Graph Pooling Research Articles

Topology-Guided Graph Learning for Process Fault Diagnosis

Faults in the process industry can be diagnosed using various data-driven methods, but the intrinsic relationships between inputs and outputs, particularly the physical consistency of model prediction logic, have received little attention. To address this issue, we propose a topology-guided graph learning fault diagnosis framework that combines the concept of graphs with process physics. Our framework focuses on knowledge embedding and explanation and includes several key components: a topology graph based on the flowchart, a self-attention mechanism to discover distinctive knowledge from data, graph convolution to capture variable relationships, graph pooling to coarsen graph data, and a gating mechanism to establish long-term dependencies. We also use a graph explainer to assess the physical consistency of the model’s prediction logic. We demonstrate the feasibility of our method using the Tennessee Eastman process and show that it is not a black-box model but rather has natural advantages in terms of effectiveness and explanation.

EC-GCN: A encrypted traffic classification framework based on multi-scale graph convolution networks

The sharp increase in encrypted traffic brings a huge challenge to traditional traffic classification methods. Combining deep learning with time series analysis techniques is a recent trend in solving this problem. Most of these approaches only capture the temporal correlation within a flow. The accuracy and robustness are unsatisfactory, especially in an unstable network environment with high packet loss and reordering. How to learn a representation with a strong generalization ability for each encrypted traffic flow remains a key challenge. Our detailed analysis indicates that there is a graph with particular local structures corresponding to each type of encrypted traffic flow. Inspired by this observation, we propose a novel deep learning framework called EC-GCN to classify encrypted traffic flows based on multi-scale graph convolutional neural networks. We first provide a novel lightweight layer that only relies on the metadata and encodes each encrypted traffic flow into graph representations. So that our framework can be independent of different encryption protocols. Then we design a novel graph pooling and structure learning layer to dynamically extract the multi-graph representations and improve the capabilities to adapt to complex network environments. EC-GCN is an end-to-end classification model that learns representative spatial–temporal traffic features hidden in a traffic time series and then classifies them in a unified framework. Our comprehensive experiments on three real-world datasets indicate that EC-GCN can achieve up to 5%–20% accuracy improvement and outperforms state-of-the-art methods.

Multimodal Graph for Unaligned Multimodal Sequence Analysis via Graph Convolution and Graph Pooling

Multimodal sequence analysis aims to draw inferences from visual, language, and acoustic sequences. A majority of existing works focus on the aligned fusion of three modalities to explore inter-modal interactions, which is impractical in real-world scenarios. To overcome this issue, we seek to focus on analyzing unaligned sequences, which is still relatively underexplored and also more challenging. We propose Multimodal Graph, whose novelty mainly lies in transforming the sequential learning problem into graph learning problem. The graph-based structure enables parallel computation in time dimension (as opposed to recurrent neural network) and can effectively learn longer intra- and inter-modal temporal dependency in unaligned sequences. First, we propose multiple ways to construct the adjacency matrix for sequence to perform sequence to graph transformation. To learn intra-modal dynamics, a graph convolution network is employed for each modality based on the defined adjacency matrix. To learn inter-modal dynamics, given that the unimodal sequences are unaligned, the commonly considered word-level fusion does not pertain. To this end, we innovatively devise graph pooling algorithms to automatically explore the associations between various time slices from different modalities and learn high-level graph representation hierarchically. Multimodal Graph outperforms state-of-the-art models on three datasets under the same experimental setting.

DAGAM: a domain adversarial graph attention model for subject-independent EEG-based emotion recognition

