Adversarial attacks on graphs have attracted considerable research interests. Existing works assume the attacker is either (partly) aware of the victim model, or able to send queries to it. These assumptions are, however, unrealistic. To bridge the gap between theoretical graph attacks and real-world scenarios, in this work, we propose a novel and more realistic setting: strict black-box graph attack, in which the attacker has no knowledge about the victim model at all and is not allowed to send any queries. To design such an attack strategy, we first propose a generic graph filter to unify different families of graph-based models. The strength of attacks can then be quantified by the change in the graph filter before and after attack. By maximizing this change, we are able to find an effective attack strategy, regardless of the underlying model. To solve this optimization problem, we also propose a relaxation technique and approximation theories to reduce the difficulty as well as the computational expense. Experiments demonstrate that, even with no exposure to the model, the Macro-F1 drops 6.4% in node classification and 29.5% in graph classification, which is a significant result compared with existent works.
Low-dimension graph embeddings have proved extremely useful in various downstream tasks in large graphs, e.g., link-related content recommendation and node classification tasks, etc. Most existing embedding approaches take nodes as the basic unit for information aggregation, e.g., node perception fields in GNN or con-textual nodes in random walks. The main drawback raised by such node-view is its lack of support for expressing the compound relationships between nodes, which results in the loss of a certain degree of graph information during embedding. To this end, this paper pro-poses PairE(Pair Embedding), a solution to use "pair", a higher level unit than a "node" as the core for graph embeddings. Accordingly, a multi-self-supervised auto-encoder is designed to fulfill two pretext tasks, to reconstruct the feature distribution for respective pairs and their surrounding context. PairE has three major advantages: 1) Informative, embedding beyond node-view are capable to preserve richer information of the graph; 2) Simple, the solutions provided by PairE are time-saving, storage-efficient, and require the fewer hyper-parameters; 3) High adaptability, with the introduced translator operator to map pair embeddings to the node embeddings, PairE can be effectively used in both the link-based and the node-based graph analysis. Experiment results show that PairE consistently outperforms the state of baselines in all four downstream tasks, especially with significant edges in the link-prediction and multi-label node classification tasks.
Deep learning models for graphs, especially Graph Convolutional Networks (GCNs), have achieved remarkable performance in the task of semi-supervised node classification. However, recent studies show that GCNs suffer from adversarial perturbations. Such vulnerability to adversarial attacks significantly decreases the stability of GCNs when being applied to security-critical applications. Defense methods such as preprocessing, attention mechanism and adversarial training have been discussed by various studies. While being able to achieve desirable performance when the perturbation rates are low, such methods are still vulnerable to high perturbation rates. Meanwhile, some defending algorithms perform poorly when the node features are not visible. Therefore, in this paper, we propose a novel mechanism called influence mechanism, which is able to enhance the robustness of the GCNs significantly. The influence mechanism divides the effect of each node into two parts: introverted influence which tries to maintain its own features and extroverted influence which exerts influences on other nodes. Utilizing the influence mechanism, we propose the Influence GCN (I-GCN) model. Extensive experiments show that our proposed model is able to achieve higher accuracy rates than state-of-the-art methods when defending against non-targeted attacks.
Graph-based semi-supervised node classification (GraphSSC) has wide applications, ranging from networking and security to data mining and machine learning, etc. However, existing centralized GraphSSC methods are impractical to solve many real-world graph-based problems, as collecting the entire graph and labeling a reasonable number of labels is time-consuming and costly, and data privacy may be also violated. Federated learning (FL) is an emerging learning paradigm that enables collaborative learning among multiple clients, which can mitigate the issue of label scarcity and protect data privacy as well. Therefore, performing GraphSSC under the FL setting is a promising solution to solve real-world graph-based problems. However, existing FL methods 1) perform poorly when data across clients are non-IID, 2) cannot handle data with new label domains, and 3) cannot leverage unlabeled data, while all these issues naturally happen in real-world graph-based problems. To address the above issues, we propose the first FL framework, namely GraphFL, for semi-supervised node classification on graphs. Our framework is motivated by meta-learning methods. Specifically, we propose two GraphFL methods to respectively address the non-IID issue in graph data and handle the tasks with new label domains. Furthermore, we design a self-training method to leverage unlabeled graph data. We adopt representative graph neural networks as GraphSSC methods and evaluate GraphFL on multiple graph datasets. Experimental results demonstrate that GraphFL significantly outperforms the compared FL baseline and GraphFL with self-training can obtain better performance.
