Majority of the existing graph neural networks (GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods map to similar embeddings in those networks. This limitation prevents accurate performance in predictive tasks that rely on position information. In this paper, we develop GraphReach, a position-aware inductive GNN that captures the global positions of nodes through reachability estimations with respect to a set of anchor nodes. The anchors are strategically selected so that reachability estimations across all the nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and, consequently, develop a greedy (1-1/e) approximation heuristic. Empirical evaluation against state-of-the-art GNN architectures reveal that GraphReach provides up to 40% relative improvement in accuracy. In addition, it is more robust to adversarial attacks.
Recent graph neural networks (GNN) has achieved remarkable performance in node representation learning. One key factor of GNN's success is the \emph{smoothness} property on node representations. Despite this, most GNN models are fragile to the perturbations on graph inputs and could learn unreliable node representations. In this paper, we study how to learn node representations against perturbations in GNN. Specifically, we consider that a node representation should remain stable under slight perturbations on the input, and node representations from different structures should be identifiable, which two are termed as the \emph{stability} and \emph{identifiability} on node representations, respectively. To this end, we propose a novel model called Stability-Identifiability GNN Against Perturbations (SIGNNAP) that learns reliable node representations in an unsupervised manner. SIGNNAP formalizes the \emph{stability} and \emph{identifiability} by a contrastive objective and preserves the \emph{smoothness} with existing GNN backbones. The proposed method is a generic framework that can be equipped with many other backbone models (e.g. GCN, GraphSage and GAT). Extensive experiments on six benchmarks under both transductive and inductive learning setups of node classification demonstrate the effectiveness of our method. Codes and data are available online:~\url{https://github.com/xuChenSJTU/SIGNNAP-master-online}
Increasing the depth of GCN, which is expected to permit more expressivity, is shown to incur performance detriment especially on node classification. The main cause of this lies in over-smoothing. The over-smoothing issue drives the output of GCN towards a space that contains limited distinguished information among nodes, leading to poor expressivity. Several works on refining the architecture of deep GCN have been proposed, but it is still unknown in theory whether or not these refinements are able to relieve over-smoothing. In this paper, we first theoretically analyze how general GCNs act with the increase in depth, including generic GCN, GCN with bias, ResGCN, and APPNP. We find that all these models are characterized by a universal process: all nodes converging to a cuboid. Upon this theorem, we propose DropEdge to alleviate over-smoothing by randomly removing a certain number of edges at each training epoch. Theoretically, DropEdge either reduces the convergence speed of over-smoothing or relieves the information loss caused by dimension collapse. Experimental evaluations on simulated dataset have visualized the difference in over-smoothing between different GCNs. Moreover, extensive experiments on several real benchmarks support that DropEdge consistently improves the performance on a variety of both shallow and deep GCNs.
In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks. More specifically, we develop optimization algorithms for the graph-based semi-supervised learning by employing the natural gradient information in the optimization process. This allows us to efficiently exploit the geometry of the underlying statistical model or parameter space for optimization and inference. To the best of our knowledge, this is the first work that has utilized the natural gradient for the optimization of graph neural networks that can be extended to other semi-supervised problems. Efficient computations algorithms are developed and extensive numerical studies are conducted to demonstrate the superior performance of our algorithms over existing algorithms such as ADAM and SGD.
Network embedding approaches are gaining momentum to analyse a large variety of networks. Indeed, these approaches have demonstrated their efficiency for tasks such as community detection, node classification, and link prediction. However, very few network embedding methods have been specifically designed to handle multiplex networks, i.e. networks composed of different layers sharing the same set of nodes but having different types of edges. Moreover, to our knowledge, existing approaches cannot embed multiple nodes from multiplex-heterogeneous networks, i.e. networks composed of several layers containing both different types of nodes and edges. In this study, we propose MultiVERSE, an extension of the VERSE method with Random Walks with Restart on Multiplex (RWR-M) and Multiplex-Heterogeneous (RWR-MH) networks. MultiVERSE is a fast and scalable method to learn node embeddings from multiplex and multiplex-heterogeneous networks. We evaluate MultiVERSE on several biological and social networks and demonstrate its efficiency. MultiVERSE indeed outperforms most of the other methods in the tasks of link prediction and network reconstruction for multiplex network embedding, and is also efficient in the task of link prediction for multiplex-heterogeneous network embedding. Finally, we apply MultiVERSE to study rare disease-gene associations using link prediction and clustering. MultiVERSE is freely available on github at https://github.com/Lpiol/MultiVERSE.