Objective. Due to individual differences in electroencephalogram (EEG) signals, the learning model built by the subject-dependent technique from one person’s data would be inaccurate when applied to another person for emotion recognition. Thus, the subject-dependent approach for emotion recognition may result in poor generalization performance when compared to the subject-independent approach. However, existing studies have attempted but have not fully utilized EEG’s topology, nor have they solved the problem caused by the difference in data distribution between the source and target domains. Approach. To eliminate individual differences in EEG signals, this paper proposes the domain adversarial graph attention model, a novel EEG-based emotion recognition model. The basic idea is to generate a graph using biological topology to model multichannel EEG signals. Graph theory can topologically describe and analyze EEG channel relationships and mutual dependencies. Then, unlike other graph convolutional networks, self-attention pooling is used to benefit from the extraction of salient EEG features from the graph, effectively improving performance. Finally, following graph pooling, the domain adversarial model based on the graph is used to identify and handle EEG variation across subjects, achieving good generalizability efficiently. Main Results. We conduct extensive evaluations on two benchmark data sets (SEED and SEED IV) and obtain cutting-edge results in subject-independent emotion recognition. Our model boosts the SEED accuracy to 92.59% (4.06% improvement) with the lowest standard deviation (STD) of 3.21% (2.46% decrements) and SEED IV accuracy to 80.74% (6.90% improvement) with the lowest STD of 4.14% (3.88% decrements), respectively. The computational complexity is drastically reduced in comparison to similar efforts (33 times lower). Significance. We have developed a model that significantly reduces the computation time while maintaining accuracy, making EEG-based emotion decoding more practical and generalizable.

BrainTGL: A dynamic graph representation learning model for brain network analysis

Modeling the dynamics characteristics in functional brain networks (FBNs) is important for understanding the functional mechanism of the human brain. However, the current works do not fully consider the potential complex spatial and temporal correlations in human brain. To solve this problem, we propose a temporal graph representation learning framework for brain networks (BrainTGL). The framework involves a temporal graph pooling for eliminating the noisy edges as well as data inconsistency, and a dual temporal graph learning for capturing the spatio-temporal features of the temporal graphs. The proposed method has been evaluated in both tasks of brain disease (ASD, MDD and BD) diagnosis/gender classification (classification task) and subtype identification (clustering task) on the four datasets: Human Connectome Project (HCP), Autism Brain Imaging Data Exchange (ABIDE), NMU-MDD and NMU-BD. A large improvement is achieved for the ASD diagnosis. Specifically, our model outperforms the GroupINN and ST-GCN by an average increase of 4.2% and 8.6% on accuracy, respectively, demonstrating its advantages in comparison to the state-of-the-art methods based on functional connectivity features or learned spatio-temporal features. The results demonstrate that learning the spatial–temporal brain network representation for modeling dynamics characteristics in FBNs can improve the model’s performance on both disease diagnosis and subtype identification tasks for multiple disorders. Apart from performance, the improvements of computational efficiency and convergence speed reduce training costs.

Heterogeneous Graph Convolutional Neural Network via Hodge-Laplacian for Brain Functional Data.

This study proposes a novel heterogeneous graph convolutional neural network (HGCNN) to handle complex brain fMRI data at regional and across-region levels. We introduce a generic formulation of spectral filters on heterogeneous graphs by introducing the k-th Hodge-Laplacian (HL) operator. In particular, we propose Laguerre polynomial approximations of HL spectral filters and prove that their spatial localization on graphs is related to the polynomial order. Furthermore, based on the bijection property of boundary operators on simplex graphs, we introduce a generic topological graph pooling (TGPool) method that can be used at any dimensional simplices. This study designs HL-node, HL-edge, and HL-HGCNN neural networks to learn signal representation at a graph node, edge levels, and both, respectively. Our experiments employ fMRI from the Adolescent Brain Cognitive Development (ABCD; n=7693) to predict general intelligence. Our results demonstrate the advantage of the HL-edge network over the HL-node network when functional brain connectivity is considered as features. The HL-HGCNN outperforms the state-of-the-art graph neural networks (GNNs) approaches, such as GAT, BrainGNN, dGCN, BrainNetCNN, and Hypergraph NN. The functional connectivity features learned from the HL-HGCNN are meaningful in interpreting neural circuits related to general intelligence.

An explainable deep learning framework for characterizing and interpreting human brain states.

