Graph Pooling Research Articles

EIDU-Net: edge-preserved inception DenseGCN U-Net for LiDAR point cloud segmentation

With the development of laser scanners and machine learning, point cloud semantic segmentation plays a significant role in autonomous driving, scene reconstruction, human-computer interaction, and other fields. In recent years, point cloud semantic segmentation based on deep learning has become one of the key research directions in point cloud processing. Due to the limited ability to exploit geometric details and contextual information in point clouds, most methods that adopt encoder-decoder architecture lose local structural information easily, especially detailed features, and extract features insufficiently. To address this issue, the edge-preserving inception DenseGCN U-Net (entitled as EIDU-Net) is proposed. EIDU-Net makes full use of the complementation between geometric details in the original point cloud and high-level features. The edge-preserved graph pooling (EGP) layer, the key module of the EIDU-Net, is designed to retain additional edge feature information from the original point cloud during pooling operations. Accordingly, the edge-preserved graph unpooling (EGU) layer can restore the feature graph more efficiently based on the additionally retained edge features. Extensive experiments demonstrate that our proposed EIDU-Net has remarkable improvements on semantic segmentation tasks under whatever S3DIS or Terracotta Warrior fragments. Our code is publicly available at https://github.com/caoxin918/EIDU-Net.

Current signal analysis using SW-GAT networks for fault diagnosis of electromechanical drive systems under extreme data imbalance

Abstract In complex industrial environments, ensuring the safe operation and effective maintenance of electromechanical equipment is of paramount importance. Intelligent fault diagnosis based on deep learning is currently the most popular data-driven method. However, conventional intelligent fault diagnosis techniques face several challenges: (1) Most diagnostic models rely heavily on analyzing vibration signals. However, vibration sensors are difficult to deploy in space-constrained environments, and vibration signals are frequently contaminated by strong noise. (2) The prevalence of class imbalance between normal and fault data in equipment condition monitoring can lead to model over-reliance on information from a few classes. (3) Traditional diagnostic models presuppose data independence, neglecting the coupling relationships between data. To address the aforementioned issue, this paper proposes a Self-Weighted Graph Attention Networks (SW-GAT) based on motor stator current signal analysis, aimed at solving the fault diagnosis problem of critical transmission components in electromechanical systems under severely imbalanced data scenarios. Firstly, the raw current data is preprocessed using Stacked Auto-Encoders (SAE), and then the decoded current frequency-domain data is utilized to construct graphical data, thereby enhancing the non-common features and weak fault information in the current signals. Secondly, by introducing the graph pooling attention mechanism into GAT, the model can more effectively focus on useful fault feature information within the graph data. Finally, a novel interclass adjustment loss function is designed to adaptively adjust and balance class weights, enabling the model to pay greater attention to minority class samples and thereby improving the recognition accuracy for minority class faults. Validating the proposed method on two cases and comparing it with other advanced approaches, our method achieved the highest accuracy among the compared methods.

State of the Art and Potentialities of Graph-level Learning

Graphs have a superior ability to represent relational data, such as chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks, including comparison, regression, classification, and more. Traditional approaches to learning a set of graphs heavily rely on hand-crafted features, such as substructures. While these methods benefit from good interpretability, they often suffer from computational bottlenecks, as they cannot skirt the graph isomorphism problem. Conversely, deep learning has helped graph-level learning adapt to the growing scale of graphs by extracting features automatically and encoding graphs into low-dimensional representations. As a result, these deep graph learning methods have been responsible for many successes. Yet, no comprehensive survey reviews graph-level learning starting with traditional learning and moving through to the deep learning approaches. This article fills this gap and frames the representative algorithms into a systematic taxonomy covering traditional learning, graph-level deep neural networks, graph-level graph neural networks, and graph pooling. In addition, the evolution and interaction between methods from these four branches within their developments are examined to provide an in-depth analysis. This is followed by a brief review of the benchmark datasets, evaluation metrics, and common downstream applications. Finally, the survey concludes with an in-depth discussion of 12 current and future directions in this booming field.

Which to select?: Analysis of speaker representation with graph attention networks.

Although the recent state-of-the-art systems show almost perfect performance, analysis of speaker embeddings has been lacking thus far. An in-depth analysis of speaker representation will be performed by looking into which features are selected. To this end, various intermediate representations of the trained model are observed using graph attentive feature aggregation, which includes a graph attention layer and graph pooling layer followed by a readout operation. To do so, the TIMIT dataset, which has comparably restricted conditions (e.g., the region and phoneme) is used after pre-training the model on the VoxCeleb dataset and then freezing the weight parameters. Through extensive experiments, there is a consistent trend in speaker representation in that the models learn to exploit sequence and phoneme information despite no supervision in that direction. The results shed light to help understand speaker embedding, which is yet considered to be a black box.