Message passing has evolved as an effective tool for designing Graph Neural Networks (GNNs). However, most existing methods for message passing simply sum or average all the neighboring features to update node representations. They are restricted by two problems, i.e., (i) lack of interpretability to identify node features significant to the prediction of GNNs, and (ii) feature over-mixing that leads to the over-smoothing issue in capturing long-range dependencies and inability to handle graphs under heterophily or low homophily. In this paper, we propose a Node-level Capsule Graph Neural Network (NCGNN) to address these problems with an improved message passing scheme. Specifically, NCGNN represents nodes as groups of node-level capsules, in which each capsule extracts distinctive features of its corresponding node. For each node-level capsule, a novel dynamic routing procedure is developed to adaptively select appropriate capsules for aggregation from a subgraph identified by the designed graph filter. NCGNN aggregates only the advantageous capsules and restrains irrelevant messages to avoid over-mixing features of interacting nodes. Therefore, it can relieve the over-smoothing issue and learn effective node representations over graphs with homophily or heterophily. Furthermore, our proposed message passing scheme is inherently interpretable and exempt from complex post-hoc explanations, as the graph filter and the dynamic routing procedure identify a subset of node features that are most significant to the model prediction from the extracted subgraph. Extensive experiments on synthetic as well as real-world graphs demonstrate that NCGNN can well address the over-smoothing issue and produce better node representations for semisupervised node classification. It outperforms the state of the arts under both homophily and heterophily.
Learning low-dimensional representations on graphs has proved to be effective in various downstream tasks. However, noises prevail in real-world networks, which compromise networks to a large extent in that edges in networks propagate noises through the whole network instead of only the node itself. While existing methods tend to focus on preserving structural properties, the robustness of the learned representations against noises is generally ignored. In this paper, we propose a novel framework to learn noise-free node representations and eliminate noises simultaneously. Since noises are often unknown on real graphs, we design two generators, namely a graph generator and a noise generator, to identify normal structures and noises in an unsupervised setting. On the one hand, the graph generator serves as a unified scheme to incorporate any useful graph prior knowledge to generate normal structures. We illustrate the generative process with community structures and power-law degree distributions as examples. On the other hand, the noise generator generates graph noises not only satisfying some fundamental properties but also in an adaptive way. Thus, real noises with arbitrary distributions can be handled successfully. Finally, in order to eliminate noises and obtain noise-free node representations, two generators need to be optimized jointly, and through maximum likelihood estimation, we equivalently convert the model into imposing different regularization constraints on the true graph and noises respectively. Our model is evaluated on both real-world and synthetic data. It outperforms other strong baselines for node classification and graph reconstruction tasks, demonstrating its ability to eliminate graph noises.
Unsupervised/self-supervised pre-training methods for graph representation learning have recently attracted increasing research interests, and they are shown to be able to generalize to various downstream applications. Yet, the adversarial robustness of such pre-trained graph learning models remains largely unexplored. More importantly, most existing defense techniques designed for end-to-end graph representation learning methods require pre-specified label definitions, and thus cannot be directly applied to the pre-training methods. In this paper, we propose an unsupervised defense technique to robustify pre-trained deep graph models, so that the perturbations on the input graph can be successfully identified and blocked before the model is applied to different downstream tasks. Specifically, we introduce a mutual information-based measure, \textit{graph representation vulnerability (GRV)}, to quantify the robustness of graph encoders on the representation space. We then formulate an optimization problem to learn the graph representation by carefully balancing the trade-off between the expressive power and the robustness (\emph{i.e.}, GRV) of the graph encoder. The discrete nature of graph topology and the joint space of graph data make the optimization problem intractable to solve. To handle the above difficulty and to reduce computational expense, we further relax the problem and thus provide an approximate solution. Additionally, we explore a provable connection between the robustness of the unsupervised graph encoder and that of models on downstream tasks. Extensive experiments demonstrate that even without access to labels and tasks, our model is still able to enhance robustness against adversarial attacks on three downstream tasks (node classification, link prediction, and community detection) by an average of +16.5% compared with existing methods.