Deep learning approaches have been widely adopted in the medical image analysis field. However, a most of existing deep learning approaches focus on achieving promising performances such as classification, detection, and segmentation, and much less effort is devoted to the explanation of the designed models. Similarly, in the brain imaging field, many deep learning approaches have been designed and applied to characterize and predict human brain states. However, these models lack interpretation. In response, we propose a novel domain knowledge informed self-attention graph pooling-based (SAGPool) graph convolutional neural network to study human brain states. Specifically, the dense individualized and common connectivity-based cortical landmarks system (DICCCOL, structural brain connectivity profiles) and holistic atlases of functional networks and interactions system (HAFNI, functional brain connectivity profiles) are integrated with the SAGPool model to better characterize and interpret the brain states. Extensive experiments are designed and carried out on the large-scale human connectome project (HCP) Q1 and S1200 dataset. Promising brain state classification performances are observed (e.g., an average of 93.7% for seven-task classification and 100% for binary classification). In addition, the importance of the brain regions, which contributes most to the accurate classification, is successfully quantified and visualized. A thorough neuroscientific interpretation suggests that these extracted brain regions and their importance calculated from self-attention graph pooling layer offer substantial explainability.

Co-Attention Graph Pooling for Efficient Pairwise Graph Interaction Learning

Co-Attention Graph Pooling for Efficient Pairwise Graph Interaction Learning

Multi-granularity graph pooling for video-based person re-identification

The video-based person re-identification (ReID) aims to identify the given pedestrian video sequence across multiple non-overlapping cameras. To aggregate the temporal and spatial features of the video samples, the graph neural networks (GNNs) are introduced. However, existing graph-based models, like STGCN, perform the mean/max pooling on node features to obtain the graph representation, which neglect the graph topology and node importance. In this paper, we propose the graph pooling network (GPNet) to learn the multi-granularity graph representation for the video retrieval, where the graph pooling layer is implemented to downsample the graph. We construct a multi-granular graph by using node features learned from backbone, then implement multiple graph convolutional layers to perform the spatial and temporal aggregation on nodes. To downsample the graph, we propose a multi-head full attention graph pooling (MHFAPool) layer, which integrates the advantages of existing node clustering and node selection pooling methods. Specifically, MHFAPool first learns a full attention matrix for each pooled node, then obtains the principal eigenvector of the attention matrix via the power iteration algorithm, finally takes the softmax of the principal eigenvector as the aggregation coefficients. Extensive experiments demonstrate that our GPNet achieves the competitive results on four widely-used datasets, i.e., MARS, DukeMTMC-VideoReID, iLIDS-VID and PRID-2011.

GCNCPR-ACPs: a novel graph convolution network method for ACPs prediction

BackgroundAnticancer peptide (ACP) inhibits and kills tumor cells. Research on ACP is of great significance for the development of new drugs, and the prediction of ACPs and non-ACPs is the new hotspot.ResultsWe propose a new machine learning-based method named GCNCPR-ACPs (a Graph Convolutional Neural Network Method based on collapse pooling and residual network to predict the ACPs), which automatically and accurately predicts ACPs using residual graph convolution networks, differentiable graph pooling, and features extracted using peptide sequence information extraction. The GCNCPR-ACPs method can effectively capture different levels of node attributes for amino acid node representation learning, GCNCPR-ACPs uses node2vec and one-hot embedding methods to extract initial amino acid features for ACP prediction.ConclusionsExperimental results of ten-fold cross-validation and independent validation based on different metrics showed that GCNCPR-ACPs significantly outperformed state-of-the-art methods. Specifically, the evaluation indicators of Matthews Correlation Coefficient (MCC) and AUC of our predicator were 69.5% and 90%, respectively, which were 4.3% and 2% higher than those of the other predictors, respectively, in ten-fold cross-validation. And in the independent test, the scores of MCC and SP were 69.6% and 93.9%, respectively, which were 37.6% and 5.5% higher than those of the other predictors, respectively. The overall results showed that the GCNCPR-ACPs method proposed in the current paper can effectively predict ACPs.

