Adaptive Graph Convolutional Network Research Articles

Adaptive Graph Convolutional Network for the Document Prediction employing Dollmaker Optimization Algorithm

Document prediction is the application of advanced deep learning models in the analysis and prediction of the content of documents. Thus, it effectively improves text generation, information retrieval, and automatic summarization by changing the ways relating to textual data completely. This field is particularly challenging because maintaining high prediction accuracy requires efficient computing and scaling. Hence, this paper performs the document prediction using advanced deep learning-oriented optimization methodology. The data is first collected from online sources that consist of a group of documents together with their corresponding categories. The pre-processing of this collected data is next accomplished using the stop word removal, invalid character removal, and sentence segmentation approaches. The features are then extracted from these pre-processed data employing the Difference of Gaussian (DoG) method. The final prediction stage is done by the novel Adaptive Graph Convolutional Network (AGCN), in which the parameters are tuned by the well performing optimization algorithm known as Dollmaker Optimization Algorithm (DOA) with the consideration of error minimization as the fitness function. The findings demonstrated the superiority of the proposed model when it is compared with distinct conventional models.The proposed AGCN-DOA for the document prediction model in terms of prediction accuracy, MSE, MAE, MAPE, and RMSE is 11.18%, 94.73%, 31.71%, 47.73%, and 77.03% better than the considered existing methods respectively..

Keypoints-Based Multi-Cue Feature Fusion Network (MF-Net) for Action Recognition of ADHD Children in TOVA Assessment.

Attention deficit hyperactivity disorder (ADHD) is a prevalent neurodevelopmental disorder among children and adolescents. Behavioral detection and analysis play a crucial role in ADHD diagnosis and assessment by objectively quantifying hyperactivity and impulsivity symptoms. Existing video-based action recognition algorithms focus on object or interpersonal interactions, they may overlook ADHD-specific behaviors. Current keypoints-based algorithms, although effective in attenuating environmental interference, struggle to accurately model the sudden and irregular movements characteristic of ADHD children. This work proposes a novel keypoints-based system, the Multi-cue Feature Fusion Network (MF-Net), for recognizing actions and behaviors of children with ADHD during the Test of Variables of Attention (TOVA). The system aims to assess ADHD symptoms as described in the DSM-V by extracting features from human body and facial keypoints. For human body keypoints, we introduce the Multi-scale Features and Frame-Attention Adaptive Graph Convolutional Network (MSF-AGCN) to extract irregular and impulsive motion features. For facial keypoints, we transform data into images and employ MobileVitv2 for transfer learning to capture facial and head movement features. Ultimately, a feature fusion module is designed to fuse the features from both branches, yielding the final action category prediction. The system, evaluated on 3801 video samples of ADHD children, achieves 90.6% top-1 accuracy and 97.6% top-2 accuracy across six action categories. Additional validation experiments on public datasets NW-UCLA, NTU-2D, and AFEW-VA verify the network's performance.

Federated Learning‐Based Mobile Traffic Prediction in Satellite‐Terrestrial Integrated Networks

ABSTRACTIntroductionWith the development and integration of satellite and terrestrial networks, mobile traffic prediction has become more important than before, which is the basis for service provision and resource scheduling when supporting various vertical applications. However, existing traffic prediction methods, especially deep learning‐based methods, require massive data for model training. Due to data privacy concerns, mobile traffic data are not easily shared among different parties, making it difficult to obtain a precise prediction model.MethodsTo mitigate the data leakage risk, a federated learning framework is proposed in this study for mobile traffic prediction in satellite‐terrestrial integrated networks to achieve a tradeoff between data privacy and prediction accuracy. In the proposed framework, local models are trained in base stations on the ground, and a global model is aggregated in the satellite edge server in space.ResultsA deep learning‐based prediction model with an adaptive graph convolutional network (AGCN) and long short‐term memory (LSTM) modules is proposed and validated in numerical experiments, which achieves the lowest prediction error with a real‐world traffic dataset when compared with other graph neural network (GNN) variants in the federated learning setting.ConclusionNumerical experiments with a real‐world mobile traffic dataset demonstrate the effectiveness of the proposed approach, which outperforms other GNN variants with lower prediction errors.