Sparse regularized graph pooling network optimal sensor placement method for diesel engine vibration fault perception system

Vibration sensor network optimization increases monitoring effectiveness and reduces sensor quantity and transmission burden. However, the traditional model-driven methods depend on precise finite element models, challenging for complex machinery. This paper presents a data-driven approach using the Sparse Regularized Graph Pooling Network (SRGPN), which conceptualizes sensor networks as graphs and uses graph pooling to identify optimal sensor combinations. A sparsity regularization term related to the number of sensors is included in the loss function, aiming for the minimal yet effective sensor combination. Additionally, a monitoring capability metric suited for diesel engines with multi-source impulse signals is proposed, reflecting the sensors’ monitoring capacity. Validated through simulations and tests on a diesel engine test bench, the results show that SRGPN optimally places sensors near excitation sources, balancing sensor count and monitoring needs. This approach shows potential for optimizing sensor placements in condition monitoring.

Graph pooling in graph neural networks: methods and their applications in omics studies

Graph neural networks (GNNs) process the graph-structured data using neural networks and have proven successful in various graph processing tasks. Currently, graph pooling operators have emerged as crucial components that bridge the gap between node representation learning and diverse graph-level tasks by transforming node representations into graph representations. Given the rapid growth and widespread adoption of graph pooling, this review aims to summarize the existing graph pooling operators for GNNs and their representative applications in omics. Specifically, we first present a comprehensive taxonomy of existing graph pooling algorithms, expanding the categorization for both global and hierarchical pooling operators, and for the first time reviewing the inverse operation of graph pooling, named unpooling. Next, we describe the general evaluation framework for graph pooling operators, encompassing three fundamental aspects: experimental setup, ablation analysis, and model interpretation. We also discuss open issues that significantly influence the design of graph pooling operators, including complexity, connectivity, adaptability, additional loss, and attention mechanisms. Finally, we summarize bioinformatics applications of graph pooling operators in omics, including graphs of gene interaction, medical images, and protein structures for drug discovery and disease diagnosis. Furthermore, we showcase the impact of graph pooling operators on research in specific real-world domains, with a focus on prediction performance and model interpretability. This review provides methodological insights in machine learning based graph modeling and related omics research, as well as an ongoing resource by gathering related papers and code in a dedicated GitHub repository (https://github.com/Hou-WJ/Graph-Pooling-Operators-and-Bioinformatics-Applications).

Hierarchical Glocal Attention Pooling for Graph Classification

Graph pooling is an essential operation in Graph Neural Networks that reduces the size of an input graph while preserving its core structural properties. Existing pooling methods find a compressed representation considering the Global Topological Structures (e.g., cliques, stars, clusters) or Local information at node level (e.g., top-k informative nodes). However, an effective graph pooling method does not hierarchically integrate both Global and Local graph properties. To this end, we propose a dual-fold Hierarchical Global Local Attention Pooling (HGLA-Pool) layer that exploits the aforementioned graph properties, generating more robust graph representations. Exhaustive experiments on nine publicly available graph classification benchmarks under standard metrics show that HGLA-Pool significantly outperforms eleven state-of-the-art models on seven datasets while being on par for the remaining two.

A brain structure learning-guided multi-view graph representation learning for brain network analysis.

Resting-state brain networks represent the interconnectivity of different brain regions during rest. Utilizing brain network analysis methods to model these networks can enhance our understanding of how different brain regions collaborate and communicate without explicit external stimuli. However, analyzing resting-state brain networks faces challenges due to high heterogeneity and noise correlation between subjects. This study proposes a brain structure learning-guided multi-view graph representation learning method to address the limitations of current brain network analysis and improve the diagnostic accuracy (ACC) of mental disorders. We first used multiple thresholds to generate different sparse levels of brain networks. Subsequently, we introduced graph pooling to optimize the brain network representation by reducing noise edges and data inconsistency, thereby providing more reliable input for subsequent graph convolutional networks (GCNs). Following this, we designed a multi-view GCN to comprehensively capture the complexity and variability of brain structure. Finally, we employed an attention-based adaptive module to adjust the contributions of different views, facilitating their fusion. Considering that the Smith atlas offers superior characterization of resting-state brain networks, we utilized the Smith atlas to construct the graph network. Experiments on two mental disorder datasets, the Autism Brain Imaging Data Exchange (ABIDE) dataset and the Mexican Cocaine Use Disorders (SUDMEX CONN) dataset, show that our model outperforms the state-of-the-art methods, achieving nearly 75% ACC and 70% area under the receiver operating characteristic curve (AUC) on both datasets. These findings demonstrate that our method of combining multi-view graph learning and brain structure learning can effectively capture crucial structural information in brain networks while facilitating the acquisition of feature information from diverse perspectives, thereby improving the performance of brain network analysis.