CGUN-2A: Deep Graph Convolutional Network via Contrastive Learning for Large-Scale Zero-Shot Image Classification

Taxonomy illustrates that natural creatures can be classified with a hierarchy. The connections between species are explicit and objective and can be organized into a knowledge graph (KG). It is a challenging task to mine features of known categories from KG and to reason on unknown categories. Graph Convolutional Network (GCN) has recently been viewed as a potential approach to zero-shot learning. GCN enables knowledge transfer by sharing the statistical strength of nodes in the graph. More layers of graph convolution are stacked in order to aggregate the hierarchical information in the KG. However, the Laplacian over-smoothing problem will be severe as the number of GCN layers deepens, which leads the features between nodes toward a tendency to be similar and degrade the performance of zero-shot image classification tasks. We consider two parts to mitigate the Laplacian over-smoothing problem, namely reducing the invalid node aggregation and improving the discriminability among nodes in the deep graph network. We propose a top-k graph pooling method based on the self-attention mechanism to control specific node aggregation, and we introduce a dual structural symmetric knowledge graph additionally to enhance the representation of nodes in the latent space. Finally, we apply these new concepts to the recently widely used contrastive learning framework and propose a novel Contrastive Graph U-Net with two Attention-based graph pooling (Att-gPool) layers, CGUN-2A, which explicitly alleviates the Laplacian over-smoothing problem. To evaluate the performance of the method on complex real-world scenes, we test it on the large-scale zero-shot image classification dataset. Extensive experiments show the positive effect of allowing nodes to perform specific aggregation, as well as homogeneous graph comparison, in our deep graph network. We show how it significantly boosts zero-shot image classification performance. The Hit@1 accuracy is 17.5% relatively higher than the baseline model on the ImageNet21K dataset.

Graph Multihead Attention Pooling with Self-Supervised Learning.

Graph neural networks (GNNs), which work with graph-structured data, have attracted considerable attention and achieved promising performance on graph-related tasks. While the majority of existing GNN methods focus on the convolutional operation for encoding the node representations, the graph pooling operation, which maps the set of nodes into a coarsened graph, is crucial for graph-level tasks. We argue that a well-defined graph pooling operation should avoid the information loss of the local node features and global graph structure. In this paper, we propose a hierarchical graph pooling method based on the multihead attention mechanism, namely GMAPS, which compresses both node features and graph structure into the coarsened graph. Specifically, a multihead attention mechanism is adopted to arrange nodes into a coarsened graph based on their features and structural dependencies between nodes. In addition, to enhance the expressiveness of the cluster representations, a self-supervised mechanism is introduced to maximize the mutual information between the cluster representations and the global representation of the hierarchical graph. Our experimental results show that the proposed GMAPS obtains significant and consistent performance improvements compared with state-of-the-art baselines on six benchmarks from the biological and social domains of graph classification and reconstruction tasks.

Graph pooling via Dual-view Multi-level Infomax

Graph pooling is an essential component to improve the representation ability of graph neural networks. Existing pooling methods typically select a subset of nodes to generate an induced subgraph as the representation of the entire graph. However, they ignore the potential value of augmented views and cannot exploit the multi-level dependencies between representations. To address these problems, we propose Dual-view Multi-level Infomax Pooling (DMIPool), which can obtain and maximize the multi-level mutual information across dual-view representations. First, we generate a dual-view framework for graph pooling through data augmentation to encode hierarchical information and optimize representations. Next, we design a dynamic fusion mechanism to exploit both node features and graph topology information in dual views, and achieve comprehensive node-level and graph-level representations. Finally, to evaluate and further optimize the dual-view representations, we propose multi-level infomax, which maximizes mutual information of the representations across dual views at the graph–graph level, node–node level, and graph–node level. DMIPool can learn robust representations and preserve representative nodes by leveraging multi-level dependencies between dual-view representations. Comprehensive experimental results on 9 graph classification benchmark datasets demonstrated the superior performance of DMIPool compared with 10 advanced graph pooling methods.

Differentiate preterm and term infant brains and characterize the corresponding biomarkers via DICCCOL-based multi-modality graph neural networks.

