Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In general, since real-world graphs are often complex mixtures of diverse subgraph patterns, learning a universal spectral filter on the graph from the global perspective as in most current works may still suffer from great difficulty in adapting to the variation of local patterns. On the basis of the theoretical analysis of local patterns, we rethink the existing spectral filtering methods and propose the node-oriented spectral filtering for graph neural network (namely NFGNN). By estimating the node-oriented spectral filter for each node, NFGNN is provided with the capability of precise local node positioning via the generalized translated operator, thus discriminating the variations of local homophily patterns adaptively. Meanwhile, the utilization of re-parameterization brings a good trade-off between global consistency and local sensibility for learning the node-oriented spectral filters. Furthermore, we theoretically analyze the localization property of NFGNN, demonstrating that the signal after adaptive filtering is still positioned around the corresponding node. Extensive experimental results demonstrate that the proposed NFGNN achieves more favorable performance.
Node classification for graph-structured data aims to classify nodes whose labels are unknown. While studies on static graphs are prevalent, few studies have focused on dynamic graph node classification. Node classification on dynamic graphs is challenging for two reasons. First, the model needs to capture both structural and temporal information, particularly on dynamic graphs with a long history and require large receptive fields. Second, model scalability becomes a significant concern as the size of the dynamic graph increases. To address these problems, we propose the Time Augmented Dynamic Graph Neural Network (TADGNN) framework. TADGNN consists of two modules: 1) a time augmentation module that captures the temporal evolution of nodes across time structurally, creating a time-augmented spatio-temporal graph, and 2) an information propagation module that learns the dynamic representations for each node across time using the constructed time-augmented graph. We perform node classification experiments on four dynamic graph benchmarks. Experimental results demonstrate that TADGNN framework outperforms several static and dynamic state-of-the-art (SOTA) GNN models while demonstrating superior scalability. We also conduct theoretical and empirical analyses to validate the efficiency of the proposed method. Our code is available at https://sites.google.com/view/tadgnn.
This paper presents a Temporal Graph Neural Network (TGNN) framework for detection and localization of false data injection and ramp attacks on the system state in smart grids. Capturing the topological information of the system through the GNN framework along with the state measurements can improve the performance of the detection mechanism. The problem is formulated as a classification problem through a GNN with message passing mechanism to identify abnormal measurements. The residual block used in the aggregation process of message passing and the gated recurrent unit can lead to improved computational time and performance. The performance of the proposed model has been evaluated through extensive simulations of power system states and attack scenarios showing promising performance. The sensitivity of the model to intensity and location of the attacks and model's detection delay versus detection accuracy have also been evaluated.
Graph convolutional networks (GCNs) have achieved great success in graph representation learning by extracting high-level features from nodes and their topology. Since GCNs generally follow a message-passing mechanism, each node aggregates information from its first-order neighbour to update its representation. As a result, the representations of nodes with edges between them should be positively correlated and thus can be considered positive samples. However, there are more non-neighbour nodes in the whole graph, which provide diverse and useful information for the representation update. Two non-adjacent nodes usually have different representations, which can be seen as negative samples. Besides the node representations, the structural information of the graph is also crucial for learning. In this paper, we used quality-diversity decomposition in determinant point processes (DPP) to obtain diverse negative samples. When defining a distribution on diverse subsets of all non-neighbouring nodes, we incorporate both graph structure information and node representations. Since the DPP sampling process requires matrix eigenvalue decomposition, we propose a new shortest-path-base method to improve computational efficiency. Finally, we incorporate the obtained negative samples into the graph convolution operation. The ideas are evaluated empirically in experiments on node classification tasks. These experiments show that the newly proposed methods not only improve the overall performance of standard representation learning but also significantly alleviate over-smoothing problems.
Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the original graph structure data is available. However, recent studies have shown that GNNs are vulnerable to the complex underlying structure of the graph, making it necessary to learn comprehensive and robust graph structures for downstream tasks, rather than relying only on the raw graph structure. In light of this, we seek to learn optimal graph structures for downstream tasks and propose a novel framework for semi-supervised classification. Specifically, based on the structural context information of graph and node representations, we encode the complex interactions in semantics and generate semantic graphs to preserve the global structure. Moreover, we develop a novel multi-measure attention layer to optimize the similarity rather than prescribing it a priori, so that the similarity can be adaptively evaluated by integrating measures. These graphs are fused and optimized together with GNN towards semi-supervised classification objective. Extensive experiments and ablation studies on six real-world datasets clearly demonstrate the effectiveness of our proposed model and the contribution of each component.