Aggregation or separation? Adaptive embedding message passing for knowledge graph completion

Knowledge graph completion intends to infer information within knowledge graphs, thereby bolstering the functionality of knowledge-driven applications. Recently, there has been a significant increase in the utilization of graph convolutional networks (GCNs) for knowledge graph completion. These GCN-based models primarily focus on aggregating information from neighboring entities and relations. Nonetheless, a fundamental question arises: is it beneficial to consider all neighbor information, and should some neighbor features be separated? We tackle this issue and present an adaptive graph convolutional network (AdaGCN) for knowledge graph completion, which can adaptively aggregate or separate neighbor information for knowledge embedding learning. Specifically, AdaGCN utilizes the adaptive message-passing mechanism to determine the importance of each relation, allocating weights to neighbor entity embeddings. This adaptive approach facilitates the propagation of valuable information while effectively separating less relevant or unnecessary details. Experimental results demonstrate that AdaGCN can efficiently acquire the embeddings of various triplets within knowledge graphs, and it achieves competitive performance compared to SOTA models on six datasets for the tasks of knowledge graph completion.

TEA-GCN: Transformer-Enhanced Adaptive Graph Convolutional Network for Traffic Flow Forecasting.

Traffic flow forecasting is crucial for improving urban traffic management and reducing resource consumption. Accurate traffic conditions prediction requires capturing the complex spatial-temporal dependencies inherent in traffic data. Traditional spatial-temporal graph modeling methods often rely on fixed road network structures, failing to account for the dynamic spatial correlations that vary over time. To address this, we propose a Transformer-Enhanced Adaptive Graph Convolutional Network (TEA-GCN) that alternately learns temporal and spatial correlations in traffic data layer-by-layer. Specifically, we design an adaptive graph convolutional module to dynamically capture implicit road dependencies at different time levels and a local-global temporal attention module to simultaneously capture long-term and short-term temporal dependencies. Experimental results on two public traffic datasets demonstrate the effectiveness of the proposed model compared to other state-of-the-art traffic flow prediction methods.

A Non-Contact AI-Based Approach to Multi-Failure Detection in Avionic Systems

The increasing electrification and integration of advanced controls in modern aircraft designs have significantly raised the number and complexity of installed printed circuit boards (PCBs), posing new challenges for efficient maintenance and rapid failure detection. Despite self-diagnostic features in current avionics systems, circuit damage and multiple simultaneous failures may arise, compromising safety and diagnostic accuracy. To address these challenges, this paper aims to develop a fast, accurate, and non-destructive, multi-failure diagnosis algorithm for PCBs. The proposed method combines a self-attention mechanism with an adaptive graph convolutional neural network to enhance diagnostic precision. A convolutional neural network with residual connections extracts features from scalar magnetic field data, ensuring robust input diversity. The model was tested on a typical dual-phase amplitude boosting circuit with up to four different simultaneous failures, achieving the experimental results of 99.08%, 98.50%, 98.78%, 98.01%, 98.93%, 98.25%, 97.03%, and 99.77% across metrics including overall precision, per-class precision, overall recall, per-class recall, overall F1 measure, and per-class F1 measure. The results demonstrated its effectiveness and feasibility in diagnosing complex PCBs with multiple failures, indicating the algorithm’s potential to improve failure diagnosis performance and offer a promising PCB diagnosis solution in aerospace applications.

Spatial–Temporal Similarity Fusion Graph Adversarial Convolutional Networks for traffic flow forecasting

Traffic flow forecasting is integral to the advancement of intelligent transportation systems and the development of smart cities. This paper introduces a novel model, the Spatial–Temporal Similarity Fusion Graphs Adversarial Convolutional Networks (STSF-GACN), which leverages advanced data preprocessing techniques to enhance the predictive accuracy and efficiency of traffic flow forecasting.The innovation of our approach lies in the meticulous construction of the spatial–temporal similarity matrix through the precise calculation of temporal and spatial similarities. This matrix forms the backbone of our model, serving as the generator in the integrated Generative Adversarial Network (GAN) architecture. The Spatial–Temporal Similarity Fusion Adaptive Graph Convolutional Network, developed as part of our GAN’s generator, utilizes cutting-edge techniques such as the Wasserstein distance and Dynamic Time Warping to optimize the adaptive adjacency matrix, enabling the model to capture latent spatial–temporal correlations with unprecedented depth and precision.The discriminator of the GAN further refines the model by evaluating the accuracy of the traffic predictions, ensuring that the generative model produces results that are not only accurate but also robust against varying traffic conditions. This cohesive integration of GAN into the model architecture allows for a significant improvement in prediction accuracy and convergence speed, moving beyond traditional forecasting methods.