A Self-Attention Legendre Graph Convolution Network for Rotating Machinery Fault Diagnosis.

Rotating machinery is widely used in modern industrial systems, and its health status can directly impact the operation of the entire system. Timely and accurate diagnosis of rotating machinery faults is crucial for ensuring production safety, reducing economic losses, and improving efficiency. Traditional deep learning methods can only extract features from the vertices of the input data, thereby overlooking the information contained in the relationships between vertices. This paper proposes a Legendre graph convolutional network (LGCN) integrated with a self-attention graph pooling method, which is applied to fault diagnosis of rotating machinery. The SA-LGCN model converts vibration signals from Euclidean space into graph signals in non-Euclidean space, employing a fast local spectral filter based on Legendre polynomials and a self-attention graph pooling method, significantly improving the model's stability and computational efficiency. By applying the proposed method to 10 different planetary gearbox fault tasks, we verify that it offers significant advantages in fault diagnosis accuracy and load adaptability under various working conditions.

Understanding and mitigating dimensional collapse of Graph Contrastive Learning: A non-maximum removal approach

Graph Contrastive Learning (GCL) generates graph-level embeddings by maximizing Mutual Information between different augmented views of the same graph (positive pairs), and shows promising performance in graph representation learning (GRL) without the supervision of manual annotations. However, GCL suffers from a dimensional collapse problem, i.e., embedding vectors reside in a restricted low-dimensional subspace, curtailing the expressiveness of certain embedding dimensions. In this paper, we present a theoretical analysis identifying the smoothing effect of graph pooling and graph convolution’s implicit regularization as principal causes of dimension collapse in graph contrastive learning. To mitigate the above effects, we propose a Non-Maximum Removal Graph Contrastive Learning (nmrGCL) approach, which removes “prominent” dimensions (those significantly contributing to the similarity measure) for positive pairs within the pretext task. Comprehensive experiments on multiple benchmark datasets are conducted and the results show that the proposed nmrGCL outperforms the state-of-the-art methods.

Rapid prediction for the transient dispersion of leaked airborne pollutant in urban environment based on graph neural networks

Rapidly predicting airborne pollutant dispersion in urban is vital for ventilation design and evacuation planning. Computational fluid dynamics (CFD) simulations are commonly used to provide accurate predictions, but the computational cost is too high. Although graph neural networks (GNNs) provide fast predictions of flow fields by manipulating unstructured mesh on GPU, they suffer from high memory usage and accuracy decreases when applied to large-scale urban scenes. Moreover, it is difficult for GNNs to learn the coupled relationship between wind field and pollutant concentration field. We propose a multi-objective GNN model as CFD surrogate to rapidly predict the transient dispersion of airborne pollutant under the influence of complex wind field patterns in urban environment. Based on random urban layouts generated by a 2D bin packing algorithm, we employ a validated CFD model to construct a sample dataset of wind fields and concentration fields. We leverage graph pooling and multi-scale feature fusion to improve prediction accuracy, and subgraph partitioning of both wind field and concentration field to reduce GPU memory usage. The results show that our GNN model at its best runs 1–2 orders of magnitude faster than CFD simulation with accuracy evaluation metrics R2=0.92, and achieves 70 % GPU memory reduction.

Self-adaptive selection graph pooling based fault diagnosis method under few samples and noisy environment

Neural network (NN)-based methods are extensively used for intelligent fault diagnosis in industrial systems. Nevertheless, due to the limited availability of faulty samples and the presence of noise interference, most existing NN-based methods perform limited diagnosis performance. In response to these challenges, a self-adaptive selection graph pooling method is proposed. Firstly, graph encoders with sharing parameters are designed to extract local structure-feature information (SFI) of multiple sensor-wise sub-graphs. Then, the temporal continuity of the SFI is maintained through time-by-time concatenation, resulting in a global sensor graph and reducing the dependency on data volume from the perspective of adding prior knowledge. Subsequently, leveraging a self-adaptive node selection mechanism, the noise interference of redundant and noisy sensor-wise nodes in the graph is alleviated, allowing the networks to concentrate on the fault-attention nodes. Finally, the local max pooling and global mean pooling of the node-selection graph are incorporated in the readout module to get the multi-scale graph features, which serve as input to a multi-layer perceptron for fault diagnosis. Two experimental studies involving different mechanical and electrical systems demonstrate that the proposed method not only achieves superior diagnosis performance with limited data, but also maintains strong anti-interference ability in noisy environments. Additionally, it exhibits good interpretability through the proposed self-adaptive node selection mechanism and visualization methods.