Preterm birth is a worldwide problem that affects infants throughout their lives significantly. Therefore, differentiating brain disorders, and further identifying and characterizing the corresponding biomarkers are key issues to investigate the effects of preterm birth, which facilitates the interventions for neuroprotection and improves outcomes of prematurity. Until now, many efforts have been made to study the effects of preterm birth; however, most of the studies merely focus on either functional or structural perspective. In addition, an effective framework not only jointly studies the brain function and structure at a group-level, but also retains the individual differences among the subjects. In this study, a novel dense individualized and common connectivity-based cortical landmarks (DICCCOL)-based multi-modality graph neural networks (DM-GNN) framework is proposed to differentiate preterm and term infant brains and characterize the corresponding biomarkers. This framework adopts the DICCCOL system as the initialized graph node of GNN for each subject, utilizing both functional and structural profiles and effectively retaining the individual differences. To be specific, functional magnetic resonance imaging (fMRI) of the brain provides the features for the graph nodes, and brain fiber connectivity is utilized as the structural representation of the graph edges. Self-attention graph pooling (SAGPOOL)-based GNN is then applied to jointly study the function and structure of the brain and identify the biomarkers. Our results successfully demonstrate that the proposed framework can effectively differentiate the preterm and term infant brains. Furthermore, the self-attention-based mechanism can accurately calculate the attention score and recognize the most significant biomarkers. In this study, not only 87.6% classification accuracy is observed for the developing Human Connectome Project (dHCP) dataset, but also distinguishing features are explored and extracted. Our study provides a novel and uniform framework to differentiate brain disorders and characterize the corresponding biomarkers.

Exploring Self-Attention Graph Pooling With EEG-Based Topological Structure and Soft Label for Depression Detection

Electroencephalogram (EEG) has been widely used in neurological disease detection, i.e., major depressive disorder (MDD). Recently, some deep EEG-based MDD detection attempts have been proposed and achieved promising performance. These works, however, still suffer from the following limitations, such as insufficient exploration of the EEG-based topological structure, information loss caused by high-dimensional data compression, and under-estimation of intra-class difference and inter-class similarity. To solve these issues, we propose an EEG-based MDD detection model named <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u> elf-attention <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</u> raph <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</u> ooling with <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u> oft <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</u> abel (SGP-SL). Specifically, we explore the local and global connections among EEG channels to construct an EEG-based graph in advance. By leveraging multiple self-attention graph pooling modules, the constructed graph is then gradually refined, followed by graph pooling, to aggregate information from less-important nodes to more-important ones. In this way, the feature representation with better discriminability can be learned from EEG signals. In addition, the soft label strategy is also adopted to build the loss function, aiming to further enhance the feature discriminability. Experimental results on the MODMA dataset demonstrate the superiority of the proposed method. What's more, extensive ablation studies are conducted to verify the effectiveness of the proposed elements in our model.

Local-Global Graph Pooling via Mutual Information Maximization for Video-Paragraph Retrieval

As a task of cross-modal retrieval between long videos and paragraphs, video-paragraph retrieval is a non-trivial task. Unlike traditional video-text retrieval, the video in video-paragraph retrieval usually contains multiple clips. Each clip corresponds to a descriptive sentence; all the sentences constitute the corresponding paragraph of the video. Previous methods for video-paragraph retrieval usually encode videos and para-graphs from segment-level (clips and sentences) and overall-level (videos and paragraphs). However, there are also contents about actions and objects that exist in the segment. Hence, we propose a Local-Global Graph Pooling Network (LGGP) via Mutual Information Maximization for video-paragraph retrieval. Our model disentangles videos and paragraphs into four levels: overall-level, segment-level, motion-level, and object-level. We construct the Hierarchical Local Graph (segment-level, motion-level, and object-level) and the Hierarchical Global Graph (overall-level, segment-level, motion-level, and object-level), respectively, for semantic interaction among different levels. Meanwhile, to obtain hierarchical pooling features with fine-grained semantic information, we design hierarchical graph pooling methods to maximize the mutual information between pooling features and corresponding graph nodes. We evaluate our model on two video-paragraph retrieval datasets with three different video features. The experimental results show that our model establishes state-of-the-art results for video-paragraph retrieval. Our code will be released at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/PengchengZhang1997/LGGP</uri> .

