Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framework of topological relational inference (TRI) which allows for integrating higher-order graph information to GNNs and for systematically learning a local graph structure. The key idea is to rewire the original graph by using the persistent homology of the small neighborhoods of nodes and then to incorporate the extracted topological summaries as the side information into the local algorithm. As a result, the new framework enables us to harness both the conventional information on the graph structure and information on the graph higher order topological properties. We derive theoretical stability guarantees for the new local topological representation and discuss their implications on the graph algebraic connectivity. The experimental results on node classification tasks demonstrate that the new TRI-GNN outperforms all 14 state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to perturbations, yielding up to 10\% better performance under noisy scenarios.
Various graph contrastive learning models have been proposed to improve the performance of learning tasks on graph datasets in recent years. While effective and prevalent, these models are usually carefully customized. In particular, although all recent researches create two contrastive views, they differ greatly in view augmentations, architectures, and objectives. It remains an open question how to build your graph contrastive learning model from scratch for particular graph learning tasks and datasets. In this work, we aim to fill this gap by studying how graph information is transformed and transferred during the contrastive learning process and proposing an information-aware graph contrastive learning framework called InfoGCL. The key point of this framework is to follow the Information Bottleneck principle to reduce the mutual information between contrastive parts while keeping task-relevant information intact at both the levels of the individual module and the entire framework so that the information loss during graph representation learning can be minimized. We show for the first time that all recent graph contrastive learning methods can be unified by our framework. We empirically validate our theoretical analysis on both node and graph classification benchmark datasets, and demonstrate that our algorithm significantly outperforms the state-of-the-arts.
Graph neural network (GNN)'s success in graph classification is closely related to the Weisfeiler-Lehman (1-WL) algorithm. By iteratively aggregating neighboring node features to a center node, both 1-WL and GNN obtain a node representation that encodes a rooted subtree around the center node. These rooted subtree representations are then pooled into a single representation to represent the whole graph. However, rooted subtrees are of limited expressiveness to represent a non-tree graph. To address it, we propose Nested Graph Neural Networks (NGNNs). NGNN represents a graph with rooted subgraphs instead of rooted subtrees, so that two graphs sharing many identical subgraphs (rather than subtrees) tend to have similar representations. The key is to make each node representation encode a subgraph around it more than a subtree. To achieve this, NGNN extracts a local subgraph around each node and applies a base GNN to each subgraph to learn a subgraph representation. The whole-graph representation is then obtained by pooling these subgraph representations. We provide a rigorous theoretical analysis showing that NGNN is strictly more powerful than 1-WL. In particular, we proved that NGNN can discriminate almost all r-regular graphs, where 1-WL always fails. Moreover, unlike other more powerful GNNs, NGNN only introduces a constant-factor higher time complexity than standard GNNs. NGNN is a plug-and-play framework that can be combined with various base GNNs. We test NGNN with different base GNNs on several benchmark datasets. NGNN uniformly improves their performance and shows highly competitive performance on all datasets.
Self-supervised learning has gradually emerged as a powerful technique for graph representation learning. However, transferable, generalizable, and robust representation learning on graph data still remains a challenge for pre-training graph neural networks. In this paper, we propose a simple and effective self-supervised pre-training strategy, named Pairwise Half-graph Discrimination (PHD), that explicitly pre-trains a graph neural network at graph-level. PHD is designed as a simple binary classification task to discriminate whether two half-graphs come from the same source. Experiments demonstrate that the PHD is an effective pre-training strategy that offers comparable or superior performance on 13 graph classification tasks compared with state-of-the-art strategies, and achieves notable improvements when combined with node-level strategies. Moreover, the visualization of learned representation revealed that PHD strategy indeed empowers the model to learn graph-level knowledge like the molecular scaffold. These results have established PHD as a powerful and effective self-supervised learning strategy in graph-level representation learning.