Adaptive node feature extraction in graph-based neural networks for brain diseases diagnosis using self-supervised learning

Electroencephalography (EEG) has demonstrated significant value in diagnosing brain diseases. In particular, brain networks have gained prominence as they offer additional valuable insights by establishing connections between EEG signal channels. While brain connections are typically delineated by channel signal similarity, there lacks a consistent and reliable strategy for ascertaining node characteristics. Conventional node features such as temporal and frequency domain properties of EEG signals prove inadequate for capturing the extensive EEG information. In our investigation, we introduce a novel adaptive method for extracting node features from EEG signals utilizing a distinctive task-induced self-supervised learning technique. By amalgamating these extracted node features with fundamental edge features constructed using Pearson correlation coefficients, we showed that the proposed approach can function as a plug-in module that can be integrated to many common GNN networks (e.g., GCN, GraphSAGE, GAT) as a replacement of node feature selections module. Comprehensive experiments are then conducted to demonstrate the consistently superior performance and high generality of the proposed method over other feature selection methods in various of brain disorder prediction tasks, such as depression, schizophrenia, and Parkinson’s disease. Furthermore, compared to other node features, our approach unveils profound spatial patterns through graph pooling and structural learning, shedding light on pivotal brain regions influencing various brain disorder prediction based on derived features.

Micro-expression recognition based on a novel GCN-transformer cooperation model for IoT-eHealth

If a person is truly healthy, his/her well-being encompasses both physical and psychological health. However, the existing IoT-eHealth system typically focus only on monitoring the user’s physical data through various sensors, neglecting their mental state. To enhance the intelligence level of IoT-eHealth system and enable it to have the psychological monitoring ability, a novel collaborative model based on Graph Convolutional Network (GCN) and Transformer is designed for Micro-Expression (ME) recognition in this paper. Firstly, facial information within each frame is transformed into a Spatial Topological Relationship Graph (STRG) by using facial landmarks detection and psychological relationship of local patches. Then, in order to automatically aggregate the key information on facial patches that contribute to ME recognition from the structured graph data, a Hierarchical Adaptive Graph Pooling (HAGP) module is designed for obtaining discriminative frame-level feature based on GCN utilizing graph structure and vertex global dependencies. Finally, in order to model the long-term dependencies among frames and capture the key frame-level features that are beneficial for ME recognition, a Temporal Sensitive Self-Attention (TSSA) mechanism is designed, and a novel Temporal Sensitive Transformer (TST) encoder is constructed based on TSSA to explore the evolution law of facial patterns and obtain discriminative video-level features that are helpful for ME recognition. In the comparative experiments of standard dataset verification and practical dataset testing, designed collaborative model is superior to other methods and can achieve the highest recognition accuracy, which almost can meet the application requirements of IoT-eHealth system.

Intelligent Conceptual Design of Railway Bridge Based on Graph Neural Networks

In the conceptual design stage of railway bridge, the beam type of the bridge at the main control point must be modified repeatedly to satisfy varying requirements. Thus, the demand for design efficiency is high. However, railway bridge design relies heavily on professional knowledge and experience and is typically completed manually by senior designers, thereby requiring considerable time. An intelligent beam type recommendation algorithm named AutoDis Graph Ontology Attention Matching (AGOAM) is proposed to rapidly generate bridge design plans for railway route main control points. This method acquires the node embeddings of the main control point and beam type attribute graphs through graph neural networks (GNNs) and predicts the score of each beam type through graph matching technology. The beam type with the highest prediction score is recommended. In addition, the accuracy of the recommendation results is improved through ontology-enhanced attribute interaction and attention mechanism-based graph pooling. The efficiency of the proposed method is demonstrated with a real-world railway bridge design dataset, and ablation study is conducted to evaluate the effectiveness of the ontology-enhanced attribute interaction and attention mechanism-based graph pooling.

GraphADT: empowering interpretable predictions of acute dermal toxicity with multi-view graph pooling and structure remapping.