This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no polynomial-order exact solution and, therefore, are NP-hard. Here, adopting a graph-theoretic approach, this problem is solved for general nonlinear (and also structure-invariant) systems and a P-order solution is proposed. In this direction, the dynamical system is modeled as a directed graph, called \textit{system digraph}, and two types of graph components are introduced which are tightly related with structural controllability. Two types of nodes which are required to be affected (or driven) by an input, called \textit{driver nodes}, are defined, and minimal number of these driver nodes are obtained. Polynomial-order complexity of the given algorithms to solve the problem ensures applicability of the solution for analysis of large-scale dynamical systems. {The structural results in this paper are significant as compared to the existing literature which offer approximate and computationally less-efficient, e.g. Gramian-based, solutions for the problem, while this paper provides exact solution with lower computational complexity and applicable for controllability analysis of nonlinear systems.
Network representation aims to represent the nodes in a network as continuous and compact vectors, and has attracted much attention in recent years due to its ability to capture complex structure relationships inside networks. However, existing network representation methods are commonly designed for homogeneous information networks where all the nodes (entities) of a network are of the same type, e.g., papers in a citation network. In this paper, we propose a universal network representation approach (UNRA), that represents different types of nodes in heterogeneous information networks in a continuous and common vector space. The UNRA is built on our latest mutually updated neural language module, which simultaneously captures inter-relationship among homogeneous nodes and node-content correlation. Relationships between different types of nodes are also assembled and learned in a unified framework. Experiments validate that the UNRA achieves outstanding performance, compared to six other state-of-the-art algorithms, in node representation, node classification, and network visualization. In node classification, the UNRA achieves a 3\% to 132\% performance improvement in terms of accuracy.
Graph neural networks (GNNs) are able to achieve promising performance on multiple graph downstream tasks such as node classification and link prediction. Comparatively lesser work has been done to design GNNs which can operate directly for community detection on graphs. Traditionally, GNNs are trained on a semi-supervised or self-supervised loss function and then clustering algorithms are applied to detect communities. However, such decoupled approaches are inherently sub-optimal. Designing an unsupervised loss function to train a GNN and extract communities in an integrated manner is a fundamental challenge. To tackle this problem, we combine the principle of self-expressiveness with the framework of self-supervised graph neural network for unsupervised community detection for the first time in literature. Our solution is trained in an end-to-end fashion and achieves state-of-the-art community detection performance on multiple publicly available datasets.
Graph neural networks (GNNs) are widely used in the applications based on graph structured data, such as node classification and link prediction. However, GNNs are often used as a black-box tool and rarely get in-depth investigated regarding whether they fit certain applications that may have various properties. A recently proposed technique distance encoding (DE) (Li et al. 2020) magically makes GNNs work well in many applications, including node classification and link prediction. The theory provided in (Li et al. 2020) supports DE by proving that DE improves the representation power of GNNs. However, it is not obvious how the theory assists the applications accordingly. Here, we revisit GNNs and DE from a more practical point of view. We want to explain how DE makes GNNs fit for node classification and link prediction. Specifically, for link prediction, DE can be viewed as a way to establish correlations between a pair of node representations. For node classification, the problem becomes more complicated as different classification tasks may hold node labels that indicate different physical meanings. We focus on the most widely-considered node classification scenarios and categorize the node labels into two types, community type and structure type, and then analyze different mechanisms that GNNs adopt to predict these two types of labels. We also run extensive experiments to compare eight different configurations of GNNs paired with DE to predict node labels over eight real-world graphs. The results demonstrate the uniform effectiveness of DE to predict structure-type labels. Lastly, we reach three pieces of conclusions on how to use GNNs and DE properly in tasks of node classification.
Graph neural networks (GNNs) have emerged as effective approaches for graph analysis, especially in the scenario of semi-supervised learning. Despite its success, GNN often suffers from over-smoothing and over-fitting problems, which affects its performance on node classification tasks. We analyze that an alternative method, the label propagation algorithm (LPA), avoids the aforementioned problems thus it is a promising choice for graph semi-supervised learning. Nevertheless, the intrinsic limitations of LPA on feature exploitation and relation modeling make propagating labels become less effective. To overcome these limitations, we introduce a novel framework for graph semi-supervised learning termed as Cyclic Label Propagation (CycProp for abbreviation), which integrates GNNs into the process of label propagation in a cyclic and mutually reinforcing manner to exploit the advantages of both GNNs and LPA. In particular, our proposed CycProp updates the node embeddings learned by GNN module with the augmented information by label propagation, while fine-tunes the weighted graph of label propagation with the help of node embedding in turn. After the model converges, reliably predicted labels and informative node embeddings are obtained with the LPA and GNN modules respectively. Extensive experiments on various real-world datasets are conducted, and the experimental results empirically demonstrate that the proposed CycProp model can achieve relatively significant gains over the state-of-the-art methods.
