Structural features are important features in a geometrical graph. Although there are some correlation analysis of features based on covariance, there is no relevant research on structural feature correlation analysis with graph neural networks. In this paper, we introuduce graph feature to feature (Fea2Fea) prediction pipelines in a low dimensional space to explore some preliminary results on structural feature correlation, which is based on graph neural network. The results show that there exists high correlation between some of the structural features. An irredundant feature combination with initial node features, which is filtered by graph neural network has improved its classification accuracy in some graph-based tasks. We compare differences between concatenation methods on connecting embeddings between features and show that the simplest is the best. We generalize on the synthetic geometric graphs and certify the results on prediction difficulty between structural features.
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational graph and the input graph structure. The recently proposed Message Passing Simplicial Networks naturally decouple these elements by performing message passing on the clique complex of the graph. Nevertheless, these models can be severely constrained by the rigid combinatorial structure of Simplicial Complexes (SCs). In this work, we extend recent theoretical results on SCs to regular Cell Complexes, topological objects that flexibly subsume SCs and graphs. We show that this generalisation provides a powerful set of graph "lifting" transformations, each leading to a unique hierarchical message passing procedure. The resulting methods, which we collectively call CW Networks (CWNs), are strictly more powerful than the WL test and not less powerful than the 3-WL test. In particular, we demonstrate the effectiveness of one such scheme, based on rings, when applied to molecular graph problems. The proposed architecture benefits from provably larger expressivity than commonly used GNNs, principled modelling of higher-order signals and from compressing the distances between nodes. We demonstrate that our model achieves state-of-the-art results on a variety of molecular datasets.
Graph convolution networks, like message passing graph convolution networks (MPGCNs), have been a powerful tool in representation learning of networked data. However, when data is heterogeneous, most architectures are limited as they employ a single strategy to handle multi-channel graph signals and they typically focus on low-frequency information. In this paper, we present a novel graph convolution operator, termed BankGCN, which keeps benefits of message passing models, but extends their capabilities beyond `low-pass' features. It decomposes multi-channel signals on graphs into subspaces and handles particular information in each subspace with an adapted filter. The filters of all subspaces have different frequency responses and together form a filter bank. Furthermore, each filter in the spectral domain corresponds to a message passing scheme, and diverse schemes are implemented via the filter bank. Importantly, the filter bank and the signal decomposition are jointly learned to adapt to the spectral characteristics of data and to target applications. Furthermore, this is implemented almost without extra parameters in comparison with most existing MPGCNs. Experimental results show that the proposed convolution operator permits to achieve excellent performance in graph classification on a collection of benchmark graph datasets.
Graph Neural Networks (GNNs) are a broad class of connectionist models for graph processing. Recent studies have shown that GNNs can approximate any function on graphs, modulo the equivalence relation on graphs defined by the Weisfeiler--Lehman (WL) test. However, these results suffer from some limitations, both because they were derived using the Stone--Weierstrass theorem -- which is existential in nature, -- and because they assume that the target function to be approximated must be continuous. Furthermore, all current results are dedicated to graph classification/regression tasks, where the GNN must produce a single output for the whole graph, while also node classification/regression problems, in which an output is returned for each node, are very common. In this paper, we propose an alternative way to demonstrate the approximation capability of GNNs that overcomes these limitations. Indeed, we show that GNNs are universal approximators in probability for node classification/regression tasks, as they can approximate any measurable function that satisfies the 1--WL equivalence on nodes. The proposed theoretical framework allows the approximation of generic discontinuous target functions and also suggests the GNN architecture that can reach a desired approximation. In addition, we provide a bound on the number of the GNN layers required to achieve the desired degree of approximation, namely $2r-1$, where $r$ is the maximum number of nodes for the graphs in the domain.
The recent emergence of contrastive learning approaches facilitates the application on graph representation learning (GRL), introducing graph contrastive learning (GCL) into the literature. These methods contrast semantically similar and dissimilar sample pairs to encode the semantics into node or graph embeddings. However, most existing works only performed \textbf{model-level} evaluation, and did not explore the combination space of modules for more comprehensive and systematic studies. For effective \textbf{module-level} evaluation, we propose a framework that decomposes GCL models into four modules: (1) a \textbf{sampler} to generate anchor, positive and negative data samples (nodes or graphs); (2) an \textbf{encoder} and a \textbf{readout} function to get sample embeddings; (3) a \textbf{discriminator} to score each sample pair (anchor-positive and anchor-negative); and (4) an \textbf{estimator} to define the loss function. Based on this framework, we conduct controlled experiments over a wide range of architectural designs and hyperparameter settings on node and graph classification tasks. Specifically, we manage to quantify the impact of a single module, investigate the interaction between modules, and compare the overall performance with current model architectures. Our key findings include a set of module-level guidelines for GCL, e.g., simple samplers from LINE and DeepWalk are strong and robust; an MLP encoder associated with Sum readout could achieve competitive performance on graph classification. Finally, we release our implementations and results as OpenGCL, a modularized toolkit that allows convenient reproduction, standard model and module evaluation, and easy extension. OpenGCL is available at \url{https://github.com/thunlp/OpenGCL}.
Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-range relations in real-world data. In this paper, we propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD), which serves as a generic plug-and-play module for improving the representational power of HGCNNs.Specifically, HERALD adaptively optimizes the adjacency relationship between vertices and hyperedges in an end-to-end manner and thus the task-aware hypergraph is learned. Furthermore, HERALD employs the self-attention mechanism to capture the non-local paired-nodes relation. Extensive experiments on various popular hypergraph datasets for node classification and graph classification tasks demonstrate that our approach obtains consistent and considerable performance enhancement, proving its effectiveness and generalization ability.
Recent years have witnessed tremendous interest in deep learning on graph-structured data. Due to the high cost of collecting labeled graph-structured data, domain adaptation is important to supervised graph learning tasks with limited samples. However, current graph domain adaptation methods are generally adopted from traditional domain adaptation tasks, and the properties of graph-structured data are not well utilized. For example, the observed social networks on different platforms are controlled not only by the different crowd or communities but also by the domain-specific policies and the background noise. Based on these properties in graph-structured data, we first assume that the graph-structured data generation process is controlled by three independent types of latent variables, i.e., the semantic latent variables, the domain latent variables, and the random latent variables. Based on this assumption, we propose a disentanglement-based unsupervised domain adaptation method for the graph-structured data, which applies variational graph auto-encoders to recover these latent variables and disentangles them via three supervised learning modules. Extensive experimental results on two real-world datasets in the graph classification task reveal that our method not only significantly outperforms the traditional domain adaptation methods and the disentangled-based domain adaptation methods but also outperforms the state-of-the-art graph domain adaptation algorithms.
HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-ange relations in real-world data. In this paper, we propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD), which serves as a generic plug-in-play module for improving the representational power of HGCNNs. Specifically, HERALD adaptively optimizes the adjacency relationship between hypernodes and hyperedges in an end-to-end manner and thus the task-aware hypergraph is learned. Furthermore, HERALD employs the self-attention mechanism to capture the non-local paired-nodes relation. Extensive experiments on various popular hypergraph datasets for node classification and graph classification tasks demonstrate that our approach obtains consistent and considerable performance enhancement, proving its effectiveness and generalization ability.
Graph Neural Networks (GNNs) have already been widely used in various graph mining tasks. However, recent works reveal that the learned weights (channels) in well-trained GNNs are highly redundant, which inevitably limits the performance of GNNs. Instead of removing these redundant channels for efficiency consideration, we aim to reactivate them to enlarge the representation capacity of GNNs for effective graph learning. In this paper, we propose to substitute these redundant channels with other informative channels to achieve this goal. We introduce a novel GNN learning framework named AKE-GNN, which performs the Adaptive Knowledge Exchange strategy among multiple graph views generated by graph augmentations. AKE-GNN first trains multiple GNNs each corresponding to one graph view to obtain informative channels. Then, AKE-GNN iteratively exchanges redundant channels in the weight parameter matrix of one GNN with informative channels of another GNN in a layer-wise manner. Additionally, existing GNNs can be seamlessly incorporated into our framework. AKE-GNN achieves superior performance compared with various baselines across a suite of experiments on node classification, link prediction, and graph classification. In particular, we conduct a series of experiments on 15 public benchmark datasets, 8 popular GNN models, and 3 graph tasks and show that AKE-GNN consistently outperforms existing popular GNN models and even their ensembles. Extensive ablation studies and analyses on knowledge exchange methods validate the effectiveness of AKE-GNN.
Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which measure the similaritybetween graphs and are plugged into a kernel machine such as a support vector machine.Weisfeiler-Lehman (WL) based graph kernels, which employ WL labeling scheme to extract subtree patterns and perform node embedding, are demonstrated to achieve great performance while being efficiently computable. However, one of the main drawbacks of ageneral kernel is the decoupling of kernel construction and learning process. For moleculargraphs, usual kernels such as WL subtree, based on substructures of the molecules, consider all available substructures having the same importance, which might not be suitable inpractice. In this paper, we propose a method to learn the weights of subtree patterns in the framework of WWL kernels, the state of the art method for graph classification task [14]. To overcome the computational issue on large scale data sets, we present an efficient learning algorithm and also derive a generalization gap bound to show its convergence. Finally, through experiments on synthetic and real-world data sets, we demonstrate the effectiveness of our proposed method for learning the weights of subtree patterns.
