pooling operators (e.g., Max-pooling) to effectively reduce the number of nodes while preserving the semantic information of the graph. Recently, to enhance GNNs in graph learning tasks, Manifold-Mixup, a data augmentation technique that produces synthetic graph data by linearly mixing a pair of graph data and their labels, has been widely adopted. However, the performance of Manifold-Mixup can be highly affected by graph pooling operators, and there have not been many studies that are dedicated to uncovering such affection. To bridge this gap, we take an early step to explore how graph pooling operators affect the performance of Mixup-based graph learning. To that end, we conduct a comprehensive empirical study by applying Manifold-Mixup to a formal characterization of graph pooling based on 11 graph pooling operations (9 hybrid pooling operators, 2 non-hybrid pooling operators). The experimental results on both natural language datasets (Gossipcop, Politifact) and programming language datasets (JAVA250, Python800) demonstrate that hybrid pooling operators are more effective for Manifold-Mixup than the standard Max-pooling and the state-of-the-art graph multiset transformer (GMT) pooling, in terms of producing more accurate and robust GNN models.Editor’s note: Open Science material was validated by the Journal of Systems and Software Open Science Board.

LMFLS: A new fast local multi-factor node scoring and label selection-based algorithm for community detection

Community detection is still regarded as one of the most applicable approaches for discovering latent information in complex networks. To meet the needs of processing large networks in today's world, it is important to propose fast methods that have low execution time and fast convergence speed, while maintaining algorithmic accuracy. To overcome these issues, a fast local multi-factor node scoring and label selection-based (LMFLS) method with low time complexity and fast convergence is proposed. Node scoring step incorporates diverse metrics to better assess impact of nodes from different aspects and obtain more meaningful order of nodes. In second step, to construct and stabilize initial structure of communities, an efficient label assignment technique based on the selection of the most similar neighbor is suggested. Moreover, two label selection strategies are proposed to significantly enhance the accuracy and improve convergence of the algorithm. During the label selection step, each node in graph tends to choose the most appropriate label based on a multi-criteria label influence from its surrounding nodes. Finally, by utilizing a novel merge method, small group of nodes are merged to form the final communities. Meanwhile, since drug repositioning is one of the popular research fields in therapeutics, to extend the application of the proposed algorithm in practical context, the LMFLS algorithm is applied on Drug-Drug network to find potential repositioning for drugs. Thorough experiments are conducted on both actual real-world networks and synthetic networks to assess the algorithm's performance and accuracy. The findings demonstrate that the proposed method outperforms state-of-the-art algorithms in terms of both accuracy and execution time.