Graphs play an important role in many applications. Recently, Graph Neural Networks (GNNs) have achieved promising results in graph analysis tasks. Some state-of-the-art GNN models have been proposed, e.g., Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), etc. Despite these successes, most of the GNNs only have shallow structure. This causes the low expressive power of the GNNs. To fully utilize the power of the deep neural network, some deep GNNs have been proposed recently. However, the design of deep GNNs requires significant architecture engineering. In this work, we propose a method to automate the deep GNNs design. In our proposed method, we add a new type of skip connection to the GNNs search space to encourage feature reuse and alleviate the vanishing gradient problem. We also allow our evolutionary algorithm to increase the layers of GNNs during the evolution to generate deeper networks. We evaluate our method in the graph node classification task. The experiments show that the GNNs generated by our method can obtain state-of-the-art results in Cora, Citeseer, Pubmed and PPI datasets.
Graph Neural Networks (GNNs) aim to extend deep learning techniques to graph data and have achieved significant progress in graph analysis tasks (e.g., node classification) in recent years. However, similar to other deep neural networks like Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), GNNs behave like a black box with their details hidden from model developers and users. It is therefore difficult to diagnose possible errors of GNNs. Despite many visual analytics studies being done on CNNs and RNNs, little research has addressed the challenges for GNNs. This paper fills the research gap with an interactive visual analysis tool, GNNLens, to assist model developers and users in understanding and analyzing GNNs. Specifically, Parallel Sets View and Projection View enable users to quickly identify and validate error patterns in the set of wrong predictions; Graph View and Feature Matrix View offer a detailed analysis of individual nodes to assist users in forming hypotheses about the error patterns. Since GNNs jointly model the graph structure and the node features, we reveal the relative influences of the two types of information by comparing the predictions of three models: GNN, Multi-Layer Perceptron (MLP), and GNN Without Using Features (GNNWUF). Two case studies and interviews with domain experts demonstrate the effectiveness of GNNLens in facilitating the understanding of GNN models and their errors.
Graph Neural Networks (GNNs) have shown to be powerful tools for graph analytics. The key idea is to recursively propagate and aggregate information along edges of the given graph. Despite their success, however, the existing GNNs are usually sensitive to the quality of the input graph. Real-world graphs are often noisy and contain task-irrelevant edges, which may lead to suboptimal generalization performance in the learned GNN models. In this paper, we propose PTDNet, a parameterized topological denoising network, to improve the robustness and generalization performance of GNNs by learning to drop task-irrelevant edges. PTDNet prunes task-irrelevant edges by penalizing the number of edges in the sparsified graph with parameterized networks. To take into consideration of the topology of the entire graph, the nuclear norm regularization is applied to impose the low-rank constraint on the resulting sparsified graph for better generalization. PTDNet can be used as a key component in GNN models to improve their performances on various tasks, such as node classification and link prediction. Experimental studies on both synthetic and benchmark datasets show that PTDNet can improve the performance of GNNs significantly and the performance gain becomes larger for more noisy datasets.
Graph neural networks (GNNs) have received massive attention in the field of machine learning on graphs. Inspired by the success of neural networks, a line of research has been conducted to train GNNs to deal with various tasks, such as node classification, graph classification, and link prediction. In this work, our task of interest is graph classification. Several GNN models have been proposed and shown great accuracy in this task. However, the question is whether usual training methods fully realize the capacity of the GNN models. In this work, we propose a two-stage training framework based on triplet loss. In the first stage, GNN is trained to map each graph to a Euclidean-space vector so that graphs of the same class are close while those of different classes are mapped far apart. Once graphs are well-separated based on labels, a classifier is trained to distinguish between different classes. This method is generic in the sense that it is compatible with any GNN model. By adapting five GNN models to our method, we demonstrate the consistent improvement in accuracy and utilization of each GNN's allocated capacity over the original training method of each model up to 5.4\% points in 12 datasets.