Accurate prediction of acute dermal toxicity (ADT) is essential for the safe and effective development of contact drugs. Currently, graph neural networks, a form of deep learning technology, accurately model the structure of compound molecules, enhancing predictions of their ADT. However, many existing methods emphasize atom-level information transfer and overlook crucial data conveyed by molecular bonds and their interrelationships. Additionally, these methods often generate "equal" node representations across the entire graph, failing to accentuate "important" substructures like functional groups, pharmacophores, and toxicophores, thereby reducing interpretability. We introduce a novel model, GraphADT, utilizing structure remapping and multi-view graph pooling (MVPool) technologies to accurately predict compound ADT. Initially, our model applies structure remapping to better delineate bonds, transforming "bonds" into new nodes and "bond-atom-bond" interactions into new edges, thereby reconstructing the compound molecular graph. Subsequently, we use MVPool to amalgamate data from various perspectives, minimizing biases inherent to single-view analyses. Following this, the model generates a robust node ranking collaboratively, emphasizing critical nodes or substructures to enhance model interpretability. Lastly, we apply a graph comparison learning strategy to train both the original and structure remapped molecular graphs, deriving the final molecular representation. Experimental results on public datasets indicate that the GraphADT model outperforms existing state-of-the-art models. The GraphADT model has been demonstrated to effectively predict compound ADT, offering potential guidance for the development of contact drugs and related treatments. Our code and data are accessible at: https://github.com/mxqmxqmxq/GraphADT.git.

LightSGM: Local feature matching with lightweight seeded

Addressing the quintessential challenge of local feature matching in computer vision, this study introduces a novel fast sparse seed graph structure named LightSGM. This structure aims to refine the characterization of graph features while minimizing superfluous connections. Initially, a subset of high-quality seed feature points is curated using a confidence filter. Subsequently, keypoint features are assimilated into this seed set via graph pooling, and the composite features are further processed through a memory and computation-efficient seed transformer to capture rich contextual information about the keypoints. The seed feature points are then relayed back to the original keypoints using an inverse process known as graph unpooling. The paper also introduce an adaptive mechanism to determine the optimal number of model layers based on the intricacy of matching image pairs. A Matching Point Prediction Header is employed to extract the final set of matching points. Through extensive experimentation on image matching and position estimation, LightSGM has demonstrated its prowess in delivering competitive matching accuracy while maintaining a balance with real-time processing capabilities.

EEG Emotion Recognition Employing RGPCN-BiGRUAM: ReliefF-Based Graph Pooling Convolutional Network and BiGRU Attention Mechanism

Emotion recognition plays a crucial role in affective computing, and electroencephalography (EEG) signals are increasingly applied in this field due to their effectiveness in reflecting brain activity. In this paper, we propose a novel EEG emotion recognition model that combines the ReliefF-based Graph Pooling Convolutional Network and BiGRU Attention Mechanisms (RGPCN-BiGRUAM). RGPCN-BiGRUAM effectively integrates the advantages of graph convolutional networks and recurrent neural networks. By incorporating ReliefF weights and an attention mechanism into graph pooling, our model enhances the aggregation of high-quality features while discarding irrelevant ones, thereby improving the efficiency of information transmission. The implementation of a multi-head attention mechanism fusion in BiGRU addresses the limitations of single-output features, achieving optimal selection of global features. Comparative experiments on public datasets SEED and DEAP demonstrate that our proposed RGPCN-BiGRUAM significantly improves classification performance compared to classic algorithms, achieving state-of-the-art results. Ablation studies further validate the design principles of our model. The results of this study indicate that RGPCN-BiGRUAM has strong potential for EEG emotion recognition, offering substantial possibilities for future applications.

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.

TodyNet: Temporal dynamic graph neural network for multivariate time series classification

Multivariate time series classification (MTSC) is a crucial data mining task that can be effectively tackled using prevalent deep learning technology. However, current methods often overlook hidden dependencies across dimensions and struggle to capture dynamic time series features adequately, leading to poor accuracy. To tackle this challenge, we propose TodyNet, a novel dynamic temporal graph neural network. TodyNet extracts latent spatio-temporal dependencies without predefined graph structures, facilitating information flow among isolated but implicitly interdependent variables. It captures associations between time slots through dynamic graphs, boosting classification performance. Furthermore, to address the limitation that the hierarchical representations of graphs are challenging to learn with graph neural networks (GNNs), we introduce a temporal graph pooling layer for obtaining a global graph-level representation. The dynamic graph, graph information propagation, and temporal convolution are jointly learned within an end-to-end framework. Experimental results on 26 UEA benchmark datasets indicate that compared to current state-of-the-art deep learning methods in the MTSC task, the proposed Todynet achieved a performance improvement of 5.5%.