The core operation of current Graph Neural Networks (GNNs) is the aggregation enabled by the graph Laplacian or message passing, which filters the neighborhood node information. Though effective for various tasks, in this paper, we show that they are potentially a problematic factor underlying all GNN methods for learning on certain datasets, as they force the node representations similar, making the nodes gradually lose their identity and become indistinguishable. Hence, we augment the aggregation operations with their dual, i.e. diversification operators that make the node more distinct and preserve the identity. Such augmentation replaces the aggregation with a two-channel filtering process that, in theory, is beneficial for enriching the node representations. In practice, the proposed two-channel filters can be easily patched on existing GNN methods with diverse training strategies, including spectral and spatial (message passing) methods. In the experiments, we observe desired characteristics of the models and significant performance boost upon the baselines on 9 node classification tasks.
Graph Neural Networks (GNNs) have been widely applied to fraud detection problems in recent years, revealing the suspiciousness of nodes by aggregating their neighborhood information via different relations. However, few prior works have noticed the camouflage behavior of fraudsters, which could hamper the performance of GNN-based fraud detectors during the aggregation process. In this paper, we introduce two types of camouflages based on recent empirical studies, i.e., the feature camouflage and the relation camouflage. Existing GNNs have not addressed these two camouflages, which results in their poor performance in fraud detection problems. Alternatively, we propose a new model named CAmouflage-REsistant GNN (CARE-GNN), to enhance the GNN aggregation process with three unique modules against camouflages. Concretely, we first devise a label-aware similarity measure to find informative neighboring nodes. Then, we leverage reinforcement learning (RL) to find the optimal amounts of neighbors to be selected. Finally, the selected neighbors across different relations are aggregated together. Comprehensive experiments on two real-world fraud datasets demonstrate the effectiveness of the RL algorithm. The proposed CARE-GNN also outperforms state-of-the-art GNNs and GNN-based fraud detectors. We integrate all GNN-based fraud detectors as an opensource toolbox: https://github.com/safe-graph/DGFraud. The CARE-GNN code and datasets are available at https://github.com/YingtongDou/CARE-GNN.
Network representation learning (NRL) plays a vital role in a variety of tasks such as node classification and link prediction. It aims to learn low-dimensional vector representations for nodes based on network structures or node attributes. While embedding techniques on complete networks have been intensively studied, in real-world applications, it is still a challenging task to collect complete networks. To bridge the gap, in this paper, we propose a Deep Incomplete Network Embedding method, namely DINE. Specifically, we first complete the missing part including both nodes and edges in a partially observable network by using the expectation-maximization framework. To improve the embedding performance, we consider both network structures and node attributes to learn node representations. Empirically, we evaluate DINE over three networks on multi-label classification and link prediction tasks. The results demonstrate the superiority of our proposed approach compared against state-of-the-art baselines.
Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QGNN}.
Graph neural networks (GNNs) have demonstrated strong performance on a wide variety of tasks due to their ability to model non-uniform structured data. Despite their promise, there exists little research exploring methods to make them more efficient at inference time. In this work, we explore the viability of training quantized GNNs, enabling the usage of low precision integer arithmetic during inference. We identify the sources of error that uniquely arise when attempting to quantize GNNs, and propose an architecturally-agnostic method, Degree-Quant, to improve performance over existing quantization-aware training baselines commonly used on other architectures, such as CNNs. We validate our method on six datasets and show, unlike previous attempts, that models generalize to unseen graphs. Models trained with Degree-Quant for INT8 quantization perform as well as FP32 models in most cases; for INT4 models, we obtain up to 26% gains over the baselines. Our work enables up to 4.7x speedups on CPU when using INT8 arithmetic.
Multivariate relations are general in various types of networks, such as biological networks, social networks, transportation networks, and academic networks. Due to the principle of ternary closures and the trend of group formation, the multivariate relationships in social networks are complex and rich. Therefore, in graph learning tasks of social networks, the identification and utilization of multivariate relationship information are more important. Existing graph learning methods are based on the neighborhood information diffusion mechanism, which often leads to partial omission or even lack of multivariate relationship information, and ultimately affects the accuracy and execution efficiency of the task. To address these challenges, this paper proposes the multivariate relationship aggregation learning (MORE) method, which can effectively capture the multivariate relationship information in the network environment. By aggregating node attribute features and structural features, MORE achieves higher accuracy and faster convergence speed. We conducted experiments on one citation network and five social networks. The experimental results show that the MORE model has higher accuracy than the GCN (Graph Convolutional Network) model in node classification tasks, and can significantly reduce time cost.
