Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of distinguishing non-isomorphic graphs. However, it was recently shown that this test cannot identify fundamental graph properties such as connectivity and triangle freeness. We show that GNNs also suffer from the same limitation. To address this limitation, we propose a more expressive architecture, k-hop GNNs, which updates a node's representation by aggregating information not only from its direct neighbors, but from its k-hop neighborhood. We show that the proposed architecture can identify fundamental graph properties. We evaluate the proposed architecture on standard node classification and graph classification datasets. Our experimental evaluation confirms our theoretical findings since the proposed model achieves performance better or comparable to standard GNNs and to state-of-the-art algorithms.
Graph Convolutional Networks (GCNs) are powerful models for learning representations of attributed graphs. To scale GCNs to large graphs, state-of-the-art methods use various layer sampling techniques to alleviate the "neighbor explosion" problem during minibatch training. We propose GraphSAINT, a graph sampling based inductive learning method that improves training efficiency and accuracy in a fundamentally different way. By changing perspective, GraphSAINT constructs minibatches by sampling the training graph, rather than the nodes or edges across GCN layers. Each iteration, a complete GCN is built from the properly sampled subgraph. Thus, we ensure fixed number of well-connected nodes in all layers. We further propose normalization technique to eliminate bias, and sampling algorithms for variance reduction. Importantly, we can decouple the sampling from the forward and backward propagation, and extend GraphSAINT with many architecture variants (e.g., graph attention, jumping connection). GraphSAINT demonstrates superior performance in both accuracy and training time on five large graphs, and achieves new state-of-the-art F1 scores for PPI (0.995) and Reddit (0.970).
Graph Neural Networks (GNNs) are powerful to learn the representation of graph-structured data. Most of the GNNs use the message-passing scheme, where the embedding of a node is iteratively updated by aggregating the information of its neighbors. To achieve a better expressive capability of node influences, attention mechanism has grown to be popular to assign trainable weights to the nodes in aggregation. Though the attention-based GNNs have achieved remarkable results in various tasks, a clear understanding of their discriminative capacities is missing. In this work, we present a theoretical analysis of the representational properties of the GNN that adopts the attention mechanism as an aggregator. Our analysis determines all cases when those attention-based GNNs can always fail to distinguish certain distinct structures. Those cases appear due to the ignorance of cardinality information in attention-based aggregation. To improve the performance of attention-based GNNs, we propose cardinality preserved attention (CPA) models that can be applied to any kind of attention mechanisms. Our experiments on node and graph classification confirm our theoretical analysis and show the competitive performance of our CPA models.
Graph or network data is ubiquitous in the real world, including social networks, information networks, traffic networks, biological networks and various technical networks. The non-Euclidean nature of graph data poses the challenge for modeling and analyzing graph data. Recently, Graph Neural Network (GNNs) are proposed as a general and powerful framework to handle tasks on graph data, e.g., node embedding, link prediction and node classification. As a representative implementation of GNNs, Graph Attention Networks (GATs) are successfully applied in a variety of tasks on real datasets. However, GAT is designed to networks with only positive links and fails to handle signed networks which contain both positive and negative links. In this paper, we propose Signed Graph Attention Networks (SiGATs), generalizing GAT to signed networks. SiGAT incorporates graph motifs into GAT to capture two well-known theories in signed network research, i.e., balance theory and status theory. In SiGAT, motifs offer us the flexible structural pattern to aggregate and propagate messages on the signed network to generate node embeddings. We evaluate the proposed SiGAT method by applying it to the signed link prediction task. Experimental results on three real datasets demonstrate that SiGAT outperforms feature-based method, network embedding method and state-of-the-art GNN-based methods like signed graph convolutional network (SGCN).