Graph Neural Networks (GNNs) have achieved promising performance in various real-world applications. Building a powerful GNN model is not a trivial task, as it requires a large amount of training data, powerful computing resources, and human expertise in fine-tuning the model. Moreover, with the development of adversarial attacks, e.g., model stealing attacks, GNNs raise challenges to model authentication. To avoid copyright infringement on GNNs, verifying the ownership of the GNN models is necessary. This paper presents a watermarking framework for GNNs for both graph and node classification tasks. We 1) design two strategies to generate watermarked data for the graph classification task and one for the node classification task, 2) embed the watermark into the host model through training to obtain the watermarked GNN model, and 3) verify the ownership of the suspicious model in a black-box setting. The experiments show that our framework can verify the ownership of GNN models with a very high probability (up to $99\%$) for both tasks. Finally, we experimentally show that our watermarking approach is robust against a state-of-the-art model extraction technique and four state-of-the-art defenses against backdoor attacks.
To effectively classify graph instances, graph neural networks need to have the capability to capture the part-whole relationship existing in a graph. A capsule is a group of neurons representing complicated properties of entities, which has shown its advantages in traditional convolutional neural networks. This paper proposed novel Capsule Graph Neural Networks that use the EM routing mechanism (CapsGNNEM) to generate high-quality graph embeddings. Experimental results on a number of real-world graph datasets demonstrate that the proposed CapsGNNEM outperforms nine state-of-the-art models in graph classification tasks.
Graph Neural Networks (GNNs) are widely adopted to analyse non-Euclidean data, such as chemical networks, brain networks, and social networks, modelling complex relationships and interdependency between objects. Recently, Membership Inference Attack (MIA) against GNNs raises severe privacy concerns, where training data can be leaked from trained GNN models. However, prior studies focus on inferring the membership of only the components in a graph, e.g., an individual node or edge. How to infer the membership of an entire graph record is yet to be explored. In this paper, we take the first step in MIA against GNNs for graph-level classification. Our objective is to infer whether a graph sample has been used for training a GNN model. We present and implement two types of attacks, i.e., training-based attacks and threshold-based attacks from different adversarial capabilities. We perform comprehensive experiments to evaluate our attacks in seven real-world datasets using five representative GNN models. Both our attacks are shown effective and can achieve high performance, i.e., reaching over 0.7 attack F1 scores in most cases. Furthermore, we analyse the implications behind the MIA against GNNs. Our findings confirm that GNNs can be even more vulnerable to MIA than the models with non-graph structures. And unlike the node-level classifier, MIAs on graph-level classification tasks are more co-related with the overfitting level of GNNs rather than the statistic property of their training graphs.
We present a simple and yet effective interpolation-based regularization technique, aiming to improve the generalization of Graph Neural Networks (GNNs) on supervised graph classification. We leverage Mixup, an effective regularizer for vision, where random sample pairs and their labels are interpolated to create synthetic images for training. Unlike images with grid-like coordinates, graphs have arbitrary structure and topology, which can be very sensitive to any modification that alters the graph's semantic meanings. This posts two unanswered questions for Mixup-like regularization schemes: Can we directly mix up a pair of graph inputs? If so, how well does such mixing strategy regularize the learning of GNNs? To answer these two questions, we propose ifMixup, which first adds dummy nodes to make two graphs have the same input size and then simultaneously performs linear interpolation between the aligned node feature vectors and the aligned edge representations of the two graphs. We empirically show that such simple mixing schema can effectively regularize the classification learning, resulting in superior predictive accuracy to popular graph augmentation and GNN methods.
Graph Convolutional Networks (GCNs) are powerful for processing graph-structured data and have achieved state-of-the-art performance in several tasks such as node classification, link prediction, and graph classification. However, it is inevitable for deep GCNs to suffer from an over-smoothing issue that the representations of nodes will tend to be indistinguishable after repeated graph convolution operations. To address this problem, we propose the Graph Partner Neural Network (GPNN) which incorporates a de-parameterized GCN and a parameter-sharing MLP. We provide empirical and theoretical evidence to demonstrate the effectiveness of the proposed MLP partner on tackling over-smoothing while benefiting from appropriate smoothness. To further tackle over-smoothing and regulate the learning process, we introduce a well-designed consistency contrastive loss and KL divergence loss. Besides, we present a graph enhancement technique to improve the overall quality of edges in graphs. While most GCNs can work with shallow architecture only, GPNN can obtain better results through increasing model depth. Experiments on various node classification tasks have demonstrated the state-of-the-art performance of GPNN. Meanwhile, extensive ablation studies are conducted to investigate the contributions of each component in tackling over-smoothing and improving performance.