To deal with irregular data structure, graph convolution neural networks have been developed by a lot of data scientists. However, data scientists just have concentrated primarily on developing deep neural network method for un-directed graph. In this paper, we will present the novel neural network method for directed hypergraph. In the other words, we will develop not only the novel directed hypergraph neural network method but also the novel directed hypergraph based semi-supervised learning method. These methods are employed to solve the node classification task. The two datasets that are used in the experiments are the cora and the citeseer datasets. Among the classic directed graph based semi-supervised learning method, the novel directed hypergraph based semi-supervised learning method, the novel directed hypergraph neural network method that are utilized to solve this node classification task, we recognize that the novel directed hypergraph neural network achieves the highest accuracies.
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction , etc. However, most of the existing approaches start from the binary relationship (i.e., edges) in the graph and have not leveraged the higher order local structure (i.e., motifs) of the graph. Here, we propose mGCMN -- a novel framework which utilizes node feature information and the higher order local structure of the graph to effectively generate node embeddings for previously unseen data. Through research we have found that different types of networks have different key motifs. And the advantages of our method over the baseline methods have been demonstrated in a large number of experiments on citation network and social network datasets. At the same time, a positive correlation between increase of the classification accuracy and the clustering coefficient is revealed. It is believed that using high order structural information can truly manifest the potential of the network, which will greatly improve the learning efficiency of the graph neural network and promote a brand-new learning mode establishment.
In order to perform network analysis tasks, representations that capture the most relevant information in the graph structure are needed. However, existing methods do not learn representations that can be interpreted in a straightforward way and that are robust to perturbations to the graph structure. In this work, we address these two limitations by proposing node2coords, a representation learning algorithm for graphs, which learns simultaneously a low-dimensional space and coordinates for the nodes in that space. The patterns that span the low dimensional space reveal the graph's most important structural information. The coordinates of the nodes reveal the proximity of their local structure to the graph structural patterns. In order to measure this proximity by taking into account the underlying graph, we propose to use Wasserstein distances. We introduce an autoencoder that employs a linear layer in the encoder and a novel Wasserstein barycentric layer at the decoder. Node connectivity descriptors, that capture the local structure of the nodes, are passed through the encoder to learn the small set of graph structural patterns. In the decoder, the node connectivity descriptors are reconstructed as Wasserstein barycenters of the graph structural patterns. The optimal weights for the barycenter representation of a node's connectivity descriptor correspond to the coordinates of that node in the low-dimensional space. Experimental results demonstrate that the representations learned with node2coords are interpretable, lead to node embeddings that are stable to perturbations of the graph structure and achieve competitive or superior results compared to state-of-the-art methods in node classification.
Graph neural networks (GNNs) achieve remarkable success in graph-based semi-supervised node classification, leveraging the information from neighboring nodes to improve the representation learning of target node. The success of GNNs at node classification depends on the assumption that connected nodes tend to have the same label. However, such an assumption does not always work, limiting the performance of GNNs at node classification. In this paper, we propose label-consistency based graph neural network(LC-GNN), leveraging node pairs unconnected but with the same labels to enlarge the receptive field of nodes in GNNs. Experiments on benchmark datasets demonstrate the proposed LC-GNN outperforms traditional GNNs in graph-based semi-supervised node classification.We further show the superiority of LC-GNN in sparse scenarios with only a handful of labeled nodes.
Entity alignment to find equivalent entities in cross-lingual Knowledge Graphs (KGs) plays a vital role in automatically integrating multiple KGs. Existing translation-based entity alignment methods jointly model the cross-lingual knowledge and monolingual knowledge into one unified optimization problem. On the other hand, the Graph Neural Network (GNN) based methods either ignore the node differentiations, or represent relation through entity or triple instances. They all fail to model the meta semantics embedded in relation nor complex relations such as n-to-n and multi-graphs. To tackle these challenges, we propose a novel Meta Relation Aware Entity Alignment (MRAEA) to directly model cross-lingual entity embeddings by attending over the node's incoming and outgoing neighbors and its connected relations' meta semantics. In addition, we also propose a simple and effective bi-directional iterative strategy to add new aligned seeds during training. Our experiments on all three benchmark entity alignment datasets show that our approach consistently outperforms the state-of-the-art methods, exceeding by 15%-58% on Hit@1. Through an extensive ablation study, we validate that the proposed meta relation aware representations, relation aware self-attention and bi-directional iterative strategy of new seed selection all make contributions to significant performance improvement. The code is available at https://github.com/MaoXinn/MRAEA.
