Existing graph neural networks (GNNs) largely rely on node embeddings, which represent a node as a vector by its identity, type, or content. However, graphs with unattributed nodes widely exist in real-world applications (e.g., anonymized social networks). Previous GNNs either assign random labels to nodes (which introduces artefacts to the GNN) or assign one embedding to all nodes (which fails to explicitly distinguish one node from another). Further, when these GNNs are applied to unattributed node classification problems, they have an undesired equivariance property, which are fundamentally unable to address the data with multiple possible outputs. In this paper, we analyze the limitation of existing approaches to node classification problems. Inspired by our analysis, we propose a generalized equivariance property and a Preferential Labeling technique that satisfies the desired property asymptotically. Experimental results show that we achieve high performance in several unattributed node classification tasks.
Graph neural networks have been widely used on modeling graph data, achieving impressive results on node classification and link prediction tasks. Yet, obtaining an accurate representation for a graph further requires a pooling function that maps a set of node representations into a compact form. A simple sum or average over all node representations considers all node features equally without consideration of their task relevance, and any structural dependencies among them. Recently proposed hierarchical graph pooling methods, on the other hand, may yield the same representation for two different graphs that are distinguished by the Weisfeiler-Lehman test, as they suboptimally preserve information from the node features. To tackle these limitations of existing graph pooling methods, we first formulate the graph pooling problem as a multiset encoding problem with auxiliary information about the graph structure, and propose a Graph Multiset Transformer (GMT) which is a multi-head attention based global pooling layer that captures the interaction between nodes according to their structural dependencies. We show that GMT satisfies both injectiveness and permutation invariance, such that it is at most as powerful as the Weisfeiler-Lehman graph isomorphism test. Moreover, our methods can be easily extended to the previous node clustering approaches for hierarchical graph pooling. Our experimental results show that GMT significantly outperforms state-of-the-art graph pooling methods on graph classification benchmarks with high memory and time efficiency, and obtains even larger performance gain on graph reconstruction and generation tasks.
Machine learning on graph-structured data has attracted high research interest due to the emergence of Graph Neural Networks (GNNs). Most of the proposed GNNs are based on the node homophily, i.e neighboring nodes share similar characteristics. However, in many complex networks, nodes that lie to distant parts of the graph share structurally equivalent characteristics and exhibit similar roles (e.g chemical properties of distant atoms in a molecule, type of social network users). A growing literature proposed representations that identify structurally equivalent nodes. However, most of the existing methods require high time and space complexity. In this paper, we propose VNEstruct, a simple approach, based on entropy measures of the neighborhood's topology, for generating low-dimensional structural representations, that is time-efficient and robust to graph perturbations. Empirically, we observe that VNEstruct exhibits robustness on structural role identification tasks. Moreover, VNEstruct can achieve state-of-the-art performance on graph classification, without incorporating the graph structure information in the optimization, in contrast to GNN competitors.
We propose CRaWl, a novel neural network architecture for graph learning. Like graph neural networks, CRaWl layers update node features on a graph and thus can freely be combined or interleaved with GNN layers. Yet CRaWl operates fundamentally different from message passing graph neural networks. CRaWl layers extract and aggregate information on subgraphs appearing along random walks through a graph using 1D Convolutions. Thereby it detects long range interactions and computes non-local features. As the theoretical basis for our approach, we prove a theorem stating that the expressiveness of CRaWl is incomparable with that of the Weisfeiler Leman algorithm and hence with graph neural networks. That is, there are functions expressible by CRaWl, but not by GNNs and vice versa. This result extends to higher levels of the Weisfeiler Leman hierarchy and thus to higher-order GNNs. Empirically, we show that CRaWl matches state-of-the-art GNN architectures across a multitude of benchmark datasets for classification and regression on graphs.
Adversarial Machine Learning has emerged as a substantial subfield of Computer Science due to a lack of robustness in the models we train along with crowdsourcing practices that enable attackers to tamper with data. In the last two years, interest has surged in adversarial attacks on graphs yet the Graph Classification setting remains nearly untouched. Since a Graph Classification dataset consists of discrete graphs with class labels, related work has forgone direct gradient optimization in favor of an indirect Reinforcement Learning approach. We will study the novel problem of Data Poisoning (training time) attack on Neural Networks for Graph Classification using Reinforcement Learning Agents.
Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.
Training scene graph classification models requires a large amount of annotated image data. Meanwhile, scene graphs represent relational knowledge that can be modeled with symbolic data from texts or knowledge graphs. While image annotation demands extensive labor, collecting textual descriptions of natural scenes requires less effort. In this work, we investigate whether textual scene descriptions can substitute for annotated image data. To this end, we employ a scene graph classification framework that is trained not only from annotated images but also from symbolic data. In our architecture, the symbolic entities are first mapped to their correspondent image-grounded representations and then fed into the relational reasoning pipeline. Even though a structured form of knowledge, such as the form in knowledge graphs, is not always available, we can generate it from unstructured texts using a transformer-based language model. We show that by fine-tuning the classification pipeline with the extracted knowledge from texts, we can achieve ~8x more accurate results in scene graph classification, ~3x in object classification, and ~1.5x in predicate classification, compared to the supervised baselines with only 1% of the annotated images.
Graph neural networks are emerging as continuation of deep learning success w.r.t. graph data. Tens of different graph neural network variants have been proposed, most following a neighborhood aggregation scheme, where the node features are updated via aggregating features of its neighboring nodes from layer to layer. Though related research surges, the power of GNNs are still not on-par-with their counterpart CNNs in computer vision and RNNs in natural language processing. We rethink this problem from the perspective of information propagation, and propose to enhance information propagation among GNN layers by combining heterogeneous aggregations. We argue that as richer information are propagated from shallow to deep layers, the discriminative capability of features formulated by GNN can benefit from it. As our first attempt in this direction, a new generic GNN layer formulation and upon this a new GNN variant referred as HAG-Net is proposed. We empirically validate the effectiveness of HAG-Net on a number of graph classification benchmarks, and elaborate all the design options and criterions along with.
Social and information networks are gaining huge popularity recently due to their various applications. Knowledge representation through graphs in the form of nodes and edges should preserve as many characteristics of the original data as possible. Some of the interesting and useful applications on these graphs are graph classification, node classification, link prediction, etc. The Graph Neural Networks have evolved over the last few years. Graph Neural Networks (GNNs) are efficient ways to get insight into large and dynamic graph datasets capturing relationships among billions of entities also known as knowledge graphs. In this paper, we discuss the graph convolutional neural networks graph autoencoders and spatio-temporal graph neural networks. The representations of the graph in lower dimensions can be learned using these methods. The representations in lower dimensions can be used further for downstream machine learning tasks.
Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named GraphCSC that realizes classification based on skeleton information using fixed-order structures learned in anonymous random walks manner, and component information using different size subgraphs. Two graphs are similar if their skeletons and components are both similar, thus in our model, we integrate both of them together into embeddings as graph homogeneity characterization. We demonstrate our model on different datasets in comparison with a comprehensive list of up-to-date state-of-the-art baselines, and experiments show that our work is superior in real-world graph classification tasks.
We introduce tf_geometric, an efficient and friendly library for graph deep learning, which is compatible with both TensorFlow 1.x and 2.x. tf_geometric provides kernel libraries for building Graph Neural Networks (GNNs) as well as implementations of popular GNNs. The kernel libraries consist of infrastructures for building efficient GNNs, including graph data structures, graph map-reduce framework, graph mini-batch strategy, etc. These infrastructures enable tf_geometric to support single-graph computation, multi-graph computation, graph mini-batch, distributed training, etc.; therefore, tf_geometric can be used for a variety of graph deep learning tasks, such as transductive node classification, inductive node classification, link prediction, and graph classification. Based on the kernel libraries, tf_geometric implements a variety of popular GNN models for different tasks. To facilitate the implementation of GNNs, tf_geometric also provides some other libraries for dataset management, graph sampling, etc. Different from existing popular GNN libraries, tf_geometric provides not only Object-Oriented Programming (OOP) APIs, but also Functional APIs, which enable tf_geometric to handle advanced graph deep learning tasks such as graph meta-learning. The APIs of tf_geometric are friendly, and they are suitable for both beginners and experts. In this paper, we first present an overview of tf_geometric's framework. Then, we conduct experiments on some benchmark datasets and report the performance of several popular GNN models implemented by tf_geometric.
Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means GNNs that are not able to predict node clustering coefficients and shortest path distances, and cannot differentiate between different d-regular graphs. Here we develop a class of message passing GNNs, named Identity-aware Graph Neural Networks (ID-GNNs), with greater expressive power than the 1-WL test. ID-GNN offers a minimal but powerful solution to limitations of existing GNNs. ID-GNN extends existing GNN architectures by inductively considering nodes' identities during message passing. To embed a given node, ID-GNN first extracts the ego network centered at the node, then conducts rounds of heterogeneous message passing, where different sets of parameters are applied to the center node than to other surrounding nodes in the ego network. We further propose a simplified but faster version of ID-GNN that injects node identity information as augmented node features. Altogether, both versions of ID-GNN represent general extensions of message passing GNNs, where experiments show that transforming existing GNNs to ID-GNNs yields on average 40% accuracy improvement on challenging node, edge, and graph property prediction tasks; 3% accuracy improvement on node and graph classification benchmarks; and 15% ROC AUC improvement on real-world link prediction tasks. Additionally, ID-GNNs demonstrate improved or comparable performance over other task-specific graph networks.
In many domains data is currently represented as graphs and therefore, the graph representation of this data becomes increasingly important in machine learning. Network data is, implicitly or explicitly, always represented using a graph shift operator (GSO) with the most common choices being the adjacency, Laplacian matrices and their normalisations. In this paper, a novel parametrised GSO (PGSO) is proposed, where specific parameter values result in the most commonly used GSOs and message-passing operators in graph neural network (GNN) frameworks. The PGSO is suggested as a replacement of the standard GSOs that are used in state-of-the-art GNN architectures and the optimisation of the PGSO parameters is seamlessly included in the model training. It is proved that the PGSO has real eigenvalues and a set of real eigenvectors independent of the parameter values and spectral bounds on the PGSO are derived. PGSO parameters are shown to adapt to the sparsity of the graph structure in a study on stochastic blockmodel networks, where they are found to automatically replicate the GSO regularisation found in the literature. On several real-world datasets the accuracy of state-of-the-art GNN architectures is improved by the inclusion of the PGSO in both node- and graph-classification tasks.
Graph representation learning has attracted increasing research attention. However, most existing studies fuse all structural features and node attributes to provide an overarching view of graphs, neglecting finer substructures' semantics, and suffering from interpretation enigmas. This paper presents a novel hierarchical subgraph-level selection and embedding based graph neural network for graph classification, namely SUGAR, to learn more discriminative subgraph representations and respond in an explanatory way. SUGAR reconstructs a sketched graph by extracting striking subgraphs as the representative part of the original graph to reveal subgraph-level patterns. To adaptively select striking subgraphs without prior knowledge, we develop a reinforcement pooling mechanism, which improves the generalization ability of the model. To differentiate subgraph representations among graphs, we present a self-supervised mutual information mechanism to encourage subgraph embedding to be mindful of the global graph structural properties by maximizing their mutual information. Extensive experiments on six typical bioinformatics datasets demonstrate a significant and consistent improvement in model quality with competitive performance and interpretability.
Graph neural networks (GNNs) have been successfully exploited in graph analysis tasks in many real-world applications. The competition between attack and defense methods also enhances the robustness of GNNs. In this competition, the development of adversarial training methods put forward higher requirement for the diversity of attack examples. By contrast, most attack methods with specific attack strategies are difficult to satisfy such a requirement. To address this problem, we propose GraphAttacker, a novel generic graph attack framework that can flexibly adjust the structures and the attack strategies according to the graph analysis tasks. GraphAttacker generates adversarial examples through alternate training on three key components: the multi-strategy attack generator (MAG), the similarity discriminator (SD), and the attack discriminator (AD), based on the generative adversarial network (GAN). Furthermore, we introduce a novel similarity modification rate SMR to conduct a stealthier attack considering the change of node similarity distribution. Experiments on various benchmark datasets demonstrate that GraphAttacker can achieve state-of-the-art attack performance on graph analysis tasks of node classification, graph classification, and link prediction, no matter the adversarial training is conducted or not. Moreover, we also analyze the unique characteristics of each task and their specific response in the unified attack framework. The project code is available at https://github.com/honoluluuuu/GraphAttacker.
