Graph Neural Networks (GNNs) have attracted considerable attention and have emerged as a new promising paradigm to process graph-structured data. GNNs are usually stacked to multiple layers and the node representations in each layer are computed through propagating and aggregating the neighboring node features with respect to the graph. By stacking to multiple layers, GNNs are able to capture the long-range dependencies among the data on the graph and thus bring performance improvements. To train a GNN with multiple layers effectively, some normalization techniques (e.g., node-wise normalization, batch-wise normalization) are necessary. However, the normalization techniques for GNNs are highly task-relevant and different application tasks prefer to different normalization techniques, which is hard to know in advance. To tackle this deficiency, in this paper, we propose to learn graph normalization by optimizing a weighted combination of normalization techniques at four different levels, including node-wise normalization, adjacency-wise normalization, graph-wise normalization, and batch-wise normalization, in which the adjacency-wise normalization and the graph-wise normalization are newly proposed in this paper to take into account the local structure and the global structure on the graph, respectively. By learning the optimal weights, we are able to automatically select a single best or a best combination of multiple normalizations for a specific task. We conduct extensive experiments on benchmark datasets for different tasks, including node classification, link prediction, graph classification and graph regression, and confirm that the learned graph normalization leads to competitive results and that the learned weights suggest the appropriate normalization techniques for the specific task. Source code is released here https://github.com/cyh1112/GraphNormalization.
Graph neural networks (GNN) are powerful models for many graph-structured tasks. Existing models often assume that the complete structure of the graph is available during training. In practice, however, graph-structured data is usually formed in a streaming fashion so that learning a graph continuously is often necessary. In this paper, we bridge GNN and lifelong learning by converting a continual graph learning problem to a regular graph learning problem so GNN can inherit the lifelong learning techniques developed for convolutional neural networks (CNN). We propose a new topology, the feature graph, which takes features as new nodes and turns nodes into independent graphs. This successfully converts the original problem of node classification to graph classification. In the experiments, we demonstrate the efficiency and effectiveness of feature graph networks (FGN) by continuously learning a sequence of classical graph datasets. We also show that FGN achieves superior performance in two applications, i.e., lifelong human action recognition with wearable devices and feature matching. To the best of our knowledge, FGN is the first method to bridge graph learning and lifelong learning via a novel graph topology. Source code is available at https://github.com/wang-chen/LGL
Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QGNN}.
We propose PiNet, a generalised differentiable attention-based pooling mechanism for utilising graph convolution operations for graph level classification. We demonstrate high sample efficiency and superior performance over other graph neural networks in distinguishing isomorphic graph classes, as well as competitive results with state of the art methods on standard chemo-informatics datasets.
Feature interactions are essential for achieving high accuracy in recommender systems. Many studies take into account the interaction between every pair of features. However, this is suboptimal because some feature interactions may not be that relevant to the recommendation result, and taking them into account may introduce noise and decrease recommendation accuracy. To make the best out of feature interactions, we propose a graph neural network approach to effectively model them, together with a novel technique to automatically detect those feature interactions that are beneficial in terms of recommendation accuracy. The automatic feature interaction detection is achieved via edge prediction with an L0 activation regularization. Our proposed model is proved to be effective through the information bottleneck principle and statistical interaction theory. Experimental results show that our model (i) outperforms existing baselines in terms of accuracy, and (ii) automatically identifies beneficial feature interactions.
Graph neural networks have achieved great success in learning node representations for graph tasks such as node classification and link prediction. Graph representation learning requires graph pooling to obtain graph representations from node representations. It is challenging to develop graph pooling methods due to the variable sizes and isomorphic structures of graphs. In this work, we propose to use second-order pooling as graph pooling, which naturally solves the above challenges. In addition, compared to existing graph pooling methods, second-order pooling is able to use information from all nodes and collect second-order statistics, making it more powerful. We show that direct use of second-order pooling with graph neural networks leads to practical problems. To overcome these problems, we propose two novel global graph pooling methods based on second-order pooling; namely, bilinear mapping and attentional second-order pooling. In addition, we extend attentional second-order pooling to hierarchical graph pooling for more flexible use in GNNs. We perform thorough experiments on graph classification tasks to demonstrate the effectiveness and superiority of our proposed methods. Experimental results show that our methods improve the performance significantly and consistently.