Graph neural networks have achieved great success in learning node representations for graph tasks such as node classification and link prediction. Graph representation learning requires graph pooling to obtain graph representations from node representations. It is challenging to develop graph pooling methods due to the variable sizes and isomorphic structures of graphs. In this work, we propose to use second-order pooling as graph pooling, which naturally solves the above challenges. In addition, compared to existing graph pooling methods, second-order pooling is able to use information from all nodes and collect second-order statistics, making it more powerful. We show that direct use of second-order pooling with graph neural networks leads to practical problems. To overcome these problems, we propose two novel global graph pooling methods based on second-order pooling; namely, bilinear mapping and attentional second-order pooling. In addition, we extend attentional second-order pooling to hierarchical graph pooling for more flexible use in GNNs. We perform thorough experiments on graph classification tasks to demonstrate the effectiveness and superiority of our proposed methods. Experimental results show that our methods improve the performance significantly and consistently.
Learning unsupervised node embeddings facilitates several downstream tasks such as node classification and link prediction. A node embedding is universal if it is designed to be used by and benefit various downstream tasks. This work introduces PanRep, a graph neural network (GNN) model, for unsupervised learning of universal node representations for heterogenous graphs. PanRep consists of a GNN encoder that obtains node embeddings and four decoders, each capturing different topological and node feature properties. Abiding to these properties the novel unsupervised framework learns universal embeddings applicable to different downstream tasks. PanRep can be furthered fine-tuned to account for possible limited labels. In this operational setting PanRep is considered as a pretrained model for extracting node embeddings of heterogenous graph data. PanRep outperforms all unsupervised and certain supervised methods in node classification and link prediction, especially when the labeled data for the supervised methods is small. PanRep-FT (with fine-tuning) outperforms all other supervised approaches, which corroborates the merits of pretraining models. Finally, we apply PanRep-FT for discovering novel drugs for Covid-19. We showcase the advantage of universal embeddings in drug repurposing and identify several drugs used in clinical trials as possible drug candidates.
Graph neural networks have shown significant success in the field of graph representation learning. Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Nevertheless, one layer of these neighborhood aggregation methods only consider immediate neighbors, and the performance decreases when going deeper to enable larger receptive fields. Several recent studies attribute this performance deterioration to the over-smoothing issue, which states that repeated propagation makes node representations of different classes indistinguishable. In this work, we study this observation systematically and develop new insights towards deeper graph neural networks. First, we provide a systematical analysis on this issue and argue that the key factor compromising the performance significantly is the entanglement of representation transformation and propagation in current graph convolution operations. After decoupling these two operations, deeper graph neural networks can be used to learn graph node representations from larger receptive fields. We further provide a theoretical analysis of the above observation when building very deep models, which can serve as a rigorous and gentle description of the over-smoothing issue. Based on our theoretical and empirical analysis, we propose Deep Adaptive Graph Neural Network (DAGNN) to adaptively incorporate information from large receptive fields. A set of experiments on citation, co-authorship, and co-purchase datasets have confirmed our analysis and insights and demonstrated the superiority of our proposed methods.
Despite achieving strong performance in semi-supervised node classification task, graph neural networks (GNNs) are vulnerable to adversarial attacks, similar to other deep learning models. Existing researches focus on developing either robust GNN models or attack detection methods against adversarial attacks on graphs. However, little research attention is paid to the potential and practice of immunization to adversarial attacks on graphs. In this paper, we propose and formulate the graph adversarial immunization problem, i.e., vaccinating an affordable fraction of node pairs, connected or unconnected, to improve the certifiable robustness of graph against any admissible adversarial attack. We further propose an effective algorithm, called AdvImmune, which optimizes with meta-gradient in a discrete way to circumvent the computationally expensive combinatorial optimization when solving the adversarial immunization problem. Experiments are conducted on two citation networks and one social network. Experimental results demonstrate that the proposed AdvImmune method remarkably improves the ratio of robust nodes by 12%, 42%, 65%, with an affordable immune budget of only 5% edges.