We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar features. Many popular GNNs fail to generalize to this setting, and are even outperformed by models that ignore the graph structure (e.g., multilayer perceptrons). Motivated by this limitation, we identify a set of key designs -- ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations -- that boost learning from the graph structure under heterophily. We combine them into a graph neural network, H2GCN, which we use as the base method to empirically evaluate the effectiveness of the identified designs. Going beyond the traditional benchmarks with strong homophily, our empirical analysis shows that the identified designs increase the accuracy of GNNs by up to 40% and 27% over models without them on synthetic and real networks with heterophily, respectively, and yield competitive performance under homophily.
One intriguing property of deep neural networks (DNNs) is their inherent vulnerability to backdoor attacks -- a trojan model responds to trigger-embedded inputs in a highly predictable manner while functioning normally otherwise. Despite the plethora of prior work on DNNs for continuous data (e.g., images), the vulnerability of graph neural networks (GNNs) for discrete-structured data (e.g., graphs) is largely unexplored, which is highly concerning given their increasing use in security-sensitive domains. To bridge this gap, we present GTA, the first backdoor attack on GNNs. Compared with prior work, GTA departs in significant ways: graph-oriented -- it defines triggers as specific subgraphs, including both topological structures and descriptive features, entailing a large design spectrum for the adversary; input-tailored -- it dynamically adapts triggers to individual graphs, thereby optimizing both attack effectiveness and evasiveness; downstream model-agnostic -- it can be readily launched without knowledge regarding downstream models or fine-tuning strategies; and attack-extensible -- it can be instantiated for both transductive (e.g., node classification) and inductive (e.g., graph classification) tasks, constituting severe threats for a range of security-critical applications. Through extensive evaluation using benchmark datasets and state-of-the-art models, we demonstrate the effectiveness of GTA. We further provide analytical justification for its effectiveness and discuss potential countermeasures, pointing to several promising research directions.
In this paper we present Spektral, an open-source Python library for building graph neural networks with TensorFlow and the Keras application programming interface. Spektral implements a large set of methods for deep learning on graphs, including message-passing and pooling operators, as well as utilities for processing graphs and loading popular benchmark datasets. The purpose of this library is to provide the essential building blocks for creating graph neural networks, focusing on the guiding principles of user-friendliness and quick prototyping on which Keras is based. Spektral is, therefore, suitable for absolute beginners and expert deep learning practitioners alike. In this work, we present an overview of Spektral's features and report the performance of the methods implemented by the library in scenarios of node classification, graph classification, and graph regression.
Despite several signs of progress have been made recently, limited research has been conducted for an inductive setting where embeddings are required for newly unseen nodes -- a setting encountered commonly in practical applications of deep learning for graph networks. This significantly affects the performances of downstream tasks such as node classification, link prediction or community extraction. To this end, we propose SANNE -- a novel unsupervised embedding model -- whose central idea is to employ a transformer self-attention network to iteratively aggregate vector representations of nodes in random walks. Our SANNE aims to produce plausible embeddings not only for present nodes, but also for newly unseen nodes. Experimental results show that the proposed SANNE obtains state-of-the-art results for the node classification task on well-known benchmark datasets.
In this work, we propose the first backdoor attack to graph neural networks (GNN). Specifically, we propose a \emph{subgraph based backdoor attack} to GNN for graph classification. In our backdoor attack, a GNN classifier predicts an attacker-chosen target label for a testing graph once a predefined subgraph is injected to the testing graph. Our empirical results on three real-world graph datasets show that our backdoor attacks are effective with a small impact on a GNN's prediction accuracy for clean testing graphs. Moreover, we generalize a randomized smoothing based certified defense to defend against our backdoor attacks. Our empirical results show that the defense is effective in some cases but ineffective in other cases, highlighting the needs of new defenses for our backdoor attacks.
Graph representation learning has emerged as a powerful technique for addressing real-world problems. Various downstream graph learning tasks have benefited from its recent developments, such as node classification, similarity search, and graph classification. However, prior arts on graph representation learning focus on domain specific problems and train a dedicated model for each graph dataset, which is usually non-transferable to out-of-domain data. Inspired by the recent advances in pre-training from natural language processing and computer vision, we design Graph Contrastive Coding (GCC) -- a self-supervised graph neural network pre-training framework -- to capture the universal network topological properties across multiple networks. We design GCC's pre-training task as subgraph instance discrimination in and across networks and leverage contrastive learning to empower graph neural networks to learn the intrinsic and transferable structural representations. We conduct extensive experiments on three graph learning tasks and ten graph datasets. The results show that GCC pre-trained on a collection of diverse datasets can achieve competitive or better performance to its task-specific and trained-from-scratch counterparts. This suggests that the pre-training and fine-tuning paradigm presents great potential for graph representation learning.
In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally trade-off their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.
Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.