Graph convolution networks (GCN) have emerged as the leading method to classify node classes in networks, and have reached the highest accuracy in multiple node classification tasks. In the absence of available tagged samples, active learning methods have been developed to obtain the highest accuracy using the minimal number of queries to an oracle. The current best active learning methods use the sample class uncertainty as selection criteria. However, in graph based classification, the class of each node is often related to the class of its neighbors. As such, the uncertainty in the class of a node's neighbor may be a more appropriate selection criterion. We here propose two such criteria, one extending the classical uncertainty measure, and the other extending the page-rank algorithm. We show that the latter is optimal when the fraction of tagged nodes is low, and when this fraction grows to one over the average degree, the regional uncertainty performs better than all existing methods. While we have tested this methods on graphs, such methods can be extended to any classification problem, where a distance metrics can be defined between the input samples. All the code used can be accessed at : https://github.com/louzounlab/graph-al All the datasets used can be accessed at : https://github.com/louzounlab/DataSets
Graph embedding learning that aims to automatically learn low-dimensional node representations, has drawn increasing attention in recent years. To date, most recent graph embedding methods are evaluated on social and information networks and are not comprehensively studied on biomedical networks under systematic experiments and analyses. On the other hand, for a variety of biomedical network analysis tasks, traditional techniques such as matrix factorization (which can be seen as a type of graph embedding methods) have shown promising results, and hence there is a need to systematically evaluate the more recent graph embedding methods (e.g. random walk-based and neural network-based) in terms of their usability and potential to further the state-of-the-art. We select 11 representative graph embedding methods and conduct a systematic comparison on 3 important biomedical link prediction tasks: drug-disease association (DDA) prediction, drug-drug interaction (DDI) prediction, protein-protein interaction (PPI) prediction; and 2 node classification tasks: medical term semantic type classification, protein function prediction. Our experimental results demonstrate that the recent graph embedding methods achieve promising results and deserve more attention in the future biomedical graph analysis. Compared with three state-of-the-art methods for DDAs, DDIs and protein function predictions, the recent graph embedding methods achieve competitive performance without using any biological features and the learned embeddings can be treated as complementary representations for the biological features. By summarizing the experimental results, we provide general guidelines for properly selecting graph embedding methods and setting their hyper-parameters for different biomedical tasks.
Graph neural networks (GNNs) which apply the deep neural networks to graph data have achieved significant performance for the task of semi-supervised node classification. However, only few work has addressed the adversarial robustness of GNNs. In this paper, we first present a novel gradient-based attack method that facilitates the difficulty of tackling discrete graph data. When comparing to current adversarial attacks on GNNs, the results show that by only perturbing a small number of edge perturbations, including addition and deletion, our optimization-based attack can lead to a noticeable decrease in classification performance. Moreover, leveraging our gradient-based attack, we propose the first optimization-based adversarial training for GNNs. Our method yields higher robustness against both different gradient based and greedy attack methods without sacrificing classification accuracy on original graph.
Graph data widely exist in many high-impact applications. Inspired by the success of deep learning in grid-structured data, graph neural network models have been proposed to learn powerful node-level or graph-level representation. However, most of the existing graph neural networks suffer from the following limitations: (1) there is limited analysis regarding the graph convolution properties, such as seed-oriented, degree-aware and order-free; (2) the node's degree-specific graph structure is not explicitly expressed in graph convolution for distinguishing structure-aware node neighborhoods; (3) the theoretical explanation regarding the graph-level pooling schemes is unclear. To address these problems, we propose a generic degree-specific graph neural network named DEMO-Net motivated by Weisfeiler-Lehman graph isomorphism test that recursively identifies 1-hop neighborhood structures. In order to explicitly capture the graph topology integrated with node attributes, we argue that graph convolution should have three properties: seed-oriented, degree-aware, order-free. To this end, we propose multi-task graph convolution where each task represents node representation learning for nodes with a specific degree value, thus leading to preserving the degree-specific graph structure. In particular, we design two multi-task learning methods: degree-specific weight and hashing functions for graph convolution. In addition, we propose a novel graph-level pooling/readout scheme for learning graph representation provably lying in a degree-specific Hilbert kernel space. The experimental results on several node and graph classification benchmark data sets demonstrate the effectiveness and efficiency of our proposed DEMO-Net over state-of-the-art graph neural network models.