TAWFN: a deep learning framework for protein function prediction.

Proteins play pivotal roles in biological systems, and precise prediction of their functions is indispensable for practical applications. Despite the surge in protein sequence data facilitated by high-throughput techniques, unraveling the exact functionalities of proteins still demands considerable time and resources. Currently, numerous methods rely on protein sequences for prediction, while methods targeting protein structures are scarce, often employing convolutional neural networks (CNN) or graph convolutional networks (GCNs) individually. To address these challenges, our approach starts from protein structures and proposes a method that combines CNN and GCN into a unified framework called the two-model adaptive weight fusion network (TAWFN) for protein function prediction. First, amino acid contact maps and sequences are extracted from the protein structure. Then, the sequence is used to generate one-hot encoded features and deep semantic features. These features, along with the constructed graph, are fed into the adaptive graph convolutional networks (AGCN) module and the multi-layer convolutional neural network (MCNN) module as needed, resulting in preliminary classification outcomes. Finally, the preliminary classification results are inputted into the adaptive weight computation network, where adaptive weights are calculated to fuse the initial predictions from both networks, yielding the final prediction result. To evaluate the effectiveness of our method, experiments were conducted on the PDBset and AFset datasets. For molecular function, biological process, and cellular component tasks, TAWFN achieved area under the precision-recall curve (AUPR) values of 0.718, 0.385, and 0.488 respectively, with corresponding Fmax scores of 0.762, 0.628, and 0.693, and Smin scores of 0.326, 0.483, and 0.454. The experimental results demonstrate that TAWFN exhibits promising performance, outperforming existing methods. The TAWFN source code can be found at: https://github.com/ss0830/TAWFN.

Improved semantic-guided network for skeleton-based action recognition

A fundamental issue in skeleton-based action recognition is the extraction of useful features from skeleton joints. Unfortunately, the current state-of-the-art models for this task have a tendency to be overly complex and parameterized, which results in low model training and inference time efficiency for large-scale datasets. In this work, we develop a simple but yet an efficient baseline for skeleton-based Human Action Recognition (HAR). The architecture is based on adaptive GCNs (Graph Convolutional Networks) to capture the complex interconnections within skeletal structures automatically without the need of a predefined topology. The GCNs are followed and empowered with an attention mechanism to learn more informative representations. This paper reports interesting accuracy on a large-scale dataset NTU-RGB+D 60, 89.7% and 95.0% on respectively Cross-Subject, and Cross-View benchmarks. On NTU-RGB+D 120, 84.6% and 85.8% over Cross-Subject and Cross-Setup settings, respectively. This work provides an improvement of the existing model SGN (Semantic-Guided Neural Networks) when extracting more discriminant spatial and temporal features.

Dynamic Spatio-Temporal Adaptive Graph Convolutional Recurrent Networks for Vacant Parking Space Prediction

The prediction of vacant parking spaces (VPSs) can reduce the time drivers spend searching for parking, thus alleviating traffic congestion. However, previous studies have mostly focused on modeling the temporal features of VPSs using historical data, neglecting the complex and extensive spatial characteristics of different parking lots within the transportation network. This is mainly due to the lack of direct physical connections between parking lots, making it challenging to quantify the spatio-temporal features among them. To address this issue, we propose a dynamic spatio-temporal adaptive graph convolutional recursive network (DSTAGCRN) for VPS prediction. Specifically, DSTAGCRN divides VPS data into seasonal and periodic trend components and combines daily and weekly information with node embeddings using the dynamic parameter-learning module (DPLM) to generate dynamic graphs. Then, by integrating gated recurrent units (GRUs) with the parameter-learning graph convolutional recursive module (PLGCRM) of DPLM, we infer the spatio-temporal dependencies for each time step. Furthermore, we introduce a multihead attention mechanism to effectively capture and fuse the spatio-temporal dependencies and dynamic changes in the VPS data, thereby enhancing the prediction performance. Finally, we evaluate the proposed DSTAGCRN on three real parking datasets. Extensive experiments and analyses demonstrate that the DSTAGCRN model proposed in this study not only improves the prediction accuracy but can also better extract the dynamic spatio-temporal characteristics of available parking space data in multiple parking lots.