Temporal activity localization in long videos is an important problem. The cost of obtaining frame level label for long Wireless Capsule Endoscopy (WCE) videos is prohibitive. In this paper, we propose an end-to-end temporal abnormality localization for long WCE videos using only weak video level labels. Physicians use Capsule Endoscopy (CE) as a non-surgical and non-invasive method to examine the entire digestive tract in order to diagnose diseases or abnormalities. While CE has revolutionized traditional endoscopy procedures, a single CE examination could last up to 8 hours generating as much as 100,000 frames. Physicians must review the entire video, frame-by-frame, in order to identify the frames capturing relevant abnormality. This, sometimes could be as few as just a single frame. Given this very high level of redundancy, analyzing long CE videos can be very tedious, time consuming and also error prone. This paper presents a novel multi-step method for an end-to-end localization of target frames capturing abnormalities of interest in the long video using only weak video labels. First we developed an automatic temporal segmentation using change point detection technique to temporally segment the video into uniform, homogeneous and identifiable segments. Then we employed Graph Convolutional Neural Network (GCNN) to learn a representation of each video segment. Using weak video segment labels, we trained our GCNN model to recognize each video segment as abnormal if it contains at least a single abnormal frame. Finally, leveraging the parameters of the trained GCNN model, we replaced the final layer of the network with a temporal pool layer to localize the relevant abnormal frames within each abnormal video segment. Our method achieved an accuracy of 89.9\% on the graph classification task and a specificity of 97.5\% on the abnormal frames localization task.
Graph convolutional network (GCN) is one of the most favorable semi-supervised approaches, which demonstrates encouraging performance for hyperspectral image classification (HSIC), especially under the condition of small sample sizes. In this paper, we propose a novel semi-supervised graph prototypical network (SSGPN) for high-precise HSIC. Different from prevenient GCN, we devise a prototypical layer comprising a distance-based cross-entropy (DCE) loss function and a novel temporal entropy-based regularizer (TER) in the frameworks of SSGPN. This effective layer can facilitate to generate more discriminative embedding features along with the representative prototypes to each class, so as to achieve accurate identification of various land-cover categories. Additionally, to promote computational efficiency, we present a graph normalization (G-Norm) to accelerate the convergence speed and boost the training procedure. Experimental results demonstrate that our proposed SSGPN can obtain promising performance compared with the state-of-the-art methods.
Graph Convolutional Networks (GCN) with multi-hop aggregation is more expressive than one-hop GCN but suffers from higher model complexity. Finding the shortest aggregation range that achieves comparable expressiveness and minimizes this side effect remains an open question. We answer this question by showing that multi-layer second-order graph convolution (SoGC) is sufficient to attain the ability of expressing polynomial spectral filters with arbitrary coefficients. Compared to models with one-hop aggregation, multi-hop propagation, and jump connections, SoGC possesses filter representational completeness while being lightweight, efficient, and easy to implement. Thereby, we suggest that SoGC is a simple design capable of forming the basic building block of GCNs, playing the same role as $3 \times 3$ kernels in CNNs. We build our Second-Order Graph Convolutional Networks (SoGCN) with SoGC and design a synthetic dataset to verify its filter fitting capability to validate these points. For real-world tasks, we present the state-of-the-art performance of SoGCN on the benchmark of node classification, graph classification, and graph regression datasets.