Recently, there has been an increasing interest in (supervised) learning with graph data, especially using graph neural networks. However, the development of meaningful benchmark datasets and standardized evaluation procedures is lagging, consequently hindering advancements in this area. To address this, we introduce the TUDataset for graph classification and regression. The collection consists of over 120 datasets of varying sizes from a wide range of applications. We provide Python-based data loaders, kernel and graph neural network baseline implementations, and evaluation tools. Here, we give an overview of the datasets, standardized evaluation procedures, and provide baseline experiments. All datasets are available at www.graphlearning.io. The experiments are fully reproducible from the code available at www.github.com/chrsmrrs/tudataset.
While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to the task of graph similarity learning. Recent work on graph similarity learning has considered either global-level graph-graph interactions or low-level node-node interactions, however ignoring the rich cross-level interactions (e.g., between each node of one graph and the other whole graph). In this paper, we propose a multi-level graph matching network (MGMN) framework for computing the graph similarity between any pair of graph-structured objects in an end-to-end fashion. In particular, the proposed MGMN consists of a node-graph matching network for effectively learning cross-level interactions between each node of one graph and the other whole graph, and a siamese graph neural network to learn global-level interactions between two input graphs. Furthermore, to compensate for the lack of standard benchmark datasets, we have created and collected a set of datasets for both the graph-graph classification and graph-graph regression tasks with different sizes in order to evaluate the effectiveness and robustness of our models. Comprehensive experiments demonstrate that MGMN consistently outperforms state-of-the-art baseline models on both the graph-graph classification and graph-graph regression tasks. Compared with previous work, MGMN also exhibits stronger robustness as the sizes of the two input graphs increase.
Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks. Code is available at https://github.com/chennnM/GCNII .
Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator that is based on the 2-dimensional WL test. We formally show that the resulting 2-WL-GNN architecture is more discriminative than existing GNN approaches. This theoretical result is complemented by experimental studies using synthetic and real data. On multiple common graph classification benchmarks, we demonstrate that the proposed model is competitive with state-of-the-art graph kernels and GNNs.
Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus providing a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.
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.
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.
We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Unlike prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance while having superior computational efficiency. The code is available at https://github.com/navid-naderi/WEGL.
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.
While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the expressive power of standard GNNs is bounded by the Weisfeiler-Leman (WL) graph isomorphism test, from which they inherit proven limitations such as the inability to detect and count graph substructures. On the other hand, there is significant empirical evidence, e.g. in network science and bioinformatics, that substructures are often intimately related to downstream tasks. To this end, we propose "Graph Substructure Networks" (GSN), a topologically-aware message passing scheme based on substructure encoding. We theoretically analyse the expressive power of our architecture, showing that it is strictly more expressive than the WL test, and provide sufficient conditions for universality. Importantly, we do not attempt to adhere to the WL hierarchy; this allows us to retain multiple attractive properties of standard GNNs such as locality and linear network complexity, while being able to disambiguate even hard instances of graph isomorphism. We perform an extensive experimental evaluation on graph classification and regression tasks and obtain state-of-the-art results in diverse real-world settings including molecular graphs and social networks. The code is publicly available at https://github.com/gbouritsas/graph-substructure-networks.
We introduce a self-supervised approach for learning node and graph level representations by contrasting structural views of graphs. We show that unlike visual representation learning, increasing the number of views to more than two or contrasting multi-scale encodings do not improve performance, and the best performance is achieved by contrasting encodings from first-order neighbors and a graph diffusion. We achieve new state-of-the-art results in self-supervised learning on 8 out of 8 node and graph classification benchmarks under the linear evaluation protocol. For example, on Cora (node) and Reddit-Binary (graph) classification benchmarks, we achieve 86.8% and 84.5% accuracy, which are 5.5% and 2.4% relative improvements over previous state-of-the-art. When compared to supervised baselines, our approach outperforms them in 4 out of 8 benchmarks. Source code is released at: https://github.com/kavehhassani/mvgrl
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.
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.