Multi-label image classification using adaptive graph convolutional networks: From a single domain to multiple domains

This paper proposes an adaptive graph-based approach for multi-label image classification. Graph-based methods have been largely exploited in the field of multi-label classification, given their ability to model label correlations. Specifically, their effectiveness has been proven not only when considering a single domain but also when taking into account multiple domains. However, the topology of the used graph is not optimal as it is pre-defined heuristically. In addition, consecutive Graph Convolutional Network (GCN) aggregations tend to destroy the feature similarity. To overcome these issues, an architecture for learning the graph connectivity in an end-to-end fashion is introduced. This is done by integrating an attention-based mechanism and a similarity-preserving strategy. The proposed framework is then extended to multiple domains using an adversarial training scheme. Numerous experiments are reported on well-known single-domain and multi-domain benchmarks. The results demonstrate that our approach achieves competitive results in terms of mean Average Precision (mAP) and model size as compared to the state-of-the-art. The code will be made publicly available.

DAGCN: Dynamic and Adaptive Graph Convolutional Network for Salient Object Detection.

Deep-learning-based salient object detection (SOD) has achieved significant success in recent years. The SOD focuses on the context modeling of the scene information, and how to effectively model the context relationship in the scene is the key. However, it is difficult to build an effective context structure and model it. In this article, we propose a novel SOD method called dynamic and adaptive graph convolutional network (DAGCN) that is composed of two parts, adaptive neighborhood-wise graph convolutional network (AnwGCN) and spatially restricted K-nearest neighbors (SRKNN). The AnwGCN is novel adaptive neighborhood-wise graph convolution, which is used to model and analyze the saliency context. The SRKNN constructs the topological relationship of the saliency context by measuring the non-Euclidean spatial distance within a limited range. The proposed method constructs the context relationship as a topological graph by measuring the distance of the features in the non-Euclidean space, and conducts comparative modeling of context information through AnwGCN. The model has the ability to learn the metrics from features and can adapt to the hidden space distribution of the data. The description of the feature relationship is more accurate. Through the convolutional kernel adapted to the neighborhood, the model obtains the structure learning ability. Therefore, the graph convolution process can adapt to different graph data. Experimental results demonstrate that our solution achieves satisfactory performance on six widely used datasets and can also effectively detect camouflaged objects. Our code will be available at: https://github.com/CSIM-LUT/DAGCN.git.

Adaptive Graph Convolutional Recurrent Network with Transformer and Whale Optimization Algorithm for Traffic Flow Prediction

Accurate traffic flow prediction plays a crucial role in the development of intelligent traffic management. Despite numerous investigations into spatio-temporal methods, achieving high accuracy in traffic flow prediction remains challenging. This challenge arises from the complex dynamic spatio-temporal correlations within the traffic road network and the limitations imposed by the selection of hyperparameters based on experiments and manual experience, which can affect the performance of the network architecture. This paper introduces a novel transformer-based adaptive graph convolutional recurrent network. The proposed network automatically infers the interdependencies among different traffic sequences and incorporates the capability to capture global spatio-temporal correlations. This enables the dynamic capture of long-range temporal correlations. Furthermore, the whale optimization algorithm is employed to efficiently design an optimal network structure that aligns with the requirements of the traffic domain and maximizes the utilization of limited computational resources. This design approach significantly enhances the model’s performance and improves the accuracy of traffic flow prediction. The experimental results on four real datasets demonstrate the efficacy of our approach. In PEMS03, it improves MAE by 2.6% and RMSE by 1.4%. In PEMS04, improvements are 1.6% in MAE and 1.4% in RMSE, with a similar MAPE score to the best baseline. For PEMS07, our approach shows a 4.1% improvement in MAE and 2.2% in RMSE. On PEMS08, it surpasses the current best baseline with a 3.4% improvement in MAE and 1.6% in RMSE. These results confirm the good performance of our model in traffic flow prediction across multiple datasets.

A traffic flow prediction method based on constrained dynamic graph convolutional recurrent networks

To enhance the efficiency of predicting future traffic flow trends within a transportation network, we propose a traffic flow prediction approach based on Constrained Dynamic Graph Convolutional Recurrent Network (C-DGCRN). Firstly, we employ matrix linear constraint and low-rank constraint optimization techniques to assist the Dynamic Graph Convolutional Recurrent Network (DGCRN) in extracting relevant internal correlations within the transportation network, leading to the formation of an affinity matrix. Secondly, we utilize the Hadamard product operation to effectively transfer weights from the affinity matrix to DGCRN, further enhancing its predictive accuracy. The experiments conducted an error assessment on the Metro Traffic Los Angeles and Performance Measurement System-Bay Area datasets. The Mean Absolute Error, Root Mean Square Error, and Mean Absolute Percentage Error of C-DGCRN were 2.66, 5.06, and 6.83, respectively. Compared to state-of-the-art methods like Adaptive Graph Convolutional Recurrent Network, C-DGCRN showed a reduction of 7%, 9%, and 11% in these metrics.