The conventional wisdom behind learning deep classification models is to focus on bad-classified examples and ignore well-classified examples that are far from the decision boundary. For instance, when training with cross-entropy loss, examples with higher likelihoods (i.e., well-classified examples) contribute smaller gradients in back-propagation. However, we theoretically show that this common practice hinders representation learning, energy optimization, and margin growth. To counteract this deficiency, we propose to reward well-classified examples with additive bonuses to revive their contribution to the learning process. This counterexample theoretically addresses these three issues. We empirically support this claim by directly verifying the theoretical results or significant performance improvement with our counterexample on diverse tasks, including image classification, graph classification, and machine translation. Furthermore, this paper shows that we can deal with complex scenarios, such as imbalanced classification, OOD detection, and applications under adversarial attacks because our idea can solve these three issues. Code is available at: https://github.com/lancopku/well-classified-examples-are-underestimated.
Given a node-attributed graph, how can we efficiently represent it with few numerical features that expressively reflect its topology and attribute information? We propose A-DOGE, for Attributed DOS-based Graph Embedding, based on density of states (DOS, a.k.a. spectral density) to tackle this problem. A-DOGE is designed to fulfill a long desiderata of desirable characteristics. Most notably, it capitalizes on efficient approximation algorithms for DOS, that we extend to blend in node labels and attributes for the first time, making it fast and scalable for large attributed graphs and graph databases. Being based on the entire eigenspectrum of a graph, A-DOGE can capture structural and attribute properties at multiple ("glocal") scales. Moreover, it is unsupervised (i.e. agnostic to any specific objective) and lends itself to various interpretations, which makes it is suitable for exploratory graph mining tasks. Finally, it processes each graph independent of others, making it amenable for streaming settings as well as parallelization. Through extensive experiments, we show the efficacy and efficiency of A-DOGE on exploratory graph analysis and graph classification tasks, where it significantly outperforms unsupervised baselines and achieves competitive performance with modern supervised GNNs, while achieving the best trade-off between accuracy and runtime.
Network-valued data are encountered in a wide range of applications and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of protein structures and social networks. Various methods, ranging from graph kernels to graph neural networks, have been proposed that achieve some success in graph classification problems. However, most methods have limited theoretical justification, and their applicability beyond classification remains unexplored. In this work, we propose methods for clustering multiple graphs, without vertex correspondence, that are inspired by the recent literature on estimating graphons -- symmetric functions corresponding to infinite vertex limit of graphs. We propose a novel graph distance based on sorting-and-smoothing graphon estimators. Using the proposed graph distance, we present two clustering algorithms and show that they achieve state-of-the-art results. We prove the statistical consistency of both algorithms under Lipschitz assumptions on the graph degrees. We further study the applicability of the proposed distance for graph two-sample testing problems.
Graph is an important data representation ubiquitously existing in the real world. However, analyzing the graph data is computationally difficult due to its non-Euclidean nature. Graph embedding is a powerful tool to solve the graph analytics problem by transforming the graph data into low-dimensional vectors. These vectors could also be shared with third parties to gain additional insights of what is behind the data. While sharing graph embedding is intriguing, the associated privacy risks are unexplored. In this paper, we systematically investigate the information leakage of the graph embedding by mounting three inference attacks. First, we can successfully infer basic graph properties, such as the number of nodes, the number of edges, and graph density, of the target graph with up to 0.89 accuracy. Second, given a subgraph of interest and the graph embedding, we can determine with high confidence that whether the subgraph is contained in the target graph. For instance, we achieve 0.98 attack AUC on the DD dataset. Third, we propose a novel graph reconstruction attack that can reconstruct a graph that has similar graph structural statistics to the target graph. We further propose an effective defense mechanism based on graph embedding perturbation to mitigate the inference attacks without noticeable performance degradation for graph classification tasks. Our code is available at https://github.com/Zhangzhk0819/GNN-Embedding-Leaks.