The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared to mainstream GNN variants. Therefore, it remains a mystery how Transformers could perform well for graph representation learning. In this paper, we solve this mystery by presenting Graphormer, which is built upon the standard Transformer architecture, and could attain excellent results on a broad range of graph representation learning tasks, especially on the recent OGB Large-Scale Challenge. Our key insight to utilizing Transformer in the graph is the necessity of effectively encoding the structural information of a graph into the model. To this end, we propose several simple yet effective structural encoding methods to help Graphormer better model graph-structured data. Besides, we mathematically characterize the expressive power of Graphormer and exhibit that with our ways of encoding the structural information of graphs, many popular GNN variants could be covered as the special cases of Graphormer.
We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers ``simple'' problems such as graph classification or regressing real-valued graph properties. For such tasks, the main requirement for intermediate representations of the data is to maintain the structure needed for output, i.e., keeping classes separated or maintaining the order indicated by the regressor. However, a number of learning tasks, such as regressing graph-valued output, generative models, or graph autoencoders, aim to predict a graph-structured output. In order to successfully do this, the learned representations need to preserve far more structure. We present a conditional auto-regressive model for graph-to-graph learning and illustrate its representational capabilities via experiments on challenging subgraph predictions from graph algorithmics; as a graph autoencoder for reconstruction and visualization; and on pretraining representations that allow graph classification with limited labeled data.
We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes the fixed points of a target graph system and decodes them to estimate the stationary properties of the system without the prior knowledge of existing solvers or intermediate solutions. The forward propagation of CGS proceeds in three steps: (1) constructing the input dependent linear contracting iterative maps, (2) computing the fixed-points of the linear maps, and (3) decoding the fixed-points to estimate the properties. The contractivity of the constructed linear maps guarantees the existence and uniqueness of the fixed points following the Banach fixed point theorem. To train CGS efficiently, we also derive a tractable analytical expression for its gradient by leveraging the implicit function theorem. We evaluate the performance of CGS by applying it to various network-analytic and graph benchmark problems. The results indicate that CGS has competitive capabilities for predicting the stationary properties of graph systems, irrespective of whether the target systems are linear or non-linear. CGS also shows high performance for graph classification problems where the existence or the meaning of a fixed point is hard to be clearly defined, which highlights the potential of CGS as a general graph neural network architecture.
Graph Attention Networks (GATs) are one of the most popular GNN architectures and are considered as the state-of-the-art architecture for representation learning with graphs. In GAT, every node attends to its neighbors given its own representation as the query. However, in this paper we show that GAT computes a very limited kind of attention: the ranking of the attention scores is unconditioned on the query node. We formally define this restricted kind of attention as static attention and distinguish it from a strictly more expressive dynamic attention. Because GATs use a static attention mechanism, there are simple graph problems that GAT cannot express: in a controlled problem, we show that static attention hinders GAT from even fitting the training data. To remove this limitation, we introduce a simple fix by modifying the order of operations and propose GATv2: a dynamic graph attention variant that is strictly more expressive than GAT. We perform an extensive evaluation and show that GATv2 outperforms GAT across 11 OGB and other benchmarks while we match their parametric costs. Our code is available at https://github.com/tech-srl/how_attentive_are_gats . GATv2 is available as part of the PyTorch Geometric library, the Deep Graph Library, and the TensorFlow GNN library.
We present the Topology Transformation Equivariant Representation learning, a general paradigm of self-supervised learning for node representations of graph data to enable the wide applicability of Graph Convolutional Neural Networks (GCNNs). We formalize the proposed model from an information-theoretic perspective, by maximizing the mutual information between topology transformations and node representations before and after the transformations. We derive that maximizing such mutual information can be relaxed to minimizing the cross entropy between the applied topology transformation and its estimation from node representations. In particular, we seek to sample a subset of node pairs from the original graph and flip the edge connectivity between each pair to transform the graph topology. Then, we self-train a representation encoder to learn node representations by reconstructing the topology transformations from the feature representations of the original and transformed graphs. In experiments, we apply the proposed model to the downstream node classification, graph classification and link prediction tasks, and results show that the proposed method outperforms the state-of-the-art unsupervised approaches.