A Comprehensive Interaction in Multiscale Multichannel EEG Signals for Emotion Recognition

Electroencephalogram (EEG) is the most preferred and credible source for emotion recognition, where long-short range features and a multichannel relationship are crucial for performance because numerous physiological components function at various time scales and on different channels. We propose a cascade scale-aware adaptive graph convolutional network and cross-EEG transformer (SAG-CET) to explore the comprehensive interaction between multiscale and multichannel EEG signals with two novel ideas. First, to model the relationship of multichannel EEG signals and enhance signal representation ability, the multiscale EEG signals are fed into a scale-aware adaptive graph convolutional network (SAG) before the CET model. Second, the cross-EEG transformer (CET), is used to explicitly capture multiscale features as well as their correlations. The CET consists of two self-attention encoders for gathering features from long-short time series and a cross-attention module to integrate multiscale class tokens. Our experiments show that CET significantly outperforms a vanilla unitary transformer, and the SAG module brings visible gains. Our methods also outperform state-of-the-art methods in subject-dependent tasks with 98.89%/98.92% in accuracy for valence/arousal on DEAP and 99.08%/99.21% on DREAMER.

Transformer Encoder Enhanced by an Adaptive Graph Convolutional Neural Network for Prediction of Aero-Engines’ Remaining Useful Life

Accurate prediction of remaining useful life (RUL) plays a significant role in ensuring the safe flight of aircraft. With the recent rapid development of deep learning, there has been a growing trend towards more precise RUL prediction. However, while many current deep learning methods are capable of extracting spatial features—those along the sensor dimension—through convolutional kernels or fully connected layers, their extraction capacity is often limited due to the small scale of kernels and the high uncertainty associated with linear weights. Graph neural networks (GNNs), emerging as effective approaches for processing graph-structured data, explicitly consider the relationships between sensors. This is akin to imposing a constraint on the training process, thereby allowing the learned results to better approximate real-world situations. In order to address the challenge of GNNs in extracting temporal features, we augment our proposed framework for RUL prediction with a Transformer encoder, resulting in the adaptive graph convolutional transformer encoder (AGCTE). A case study using the C-MAPSS dataset is conducted to validate the effectiveness of our proposed model.

DDAGCN: an unsupervised cross-domain identification method for tie rod bolt loosening in a rod-fastening rotor system under different working conditions

The cross-domain diagnosis of tie rod bolt loosening is essential for guaranteeing the healthy operation of rod-fastening rotor (RFR) systems. The unsupervised domain adaptation (UDA) method effectively alleviates the impact of domain discrepancy and has been applied for cross-domain diagnosis. Traditional UDA methods mainly focus on the marginal and conditional distributions with fixed weights to adapt the domain distribution discrepancy. However, the fixed distribution combination cannot satisfy the requirement of feature domain alignment under different working conditions, and the relative importance of the two distributions cannot be evaluated quantitatively. This paper proposes an improved dynamic distribution adaptive graph convolutional network (DDAGCN) for the cross-domain diagnosis of tie rod bolt loosening under different working conditions. This method can quantitatively evaluate the relative significance of each distribution in representing the distribution discrepancy. First, it combines the convolutional neural network and the graph convolutional network to extract the features in the graph structure by using the connection relationship between nodes, and realizes the full extraction of neighbourhood information of nodes. Then, the dynamic distribution adaptive alignment strategy is introduced to construct the dynamic linear combination of marginal and conditional distributions, so as to measure the distribution discrepancy between domains. Meanwhile, the domain adversarial module is combined to further reduce the domain gap and finally realize feature alignment. The extracted domain invariant features can effectively enhance the generalization ability and fault identification ability of the model. The case of the public bearing dataset verifies that the effectiveness and generalization ability of the proposed method for cross-domain fault diagnosis under different working conditions is superior to other compared methods. In addition, the identification ability of the proposed method for the degree of tie rod bolt loosening is verified by the self-made bolt loosening dataset of the RFR system.