Training labels for graph embedding algorithms could be costly to obtain in many practical scenarios. Active learning (AL) algorithms are very helpful to obtain the most useful labels for training while keeping the total number of label queries under a certain budget. The existing Active Graph Embedding framework proposes to use centrality score, density score, and entropy score to evaluate the value of unlabeled nodes, and it has been shown to be capable of bringing some improvement to the node classification tasks of Graph Convolutional Networks. However, when evaluating the importance of unlabeled nodes, it fails to consider the influence of existing labeled nodes on the value of unlabeled nodes. In other words, given the same unlabeled node, the computed informative score is always the same and is agnostic to the labeled node set. With the aim to address this limitation, in this work, we introduce 3 dissimilarity-based information scores for active learning: feature dissimilarity score (FDS), structure dissimilarity score (SDS), and embedding dissimilarity score (EDS). We find out that those three scores are able to take the influence of the labeled set on the value of unlabeled candidates into consideration, boosting our AL performance. According to experiments, our newly proposed scores boost the classification accuracy by 2.1% on average and are capable of generalizing to different Graph Neural Network architectures.
The prevalence of tree-like structures, encompassing hierarchical structures and power law distributions, exists extensively in real-world applications, including recommendation systems, ecosystems, financial networks, social networks, etc. Recently, the exploitation of hyperbolic space for tree-likeness modeling has garnered considerable attention owing to its exponential growth volume. Compared to the flat Euclidean space, the curved hyperbolic space provides a more amenable and embeddable room, especially for datasets exhibiting implicit tree-like architectures. However, the intricate nature of real-world tree-like data presents a considerable challenge, as it frequently displays a heterogeneous composition of tree-like, flat, and circular regions. The direct embedding of such heterogeneous structures into a homogeneous embedding space (i.e., hyperbolic space) inevitably leads to heavy distortions. To mitigate the aforementioned shortage, this study endeavors to explore the curvature between discrete structure and continuous learning space, aiming at encoding the message conveyed by the network topology in the learning process, thereby improving tree-likeness modeling. To the end, a curvature-aware hyperbolic graph convolutional neural network, \{kappa}HGCN, is proposed, which utilizes the curvature to guide message passing and improve long-range propagation. Extensive experiments on node classification and link prediction tasks verify the superiority of the proposal as it consistently outperforms various competitive models by a large margin.
Node classification on graph data is a major problem, and various graph neural networks (GNNs) have been proposed. Variants of GNNs such as H2GCN and CPF outperform graph convolutional networks (GCNs) by improving on the weaknesses of the traditional GNN. However, there are some graph data which these GNN variants fail to perform well than other GNNs in the node classification task. This is because H2GCN has a feature thinning on graph data with high average degree, and CPF gives rise to a problem about label-propagation suitability. Accordingly, we propose a hierarchical model selection framework (HMSF) that selects an appropriate GNN model by analyzing the indicators of each graph data. In the experiment, we show that the model selected by our HMSF achieves high performance on node classification for various types of graph data.
Graph Neural Networks (GNNs) are prominent in handling sparse and unstructured data efficiently and effectively. Specifically, GNNs were shown to be highly effective for node classification tasks, where labelled information is available for only a fraction of the nodes. Typically, the optimization process, through the objective function, considers only labelled nodes while ignoring the rest. In this paper, we propose novel objective terms for the training of GNNs for node classification, aiming to exploit all the available data and improve accuracy. Our first term seeks to maximize the mutual information between node and label features, considering both labelled and unlabelled nodes in the optimization process. Our second term promotes anisotropic smoothness in the prediction maps. Lastly, we propose a cross-validating gradients approach to enhance the learning from labelled data. Our proposed objectives are general and can be applied to various GNNs and require no architectural modifications. Extensive experiments demonstrate our approach using popular GNNs like GCN, GAT and GCNII, reading a consistent and significant accuracy improvement on 10 real-world node classification datasets.
Graph neural networks (GNNs) have been utilized for various natural language processing (NLP) tasks lately. The ability to encode corpus-wide features in graph representation made GNN models popular in various tasks such as document classification. One major shortcoming of such models is that they mainly work on homogeneous graphs, while representing text datasets as graphs requires several node types which leads to a heterogeneous schema. In this paper, we propose a transductive hybrid approach composed of an unsupervised node representation learning model followed by a node classification/edge prediction model. The proposed model is capable of processing heterogeneous graphs to produce unified node embeddings which are then utilized for node classification or link prediction as the downstream task. The proposed model is developed to classify stock market technical analysis reports, which to our knowledge is the first work in this domain. Experiments, which are carried away using a constructed dataset, demonstrate the ability of the model in embedding extraction and the downstream tasks.