Graph convolutional networks (GCNs) are widely used in graph-based applications such as graph classification and segmentation. However, current GCNs have limitations on implementation such as network architectures due to their irregular inputs. In contrast, convolutional neural networks (CNNs) are capable of extracting rich features from large-scale input data, but they do not support general graph inputs. To bridge the gap between GCNs and CNNs, in this paper we study the problem of how to effectively and efficiently map general graphs to 2D grids that CNNs can be directly applied to, while preserving graph topology as much as possible. We therefore propose two novel graph-to-grid mapping schemes, namely, {\em graph-preserving grid layout (GPGL)} and its extension {\em Hierarchical GPGL (H-GPGL)} for computational efficiency. We formulate the GPGL problem as integer programming and further propose an approximate yet efficient solver based on a penalized Kamada-Kawai method, a well-known optimization algorithm in 2D graph drawing. We propose a novel vertex separation penalty that encourages graph vertices to lay on the grid without any overlap. Along with this image representation, even extra 2D maxpooling layers contribute to the PointNet, a widely applied point-based neural network. We demonstrate the empirical success of GPGL on general graph classification with small graphs and H-GPGL on 3D point cloud segmentation with large graphs, based on 2D CNNs including VGG16, ResNet50 and multi-scale maxout (MSM) CNN.
The morphology and distribution of microcalcifications in a cluster are the most important characteristics for radiologists to diagnose breast cancer. However, it is time-consuming and difficult for radiologists to identify these characteristics, and there also lacks of effective solutions for automatic characterization. In this study, we proposed a multi-task deep graph convolutional network (GCN) method for the automatic characterization of morphology and distribution of microcalcifications in mammograms. Our proposed method transforms morphology and distribution characterization into node and graph classification problem and learns the representations concurrently. Through extensive experiments, we demonstrate significant improvements with the proposed multi-task GCN comparing to the baselines. Moreover, the achieved improvements can be related to and enhance clinical understandings. We explore, for the first time, the application of GCNs in microcalcification characterization that suggests the potential of graph learning for more robust understanding of medical images.
Online stores often utilize product relationships such as bundles and substitutes to improve their catalog quality and guide customers through myriad choices. Entity resolution using pairwise product matching models offers a means of inferring relationships between products. In mature data repositories, the relationships may be mostly correct but require incremental improvements owing to errors in the original data or in the entity resolution system. It is critical to devise incremental entity resolution (IER) approaches for improving the health of relationships. However, most existing research on IER focuses on the addition of new products or information into existing relationships. Relatively little research has been done for detecting low quality within current relationships. This paper proposes a novel method for identifying inconsistent clusters (IC), existing groups of related products that do not belong together. We propose to treat the identification of inconsistent clusters as a supervised learning task which predicts whether a graph of products with similarities as weighted edges should be partitioned into multiple clusters. In this case, the problem becomes a classification task on weighted graphs and represents an interesting application area for modern tools such as Graph Neural Networks (GNNs). We demonstrate that existing Message Passing neural networks perform well at this task, exceeding traditional graph processing techniques. We also develop a novel message aggregation scheme for Message Passing Neural Networks that further improves the performance of GNNs on this task. We apply the model to synthetic datasets, a public benchmark dataset, and an internal application. Our results demonstrate the value of graph classification in IER and the ability of graph neural networks to develop useful representations for graph partitioning.
Graph pooling is an essential ingredient of Graph Neural Networks (GNNs) in graph classification and regression tasks. For these tasks, different pooling strategies have been proposed to generate a graph-level representation by downsampling and summarizing nodes' features in a graph. However, most existing pooling methods are unable to capture distinguishable structural information effectively. Besides, they are prone to adversarial attacks. In this work, we propose a novel pooling method named as {HIBPool} where we leverage the Information Bottleneck (IB) principle that optimally balances the expressiveness and robustness of a model to learn representations of input data. Furthermore, we introduce a novel structure-aware Discriminative Pooling Readout ({DiP-Readout}) function to capture the informative local subgraph structures in the graph. Finally, our experimental results show that our model significantly outperforms other state-of-art methods on several graph classification benchmarks and more resilient to feature-perturbation attack than existing pooling methods.
Disinformation and fake news have posed detrimental effects on individuals and society in recent years, attracting broad attention to fake news detection. The majority of existing fake news detection algorithms focus on mining news content and/or the surrounding exogenous context for discovering deceptive signals; while the endogenous preference of a user when he/she decides to spread a piece of fake news or not is ignored. The confirmation bias theory has indicated that a user is more likely to spread a piece of fake news when it confirms his/her existing beliefs/preferences. Users' historical, social engagements such as posts provide rich information about users' preferences toward news and have great potential to advance fake news detection. However, the work on exploring user preference for fake news detection is somewhat limited. Therefore, in this paper, we study the novel problem of exploiting user preference for fake news detection. We propose a new framework, UPFD, which simultaneously captures various signals from user preferences by joint content and graph modeling. Experimental results on real-world datasets demonstrate the effectiveness of the proposed framework. We release our code and data as a benchmark for GNN-based fake news detection: https://github.com/safe-graph/GNN-FakeNews.