Dynamic adaptive graph convolutional transformer with broad learning system for multi-dimensional chaotic time series prediction

Chaotic time series data is extensively applied in financial stocks, climate monitoring, and sea clutter, in which data fusion from various sources and multi-sensor information make accurate predictions of chaotic time series challenging under complex nonlinear conditions. Previous works focus on designing different model frameworks to capture the temporal dependence and extract richer nonlinear features to improve the accuracy of univariate chaotic time series prediction, which ignores the spatial dependence of multivariable. However, in this paper, we argue that spatial correlation among multiple variables is essential to improve the prediction accuracy of chaotic time series. To fill the gap, we innovatively propose a Dynamic Adaptive Graph Convolutional Transformer with a Broad Learning System (DAGCT-BLS), a GCN and Transformer-based model utilizing multivariate spatial dependence for multi-dimensional chaotic time series forecasting. In DAGCT-BLS, the multivariate chaotic time series are reconstructed into the phase space, and the reconstructed data are rapidly feature-extracted using a cascade network BLS with frozen weights to maximize the retention of chaotic properties and nonlinear relationships. Then, the Dynamic Adaptive Graph Convolutional Network (DAGCN) is proposed to capture the spatial correlation among the multiple variables. Finally, improved multi-head attention of the Transformer Encoder is used to capture the temporal dependence of the phase point sequence. Experiments of our proposed model on three datasets (Lorenz, Rossler, and Sea clutter) show that DAGCT-BLS can achieve the best prediction performance and have strong interpretability, and multivariate-based joint modeling of chaotic time series helps to improve the prediction performance.

Dense Multi-Scale Graph Convolutional Network for Knee Joint Cartilage Segmentation.

In this paper, we propose a dense multi-scale adaptive graph convolutional network (DMA-GCN) method for automatic segmentation of the knee joint cartilage from MR images. Under the multi-atlas setting, the suggested approach exhibits several novelties, as described in the following. First, our models integrate both local-level and global-level learning simultaneously. The local learning task aggregates spatial contextual information from aligned spatial neighborhoods of nodes, at multiple scales, while global learning explores pairwise affinities between nodes, located globally at different positions in the image. We propose two different structures of building models, whereby the local and global convolutional units are combined by following an alternating or a sequential manner. Secondly, based on the previous models, we develop the DMA-GCN network, by utilizing a densely connected architecture with residual skip connections. This is a deeper GCN structure, expanded over different block layers, thus being capable of providing more expressive node feature representations. Third, all units pertaining to the overall network are equipped with their individual adaptive graph learning mechanism, which allows the graph structures to be automatically learned during training. The proposed cartilage segmentation method is evaluated on the entire publicly available Osteoarthritis Initiative (OAI) cohort. To this end, we have devised a thorough experimental setup, with the goal of investigating the effect of several factors of our approach on the classification rates. Furthermore, we present exhaustive comparative results, considering traditional existing methods, six deep learning segmentation methods, and seven graph-based convolution methods, including the currently most representative models from this field. The obtained results demonstrate that the DMA-GCN outperforms all competing methods across all evaluation measures, providing DSC=95.71% and DSC=94.02% for the segmentation of femoral and tibial cartilage, respectively.

Bayesian graph convolutional network for traffic prediction

Recently, adaptive graph convolutional network based traffic prediction methods, learning a latent graph structure from traffic data via various attention-based mechanisms, have achieved impressive performance. However, they are still limited to finding a better description of spatial relationships between traffic conditions due to: (1) ignoring the prior of the observed road network topology; (2) neglecting the presence of negative spatial relationships; and (3) lacking investigation on the uncertainty of the graph structure. In this paper, we propose a Bayesian Graph Convolutional Network (BGCN) framework to alleviate these issues. Under this framework, the graph structure is viewed as a random realization from a parametric generative model, and its posterior is inferred using the observed topology of the road network and traffic data. Specifically, the parametric generative model is comprised of two parts: (1) a constant adjacency matrix that discovers potential spatial relationships from the observed physical connections between roads using a Bayesian approach; (2) a learnable adjacency matrix that learns globally shared spatial correlations from traffic data in an end-to-end fashion and can model negative spatial correlations. The posterior of the graph structure is then approximated by performing Monte Carlo dropout on the parametric graph structure. We verify the effectiveness of our method on five real-world datasets, and the experimental results demonstrate that BGCN attains superior performance compared with state-of-the-art methods. The source code is available at https://github.com/JunFu1995/BGCN.git.