Representation learning of textual networks poses a significant challenge as it involves capturing amalgamated information from two modalities: (i) underlying network structure, and (ii) node textual attributes. For this, most existing approaches learn embeddings of text and network structure by enforcing embeddings of connected nodes to be similar. Then for achieving a modality fusion they use the similarities between text embedding of a node with the structure embedding of its connected node and vice versa. This implies that these approaches require edge information for learning embeddings and they cannot learn embeddings of unseen nodes. In this paper we propose an approach that achieves both modality fusion and the capability to learn embeddings of unseen nodes. The main feature of our model is that it uses an adversarial mechanism between text embedding based discriminator, and structure embedding based generator to learn efficient representations. Then for learning embeddings of unseen nodes, we use the supervision provided by the text embedding based discriminator. In addition this, we propose a novel architecture for learning text embedding that can combine both mutual attention and topological attention mechanism, which give more flexible text embeddings. Through extensive experiments on real-world datasets, we demonstrate that our model makes substantial gains over several state-of-the-art benchmarks. In comparison with previous state-of-the-art, it gives up to 7% improvement in performance in predicting links among nodes seen in the training and up to 12% improvement in performance in predicting links involving nodes not seen in training. Further, in the node classification task, it gives up to 2% improvement in performance.
Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes, in the form of features or time-series data. Modern representation learning techniques employ both the connectivity and attribute information of the nodes to produce embeddings in an unsupervised manner. In this context, deriving embeddings that preserve the geometry of the network and the attribute vectors would be highly desirable, as they would reflect both the topological neighborhood structure and proximity in feature space. While this is fairly straightforward to maintain when only observing the connectivity or attribute information of the network, preserving the geometry of both types of information is challenging. A novel tensor factorization approach for node embedding in attributed networks is proposed in this paper, that preserves the distances of both the connections and the attributes. Furthermore, an effective and lightweight algorithm is developed to tackle the learning task and judicious experiments with multiple state-of-the-art baselines suggest that the proposed algorithm offers significant performance improvements in downstream tasks.
Graph Neural Networks (GNNs) have led to state-of-the-art performance on a variety of machine learning tasks such as recommendation, node classification and link prediction. Graph neural network models generate node embeddings by merging nodes features with the aggregated neighboring nodes information. Most existing GNN models exploit a single type of aggregator (e.g., mean-pooling) to aggregate neighboring nodes information, and then add or concatenate the output of aggregator to the current representation vector of the center node. However, using only a single type of aggregator is difficult to capture the different aspects of neighboring information and the simple addition or concatenation update methods limit the expressive capability of GNNs. Not only that, existing supervised or semi-supervised GNN models are trained based on the loss function of the node label, which leads to the neglect of graph structure information. In this paper, we propose a novel graph neural network architecture, Graph Attention \& Interaction Network (GAIN), for inductive learning on graphs. Unlike the previous GNN models that only utilize a single type of aggregation method, we use multiple types of aggregators to gather neighboring information in different aspects and integrate the outputs of these aggregators through the aggregator-level attention mechanism. Furthermore, we design a graph regularized loss to better capture the topological relationship of the nodes in the graph. Additionally, we first present the concept of graph feature interaction and propose a vector-wise explicit feature interaction mechanism to update the node embeddings. We conduct comprehensive experiments on two node-classification benchmarks and a real-world financial news dataset. The experiments demonstrate our GAIN model outperforms current state-of-the-art performances on all the tasks.
Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work, we build off of semi-implicit graph variational auto-encoders to capture higher-order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a Poincare embedding to efficiently represent graphs exhibiting hierarchical structure. To address the naive posterior latent distribution assumptions in classical variational inference, we use semi-implicit hierarchical variational Bayes to implicitly capture posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and highly correlated latent structures. We show that the existing semi-implicit variational inference objective provably reduces information in the observed graph. Based on this observation, we estimate and add an additional mutual information term to the semi-implicit variational inference learning objective to capture rich correlations arising between the input and latent spaces. We show that the inclusion of this regularization term in conjunction with the Poincare embedding boosts the quality of learned high-level representations and enables more flexible and faithful graphical modeling. We experimentally demonstrate that our approach outperforms existing graph variational auto-encoders both in Euclidean and in hyperbolic spaces for edge link prediction and node classification.