Graph Neural Networks (GNNs) have demonstrated superior performance in learning node representations for various graph inference tasks. However, learning over graph data can raise privacy concerns when nodes represent people or human-related variables that involve sensitive or personal information. While numerous techniques have been proposed for privacy-preserving deep learning over non-relational data, there is less work addressing the privacy issues pertained to applying deep learning algorithms on graphs. In this paper, we study the problem of node data privacy, where graph nodes have potentially sensitive data that is kept private, but they could be beneficial for a central server for training a GNN over the graph. To address this problem, we develop a privacy-preserving, architecture-agnostic GNN learning algorithm with formal privacy guarantees based on Local Differential Privacy (LDP). Specifically, we propose an LDP encoder and an unbiased rectifier, by which the server can communicate with the graph nodes to privately collect their data and approximate the GNN's first layer. To further reduce the effect of the injected noise, we propose to prepend a simple graph convolution layer, called KProp, which is based on the multi-hop aggregation of the nodes' features acting as a denoising mechanism. Finally, we propose a robust training framework, in which we benefit from KProp's denoising capability to increase the accuracy of inference in the presence of noisy labels. Extensive experiments conducted over real-world datasets demonstrate that our method can maintain a satisfying level of accuracy with low privacy loss.
Graph representation learning nowadays becomes fundamental in analyzing graph-structured data. Inspired by recent success of contrastive methods, in this paper, we propose a novel framework for unsupervised graph representation learning by leveraging a contrastive objective at the node level. Specifically, we generate two graph views by corruption and learn node representations by maximizing the agreement of node representations in these two views. To provide diverse node contexts for the contrastive objective, we propose a hybrid scheme for generating graph views on both structure and attribute levels. Besides, we provide theoretical justification behind our motivation from two perspectives, mutual information and the classical triplet loss. We perform empirical experiments on both transductive and inductive learning tasks using a variety of real-world datasets. Experimental experiments demonstrate that despite its simplicity, our proposed method consistently outperforms existing state-of-the-art methods by large margins. Moreover, our unsupervised method even surpasses its supervised counterparts on transductive tasks, demonstrating its great potential in real-world applications.
Graph neural networks (GNNs) have attracted much attention because of their excellent performance on tasks such as node classification. However, there is inadequate understanding on how and why GNNs work, especially for node representation learning. This paper aims to provide a theoretical framework to understand GNNs, specifically, spectral graph convolutional networks and graph attention networks, from graph signal denoising perspectives. Our framework shows that GNNs are implicitly solving graph signal denoising problems: spectral graph convolutions work as denoising node features, while graph attentions work as denoising edge weights. We also show that a linear self-attention mechanism is able to compete with the state-of-the-art graph attention methods. Our theoretical results further lead to two new models, GSDN-F and GSDN-EF, which work effectively for graphs with noisy node features and/or noisy edges. We validate our theoretical findings and also the effectiveness of our new models by experiments on benchmark datasets. The source code is available at \url{https://github.com/fuguoji/GSDN}.
Sampling graphs is an important task in data mining. In this paper, we describe Little Ball of Fur a Python library that includes more than twenty graph sampling algorithms. Our goal is to make node, edge, and exploration-based network sampling techniques accessible to a large number of professionals, researchers, and students in a single streamlined framework. We created this framework with a focus on a coherent application public interface which has a convenient design, generic input data requirements, and reasonable baseline settings of algorithms. Here we overview these design foundations of the framework in detail with illustrative code snippets. We show the practical usability of the library by estimating various global statistics of social networks and web graphs. Experiments demonstrate that Little Ball of Fur can speed up node and whole graph embedding techniques considerably with mildly deteriorating the predictive value of distilled features.
Graph Attention Network (GAT) and GraphSAGE are neural network architectures that operate on graph-structured data and have been widely studied for link prediction and node classification. One challenge raised by GraphSAGE is how to smartly combine neighbour features based on graph structure. GAT handles this problem through attention, however the challenge with GAT is its scalability over large and dense graphs. In this work, we proposed a new architecture to address these issues that is more efficient and is capable of incorporating different edge type information. It generates node representations by attending to neighbours sampled from weighted multi-step transition probabilities. We conduct experiments on both transductive and inductive settings. Experiments achieved comparable or better results on several graph benchmarks, including the Cora, Citeseer, Pubmed, PPI, Twitter, and YouTube datasets.
Modern graph neural networks (GNNs) learn node embeddings through multilayer local aggregation and achieve great success in applications on assortative graphs. However, tasks on disassortative graphs usually require non-local aggregation. In addition, we find that local aggregation is even harmful for some disassortative graphs. In this work, we propose a simple yet effective non-local aggregation framework with an efficient attention-guided sorting for GNNs. Based on it, we develop various non-local GNNs. We perform thorough experiments to analyze disassortative graph datasets and evaluate our non-local GNNs. Experimental results demonstrate that our non-local GNNs significantly outperform previous state-of-the-art methods on seven benchmark datasets of disassortative graphs, in terms of both model performance and efficiency.