Recently, neural network based approaches have achieved significant improvement for solving large, complex, graph-structured problems. However, their bottlenecks still need to be addressed, and the advantages of multi-scale information and deep architectures have not been sufficiently exploited. In this paper, we theoretically analyze how existing Graph Convolutional Networks (GCNs) have limited expressive power due to the constraint of the activation functions and their architectures. We generalize spectral graph convolution and deep GCN in block Krylov subspace forms and devise two architectures, both with the potential to be scaled deeper but each making use of the multi-scale information in different ways. We further show that the equivalence of these two architectures can be established under certain conditions. On several node classification tasks, with or without the help of validation, the two new architectures achieve better performance compared to many state-of-the-art methods.
Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static relationships. We propose the Graph Learning Network (GLN), a simple yet effective process to learn node embeddings and structure prediction functions. Our model uses graph convolutions to propose expected node features, and predict the best structure based on them. We repeat these steps recursively to enhance the prediction and the embeddings.
Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add non-lineality. To tackle this problem, we investigate the expressive power of graph NNs via their asymptotic behaviors as the layer size tends to infinity. Our strategy is to generalize the forward propagation of a Graph Convolutional Network (GCN), which is a popular graph NN variant, as a specific dynamical system. In the case of a GCN, we show that when its weights satisfy the conditions determined by the spectra of the (augmented) normalized Laplacian, its output exponentially approaches the set of signals that carry information of the connected components and node degrees only for distinguishing nodes. Our theory enables us to relate the expressive power of GCNs with the topological information of the underlying graphs inherent in the graph spectra. To demonstrate this, we characterize the asymptotic behavior of GCNs on the Erd\H{o}s -- R\'{e}nyi graph. We show that when the Erd\H{o}s -- R\'{e}nyi graph is sufficiently dense and large, a broad range of GCNs on it suffers from the "information loss" in the limit of infinite layers with high probability. Based on the theory, we provide a principled guideline for weight normalization of graph NNs. We experimentally confirm that the proposed weight scaling enhances the predictive performance of GCNs in real data. Code is available at https://github.com/delta2323/gnn-asymptotics.
Meta-learning has received a tremendous recent attention as a possible approach for mimicking human intelligence, i.e., acquiring new knowledge and skills with little or even no demonstration. Most of the existing meta-learning methods are proposed to tackle few-shot learning problems such as image and text, in rather Euclidean domain. However, there are very few works applying meta-learning to non-Euclidean domains, and the recently proposed graph neural networks (GNNs) models do not perform effectively on graph few-shot learning problems. Towards this, we propose a novel graph meta-learning framework -- Meta-GNN -- to tackle the few-shot node classification problem in graph meta-learning settings. It obtains the prior knowledge of classifiers by training on many similar few-shot learning tasks and then classifies the nodes from new classes with only few labeled samples. Additionally, Meta-GNN is a general model that can be straightforwardly incorporated into any existing state-of-the-art GNN. Our experiments conducted on three benchmark datasets demonstrate that our proposed approach not only improves the node classification performance by a large margin on few-shot learning problems in meta-learning paradigm, but also learns a more general and flexible model for task adaption.
Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at https://github.com/google-research/google-research/tree/master/cluster_gcn.
We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.
Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for non-linear dimensionality reduction in a manner akin to previous efforts based on manifold learning with uses for downstream database processing, machine learning and visualization. In this systematic yet comprehensive experimental survey, we benchmark several popular network representation learning methods operating on two key tasks: link prediction and node classification. We examine the performance of 12 unsupervised embedding methods on 15 datasets. To the best of our knowledge, the scale of our study -- both in terms of the number of methods and number of datasets -- is the largest to date. Our results reveal several key insights about work-to-date in this space. First, we find that certain baseline methods (task-specific heuristics, as well as classic manifold methods) that have often been dismissed or are not considered by previous efforts can compete on certain types of datasets if they are tuned appropriately. Second, we find that recent methods based on matrix factorization offer a small but relatively consistent advantage over alternative methods (e.g., random-walk based methods) from a qualitative standpoint. Specifically, we find that MNMF, a community preserving embedding method, is the most competitive method for the link prediction task. While NetMF is the most competitive baseline for node classification. Third, no single method completely outperforms other embedding methods on both node classification and link prediction tasks. We also present several drill-down analysis that reveals settings under which certain algorithms perform well (e.g., the role of neighborhood context on performance) -- guiding the end-user.
Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. Mixhop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets.
As an efficient and scalable graph neural network, GraphSAGE has enabled an inductive capability for inferring unseen nodes or graphs by aggregating subsampled local neighborhoods and by learning in a mini-batch gradient descent fashion. The neighborhood sampling used in GraphSAGE is effective in order to improve computing and memory efficiency when inferring a batch of target nodes with diverse degrees in parallel. Despite this advantage, the default uniform sampling suffers from high variance in training and inference, leading to sub-optimum accuracy. We propose a new data-driven sampling approach to reason about the real-valued importance of a neighborhood by a non-linear regressor, and to use the value as a criterion for subsampling neighborhoods. The regressor is learned using a value-based reinforcement learning. The implied importance for each combination of vertex and neighborhood is inductively extracted from the negative classification loss output of GraphSAGE. As a result, in an inductive node classification benchmark using three datasets, our method enhanced the baseline using the uniform sampling, outperforming recent variants of a graph neural network in accuracy.
Graph Neural Networks (GNNs) have been popularly used for analyzing non-Euclidean data such as social network data and biological data. Despite their success, the design of graph neural networks requires a lot of manual work and domain knowledge. In this paper, we propose a Graph Neural Architecture Search method (GraphNAS for short) that enables automatic search of the best graph neural architecture based on reinforcement learning. Specifically, GraphNAS first uses a recurrent network to generate variable-length strings that describe the architectures of graph neural networks, and then trains the recurrent network with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation data set. Extensive experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that GraphNAS can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network. On node classification tasks, GraphNAS can design a novel network architecture that rivals the best human-invented architecture in terms of test set accuracy.
We propose a dynamic neighborhood aggregation (DNA) procedure guided by (multi-head) attention for representation learning on graphs. In contrast to current graph neural networks which follow a simple neighborhood aggregation scheme, our DNA procedure allows for a selective and node-adaptive aggregation of neighboring embeddings of potentially differing locality. In order to avoid overfitting, we propose to control the channel-wise connections between input and output by making use of grouped linear projections. In a number of transductive node-classification experiments, we demonstrate the effectiveness of our approach.
Convolutional Neural Networks (CNNs) achieve impressive performance in a wide variety of fields. Their success benefited from a massive boost when very deep CNN models were able to be reliably trained. Despite their merits, CNNs fail to properly address problems with non-Euclidean data. To overcome this challenge, Graph Convolutional Networks (GCNs) build graphs to represent non-Euclidean data, borrow concepts from CNNs, and apply them in training. GCNs show promising results, but they are usually limited to very shallow models due to the vanishing gradient problem. As a result, most state-of-the-art GCN models are no deeper than 3 or 4 layers. In this work, we present new ways to successfully train very deep GCNs. We do this by borrowing concepts from CNNs, specifically residual/dense connections and dilated convolutions, and adapting them to GCN architectures. Extensive experiments show the positive effect of these deep GCN frameworks. Finally, we use these new concepts to build a very deep 56-layer GCN, and show how it significantly boosts performance (+3.7% mIoU over state-of-the-art) in the task of point cloud semantic segmentation. We believe that the community can greatly benefit from this work, as it opens up many opportunities for advancing GCN-based research.