Graph Neural Networks (GNNs), which generalize traditional deep neural networks on graph data, have achieved state-of-the-art performance on several graph analytical tasks. We focus on how trained GNN models could leak information about the \emph{member} nodes that they were trained on. We introduce two realistic settings for performing a membership inference (MI) attack on GNNs. While choosing the simplest possible attack model that utilizes the posteriors of the trained model (black-box access), we thoroughly analyze the properties of GNNs and the datasets which dictate the differences in their robustness towards MI attack. While in traditional machine learning models, overfitting is considered the main cause of such leakage, we show that in GNNs the additional structural information is the major contributing factor. We support our findings by extensive experiments on four representative GNN models. To prevent MI attacks on GNN, we propose two effective defenses that significantly decreases the attacker's inference by up to 60% without degradation to the target model's performance. Our code is available at https://github.com/iyempissy/rebMIGraph.
Graph classification is a critical research problem in many applications from different domains. In order to learn a graph classification model, the most widely used supervision component is an output layer together with classification loss (e.g.,cross-entropy loss together with softmax or margin loss). In fact, the discriminative information among instances are more fine-grained, which can benefit graph classification tasks. In this paper, we propose the novel Label Contrastive Coding based Graph Neural Network (LCGNN) to utilize label information more effectively and comprehensively. LCGNN still uses the classification loss to ensure the discriminability of classes. Meanwhile, LCGNN leverages the proposed Label Contrastive Loss derived from self-supervised learning to encourage instance-level intra-class compactness and inter-class separability. To power the contrastive learning, LCGNN introduces a dynamic label memory bank and a momentum updated encoder. Our extensive evaluations with eight benchmark graph datasets demonstrate that LCGNN can outperform state-of-the-art graph classification models. Experimental results also verify that LCGNN can achieve competitive performance with less training data because LCGNN exploits label information comprehensively.
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their associated persistence diagrams capture features of the graphs that are best suited to a given data science problem. Since the spectral wavelet signature of a graph is derived from its Laplacian, our framework encodes geometric properties of graphs in their associated persistence diagrams and can be applied to graphs without a priori node attributes. We apply our framework to graph classification problems and obtain performances competitive with other persistence-based architectures. To provide the underlying theoretical foundations, we extend the differentiability result for ordinary persistent homology to extended persistent homology.
What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles, pre-trained models cooperate to make classification decisions. To quantify the importance of models in these ensemble games, we define \textit{Troupe} -- an efficient algorithm which allocates payoffs based on approximate Shapley values of the classifiers. We argue that the Shapley value of models in these games is an effective decision metric for choosing a high performing subset of models from the ensemble. Our analytical findings prove that our Shapley value estimation scheme is precise and scalable; its performance increases with size of the dataset and ensemble. Empirical results on real world graph classification tasks demonstrate that our algorithm produces high quality estimates of the Shapley value. We find that Shapley values can be utilized for ensemble pruning, and that adversarial models receive a low valuation. Complex classifiers are frequently found to be responsible for both correct and incorrect classification decisions.
Convolution and pooling are the key operations to learn hierarchical representation for graph classification, where more expressive $k$-order($k>1$) method requires more computation cost, limiting the further applications. In this paper, we investigate the strategy of selecting $k$ via neighborhood information gain and propose light $k$-order convolution and pooling requiring fewer parameters while improving the performance. Comprehensive and fair experiments through six graph classification benchmarks show: 1) the performance improvement is consistent to the $k$-order information gain. 2) the proposed convolution requires fewer parameters while providing competitive results. 3) the proposed pooling outperforms SOTA algorithms in terms of efficiency and performance.