We study the problem of semi-supervised learning on graphs, for which graph neural networks (GNNs) have been extensively explored. However, most existing GNNs inherently suffer from the limitations of over-smoothing, non-robustness, and weak-generalization when labeled nodes are scarce. In this paper, we propose a simple yet effective framework -- GRAPH RANDOM NEURAL NETWORKS (GRAND) -- to address these issues. In GRAND, we first design a random propagation strategy to perform graph data augmentation. Then we leverage consistency regularization to optimize the prediction consistency of unlabeled nodes across different data augmentations. Extensive experiments on graph benchmark datasets suggest that GRAND significantly outperforms state-of-the-art GNN baselines on semi-supervised node classification. Finally, we show that GRAND mitigates the issues of over-smoothing and non-robustness, exhibiting better generalization behavior than existing GNNs. The source code of GRAND is publicly available at https://github.com/Grand20/grand.
Graph representation learning has been extensively studied in recent years. Despite its potential in generating continuous embeddings for various networks, both the effectiveness and efficiency to infer high-quality representations toward large corpus of nodes are still challenging. Sampling is a critical point to achieve the performance goals. Prior arts usually focus on sampling positive node pairs, while the strategy for negative sampling is left insufficiently explored. To bridge the gap, we systematically analyze the role of negative sampling from the perspectives of both objective and risk, theoretically demonstrating that negative sampling is as important as positive sampling in determining the optimization objective and the resulted variance. To the best of our knowledge, we are the first to derive the theory and quantify that the negative sampling distribution should be positively but sub-linearly correlated to their positive sampling distribution. With the guidance of the theory, we propose MCNS, approximating the positive distribution with self-contrast approximation and accelerating negative sampling by Metropolis-Hastings. We evaluate our method on 5 datasets that cover extensive downstream graph learning tasks, including link prediction, node classification and personalized recommendation, on a total of 19 experimental settings. These relatively comprehensive experimental results demonstrate its robustness and superiorities.
Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility. In this work, we are interested in studying how much a probabilistic bias in this stochastic process affects the quality of the nodes picked by the process. In particular, our biased walk, with a certain probability, favors movement towards nodes whose neighborhoods bear a structural resemblance to the current node's neighborhood. We succinctly capture this neighborhood as a probability measure based on the spectrum of the node's neighborhood subgraph represented as a normalized laplacian matrix. We propose the use of a paragraph vector model with a novel Wasserstein regularization term. We empirically evaluate our approach against several state-of-the-art node embedding techniques on a wide variety of real-world datasets and demonstrate that our proposed method significantly improves upon existing methods on both link prediction and node classification tasks.
We systematically evaluate the (in-)stability of state-of-the-art node embedding algorithms due to randomness, i.e., the random variation of their outcomes given identical algorithms and graphs. We apply five node embeddings algorithms---HOPE, LINE, node2vec, SDNE, and GraphSAGE---to synthetic and empirical graphs and assess their stability under randomness with respect to (i) the geometry of embedding spaces as well as (ii) their performance in downstream tasks. We find significant instabilities in the geometry of embedding spaces independent of the centrality of a node. In the evaluation of downstream tasks, we find that the accuracy of node classification seems to be unaffected by random seeding while the actual classification of nodes can vary significantly. This suggests that instability effects need to be taken into account when working with node embeddings. Our work is relevant for researchers and engineers interested in the effectiveness, reliability, and reproducibility of node embedding approaches.
In this paper, we propose a flexible notion of characteristic functions defined on graph vertices to describe the distribution of vertex features at multiple scales. We introduce FEATHER, a computationally efficient algorithm to calculate a specific variant of these characteristic functions where the probability weights of the characteristic function are defined as the transition probabilities of random walks. We argue that features extracted by this procedure are useful for node level machine learning tasks. We discuss the pooling of these node representations, resulting in compact descriptors of graphs that can serve as features for graph classification algorithms. We analytically prove that FEATHER describes isomorphic graphs with the same representation and exhibits robustness to data corruption. Using the node feature characteristic functions we define parametric models where evaluation points of the functions are learned parameters of supervised classifiers. Experiments on real world large datasets show that our proposed algorithm creates high quality representations, performs transfer learning efficiently, exhibits robustness to hyperparameter changes, and scales linearly with the input size.
Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats vertices and hyperedges equally and proposes a new hypergraph formulation named the \emph{line expansion (LE)} for hypergraphs learning. The new expansion bijectively induces a homogeneous structure from the hypergraph by treating vertex-hyperedge pairs as "line nodes". By reducing the hypergraph to a simple graph, the proposed \emph{line expansion} makes existing graph learning algorithms compatible with the higher-order structure and has been proven as a unifying framework for various hypergraph expansions. We evaluate the proposed line expansion on five hypergraph datasets, the results show that our method beats SOTA baselines by a significant margin.