Graph Neural Networks (GNNs) are able to achieve high classification accuracy on many important real world datasets, but provide no rigorous notion of predictive uncertainty. Quantifying the confidence of GNN models is difficult due to the dependence between datapoints induced by the graph structure. We leverage recent advances in conformal prediction to construct prediction sets for node classification in inductive learning scenarios. We do this by taking an existing approach for conformal classification that relies on \textit{exchangeable} data and modifying it by appropriately weighting the conformal scores to reflect the network structure. We show through experiments on standard benchmark datasets using popular GNN models that our approach provides tighter and better calibrated prediction sets than a naive application of conformal prediction.
Node classification is an important task to solve in graph-based learning. Even though a lot of work has been done in this field, imbalance is neglected. Real-world data is not perfect, and is imbalanced in representations most of the times. Apart from text and images, data can be represented using graphs, and thus addressing the imbalance in graphs has become of paramount importance. In the context of node classification, one class has less examples than others. Changing data composition is a popular way to address the imbalance in node classification. This is done by resampling the data to balance the dataset. However, that can sometimes lead to loss of information or add noise to the dataset. Therefore, in this work, we implicitly solve the problem by changing the model loss. Specifically, we study how attention networks can help tackle imbalance. Moreover, we observe that using a regularizer to assign larger weights to minority nodes helps to mitigate this imbalance. We achieve State of the Art results than the existing methods on several standard citation benchmark datasets.
Heterogeneous information networks (HINs) are widely employed for describing real-world data with intricate entities and relationships. To automatically utilize their semantic information, graph neural architecture search has recently been developed on various tasks of HINs. Existing works, on the other hand, show weaknesses in instability and inflexibility. To address these issues, we propose a novel method called Partial Message Meta Multigraph search (PMMM) to automatically optimize the neural architecture design on HINs. Specifically, to learn how graph neural networks (GNNs) propagate messages along various types of edges, PMMM adopts an efficient differentiable framework to search for a meaningful meta multigraph, which can capture more flexible and complex semantic relations than a meta graph. The differentiable search typically suffers from performance instability, so we further propose a stable algorithm called partial message search to ensure that the searched meta multigraph consistently surpasses the manually designed meta-structures, i.e., meta-paths. Extensive experiments on six benchmark datasets over two representative tasks, including node classification and recommendation, demonstrate the effectiveness of the proposed method. Our approach outperforms the state-of-the-art heterogeneous GNNs, finds out meaningful meta multigraphs, and is significantly more stable.
Graph neural networks (GNNs) are commonly used in semi-supervised settings. Previous research has primarily focused on finding appropriate graph filters (e.g. aggregation methods) to perform well on both homophilic and heterophilic graphs. While these methods are effective, they can still suffer from the sparsity of node features, where the initial data contain few non-zero elements. This can lead to overfitting in certain dimensions in the first projection matrix, as training samples may not cover the entire range of graph filters (hyperplanes). To address this, we propose a novel data augmentation strategy. Specifically, by flipping both the initial features and hyperplane, we create additional space for training, which leads to more precise updates of the learnable parameters and improved robustness for unseen features during inference. To the best of our knowledge, this is the first attempt to mitigate the overfitting caused by the initial features. Extensive experiments on real-world datasets show that our proposed technique increases node classification accuracy by up to 46.5% relatively.
Graph neural networks (GNNs) are one of the most popular research topics for deep learning. GNN methods typically have been designed on top of the graph signal processing theory. In particular, diffusion equations have been widely used for designing the core processing layer of GNNs, and therefore they are inevitably vulnerable to the notorious oversmoothing problem. Recently, a couple of papers paid attention to reaction equations in conjunctions with diffusion equations. However, they all consider limited forms of reaction equations. To this end, we present a reaction-diffusion equation-based GNN method that considers all popular types of reaction equations in addition to one special reaction equation designed by us. To our knowledge, our paper is one of the most comprehensive studies on reaction-diffusion equation-based GNNs. In our experiments with 9 datasets and 28 baselines, our method, called GREAD, outperforms them in a majority of cases. Further synthetic data experiments show that it mitigates the oversmoothing problem and works well for various homophily rates.
Heterogeneous graph neural networks (HGNNs) were proposed for representation learning on structural data with multiple types of nodes and edges. To deal with the performance degradation issue when HGNNs become deep, researchers combine metapaths into HGNNs to associate nodes closely related in semantics but far apart in the graph. However, existing metapath-based models suffer from either information loss or high computation costs. To address these problems, we present a novel Metapath Context Convolution-based Heterogeneous Graph Neural Network (MECCH). MECCH leverages metapath contexts, a new kind of graph structure that facilitates lossless node information aggregation while avoiding any redundancy. Specifically, MECCH applies three novel components after feature preprocessing to extract comprehensive information from the input graph efficiently: (1) metapath context construction, (2) metapath context encoder, and (3) convolutional metapath fusion. Experiments on five real-world heterogeneous graph datasets for node classification and link prediction show that MECCH achieves superior prediction accuracy compared with state-of-the-art baselines with improved computational efficiency.