Graph neural networks (GNNs) have recently emerged as a dominant paradigm for machine learning with graphs. Research on GNNs has mainly focused on the family of message passing neural networks (MPNNs). Similar to the Weisfeiler-Leman (WL) test of isomorphism, these models follow an iterative neighborhood aggregation procedure to update vertex representations, and they next compute graph representations by aggregating the representations of the vertices. Although very successful, MPNNs have been studied intensively in the past few years. Thus, there is a need for novel architectures which will allow research in the field to break away from MPNNs. In this paper, we propose a new graph neural network model, so-called $\pi$-GNN which learns a "soft" permutation (i.e., doubly stochastic) matrix for each graph, and thus projects all graphs into a common vector space. The learned matrices impose a "soft" ordering on the vertices of the input graphs, and based on this ordering, the adjacency matrices are mapped into vectors. These vectors can be fed into fully-connected or convolutional layers to deal with supervised learning tasks. In case of large graphs, to make the model more efficient in terms of running time and memory, we further relax the doubly stochastic matrices to row stochastic matrices. We empirically evaluate the model on graph classification and graph regression datasets and show that it achieves performance competitive with state-of-the-art models.
Graph neural networks have emerged as a powerful model for graph representation learning to undertake graph-level prediction tasks. Various graph pooling methods have been developed to coarsen an input graph into a succinct graph-level representation through aggregating node embeddings obtained via graph convolution. However, most graph pooling methods are heavily node-centric and are unable to fully leverage the crucial information contained in global graph structure. This paper presents a cross-view graph pooling (Co-Pooling) method to better exploit crucial graph structure information. The proposed Co-Pooling fuses pooled representations learnt from both node view and edge view. Through cross-view interaction, edge-view pooling and node-view pooling seamlessly reinforce each other to learn more informative graph-level representations. Co-Pooling has the advantage of handling various graphs with different types of node attributes. Extensive experiments on a total of 15 graph benchmark datasets validate the effectiveness of our proposed method, demonstrating its superior performance over state-of-the-art pooling methods on both graph classification and graph regression tasks.
Graph neural networks (GNNs) have received tremendous attention due to their superiority in learning node representations. These models rely on message passing and feature transformation functions to encode the structural and feature information from neighbors. However, stacking more convolutional layers significantly decreases the performance of GNNs. Most recent studies attribute this limitation to the over-smoothing issue, where node embeddings converge to indistinguishable vectors. Through a number of experimental observations, we argue that the main factor degrading the performance is the unstable forward normalization and backward gradient resulted from the improper design of the feature transformation, especially for shallow GNNs where the over-smoothing has not happened. Therefore, we propose a novel orthogonal feature transformation, named Ortho-GConv, which could generally augment the existing GNN backbones to stabilize the model training and improve the model's generalization performance. Specifically, we maintain the orthogonality of the feature transformation comprehensively from three perspectives, namely hybrid weight initialization, orthogonal transformation, and orthogonal regularization. By equipping the existing GNNs (e.g. GCN, JKNet, GCNII) with Ortho-GConv, we demonstrate the generality of the orthogonal feature transformation to enable stable training, and show its effectiveness for node and graph classification tasks.
In this paper, we investigate the degree of explainability of graph neural networks (GNNs). Existing explainers work by finding global/local subgraphs to explain a prediction, but they are applied after a GNN has already been trained. Here, we propose a meta-learning framework for improving the level of explainability of a GNN directly at training time, by steering the optimization procedure towards what we call `interpretable minima'. Our framework (called MATE, MetA-Train to Explain) jointly trains a model to solve the original task, e.g., node classification, and to provide easily processable outputs for downstream algorithms that explain the model's decisions in a human-friendly way. In particular, we meta-train the model's parameters to quickly minimize the error of an instance-level GNNExplainer trained on-the-fly on randomly sampled nodes. The final internal representation relies upon a set of features that can be `better' understood by an explanation algorithm, e.g., another instance of GNNExplainer. Our model-agnostic approach can improve the explanations produced for different GNN architectures and use any instance-based explainer to drive this process. Experiments on synthetic and real-world datasets for node and graph classification show that we can produce models that are consistently easier to explain by different algorithms. Furthermore, this increase in explainability comes at no cost for the accuracy of the model.