NGD-Transformer: Navigation Geodesic Distance Positional Encoding with Self-Attention Pooling for Graph Transformer on 3D Triangle Mesh

Following the significant success of the transformer in NLP and computer vision, this paper attempts to extend it to 3D triangle mesh. The aim is to determine the shape’s global representation using the transformer and capture the inherent manifold information. To this end, this paper proposes a novel learning framework named Navigation Geodesic Distance Transformer (NGD-Transformer) for 3D mesh. Specifically, this approach combined farthest point sampling with the Voronoi segmentation algorithm to spawn uniform and non-overlapping manifold patches. However, the vertex number of these patches was inconsistent. Therefore, self-attention graph pooling is employed for sorting the vertices on each patch and screening out the most representative nodes, which were then reorganized according to their scores to generate tokens and their raw feature embeddings. To better exploit the manifold properties of the mesh, this paper further proposed a novel positional encoding called navigation geodesic distance positional encoding (NGD-PE), which encodes the geodesic distance between vertices relatively and spatial symmetrically. Subsequently, the raw feature embeddings and positional encodings were summed as input embeddings fed to the graph transformer encoder to determine the global representation of the shape. Experiments on several datasets were conducted, and the experimental results show the excellent performance of our proposed method.

A prior knowledge-embedded reinforcement learning method for real-time active power corrective control in complex power systems

With the increasing uncertainty and complexity of modern power grids, the real-time active power corrective control problem becomes intractable, bringing significant challenges to the stable operation of future power systems. To promote effective and efficient active power corrective control, a prior knowledge-embedded reinforcement learning method is proposed in this paper, to improve the performance of the deep reinforcement learning agent while maintaining the real-time control manner. The system-level feature is first established based on prior knowledge and cooperating with the equipment-level features, to provide a thorough description of the power network states. A global-local network structure is then constructed to integrate the two-level information accordingly by introducing the graph pooling method. Based on the multi-level representation of power system states, the Deep Q-learning from Demonstrations method is adopted to guide the deep reinforcement learning agent to learn from the expert policy along with the interactive improving process. Considering the infrequent corrective control actions in practice, the double-prioritized training mechanism combined with the λ-return is further developed to help the agent lay emphasis on learning from critical control experience. Simulation results demonstrate that the proposed method prevails over the conventional deep reinforcement learning methods in training efficiency and control effects, and has the potential to solve the complex active power corrective control problem in the future.

Learning Embedding for Signed Network in Social Media with Hierarchical Graph Pooling

Signed network embedding concentrates on learning fixed-length representations for nodes in signed networks with positive and negative links, which contributes to many downstream tasks in social media, such as link prediction. However, most signed network embedding approaches neglect hierarchical graph pooling in the networks, limiting the capacity to learn genuine signed graph topology. To overcome this limitation, this paper presents a unique deep learning-based Signed network embedding model with Hierarchical Graph Pooling (SHGP). To be more explicit, a hierarchical pooling mechanism has been developed to encode the high-level features of the networks. Moreover, a graph convolution layer is introduced to aggregate both positive and negative information from neighbor nodes, and the concatenation of two parts generates the final embedding of the nodes. Extensive experiments on three large real-world signed network datasets demonstrate the effectiveness and excellence of the proposed method.

Not all edges are peers: Accurate structure-aware graph pooling networks

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in graph-related tasks. For graph classification task, an elaborated pooling operator is vital for learning graph-level representations. Most pooling operators derived from existing GNNs generate a coarsen graph through ordering the nodes and selecting some top-ranked ones. However, these methods fail to explore the fundamental elements other than nodes in graphs, which may not efficiently utilize the structure information. Besides, all edges attached to the low-ranked nodes are discarded, which destroys graphs’ connectivity and loses information. Moreover, the selected nodes tend to concentrate on some substructures while overlooking information in others. To address these challenges, we propose a novel pooling operator called Accurate Structure-Aware Graph Pooling (ASPool), which can be integrated into various GNNs to learn graph-level representation. Specifically, ASPool adaptively retains a subset of edges to calibrate the graph structure and learns the abstracted representations, wherein all the edges are viewed as non-peers instead of simply connecting nodes. To preserve the graph’s connectivity, we further introduce the selection strategy considering both top-ranked nodes and dropped edges. Additionally, ASPool performs a two-stage calculation process to promise that the sampled nodes are distributed throughout the graph. Experiment results on 9 widely used benchmarks show that ASPool achieves superior performance over the state-of-the-art graph representation learning methods.