In recent years, Graph Neural Networks (GNNs) have been popular in graph representation learning which assumes the homophily property, i.e., the connected nodes have the same label or have similar features. However, they may fail to generalize into the heterophilous graphs which in the low/medium level of homophily. Existing methods tend to address this problem by enhancing the intra-class information extraction, i.e., either by designing better GNNs to improve the model effectiveness, or re-designing the graph structures to incorporate more potential intra-class nodes from distant hops. Despite the success, we observe two aspects that can be further improved: (a) enhancing the ego feature information extraction from node itself which is more reliable in extracting the intra-class information; (b) designing node-wise GNNs can better adapt to the nodes with different homophily ratios. In this paper, we propose a novel method IIE-GNN (Intra-class Information Enhanced Graph Neural Networks) to achieve two improvements. A unified framework is proposed based on the literature, in which the intra-class information from the node itself and neighbors can be extracted based on seven carefully designed blocks. With the help of neural architecture search (NAS), we propose a novel search space based on the framework, and then provide an architecture predictor to design GNNs for each node. We further conduct experiments to show that IIE-GNN can improve the model performance by designing node-wise GNNs to enhance intra-class information extraction.
The success of Graph Neural Networks (GNN) in learning on non-Euclidean data arouses many subtopics, such as Label-inputted GNN (LGNN) and Implicit GNN (IGNN). LGNN, explicitly inputting supervising information (a.k.a. labels) in GNN, integrates label propagation to achieve superior performance, but with the dilemma between its propagating distance and adaptiveness. IGNN, outputting an equilibrium point by iterating its network infinite times, exploits information in the entire graph to capture long-range dependencies, but with its network constrained to guarantee the existence of the equilibrium. This work unifies the two subdomains by interpreting LGNN in the theory of IGNN and reducing prevailing LGNNs to the form of IGNN. The unification facilitates the exchange between the two subdomains and inspires more studies. Specifically, implicit differentiation of IGNN is introduced to LGNN to differentiate its infinite-range label propagation with constant memory, making the propagation both distant and adaptive. Besides, the masked label strategy of LGNN is proven able to guarantee the well-posedness of IGNN in a network-agnostic manner, granting its network more complex and thus more expressive. Combining the advantages of LGNN and IGNN, Label-inputted Implicit GNN (LI-GNN) is proposed. It can be widely applied to any specific GNN to boost its performance. Node classification experiments on two synthesized and six real-world datasets demonstrate its effectiveness. Code is available at https://github.com/cf020031308/LI-GNN
The decoupled Graph Convolutional Network (GCN), a recent development of GCN that decouples the neighborhood aggregation and feature transformation in each convolutional layer, has shown promising performance for graph representation learning. Existing decoupled GCNs first utilize a simple neural network (e.g., MLP) to learn the hidden features of the nodes, then propagate the learned features on the graph with fixed steps to aggregate the information of multi-hop neighborhoods. Despite effectiveness, the aggregation operation, which requires the whole adjacency matrix as the input, is involved in the model training, causing high training cost that hinders its potential on larger graphs. On the other hand, due to the independence of node attributes as the input, the neural networks used in decoupled GCNs are very simple, and advanced techniques cannot be applied to the modeling. To this end, we further liberate the aggregation operation from the decoupled GCN and propose a new paradigm of GCN, termed Neighborhood Convolutional Network (NCN), that utilizes the neighborhood aggregation result as the input, followed by a special convolutional neural network tailored for extracting expressive node representations from the aggregation input. In this way, the model could inherit the merit of decoupled GCN for aggregating neighborhood information, at the same time, develop much more powerful feature learning modules. A training strategy called mask training is incorporated to further boost the model performance. Extensive results demonstrate the effectiveness of our model for the node classification task on diverse homophilic graphs and heterophilic graphs.
We introduce a new benchmark dataset, Placenta, for node classification in an underexplored domain: predicting microanatomical tissue structures from cell graphs in placenta histology whole slide images. This problem is uniquely challenging for graph learning for a few reasons. Cell graphs are large (>1 million nodes per image), node features are varied (64-dimensions of 11 types of cells), class labels are imbalanced (9 classes ranging from 0.21% of the data to 40.0%), and cellular communities cluster into heterogeneously distributed tissues of widely varying sizes (from 11 nodes to 44,671 nodes for a single structure). Here, we release a dataset consisting of two cell graphs from two placenta histology images totalling 2,395,747 nodes, 799,745 of which have ground truth labels. We present inductive benchmark results for 7 scalable models and show how the unique qualities of cell graphs can help drive the development of novel graph neural network architectures.