Graph Neural Networks (GNNs) have achieved remarkable performance in modeling graphs for various applications. However, most existing GNNs assume the graphs exhibit strong homophily in node labels, i.e., nodes with similar labels are connected in the graphs. They fail to generalize to heterophilic graphs where linked nodes may have dissimilar labels and attributes. Therefore, in this paper, we investigate a novel framework that performs well on graphs with either homophily or heterophily. More specifically, we propose a label-wise message passing mechanism to avoid the negative effects caused by aggregating dissimilar node representations and preserve the heterophilic contexts for representation learning. We further propose a bi-level optimization method to automatically select the model for graphs with homophily/heterophily. Theoretical analysis and extensive experiments demonstrate the effectiveness of our proposed framework for node classification on both homophilic and heterophilic graphs.
User profiling has long been an important problem that investigates user interests in many real applications. Some recent works regard users and their interacted objects as entities of a graph and turn the problem into a node classification task. However, they neglect the difference of distinct interaction types, e.g. user clicks an item v.s.user purchases an item, and thus cannot incorporate such information well. To solve these issues, we propose to leverage the relation-aware heterogeneous graph method for user profiling, which also allows capturing significant meta relations. We adopt the query, key, and value mechanism in a transformer fashion for heterogeneous message passing so that entities can effectively interact with each other. Via such interactions on different relation types, our model can generate representations with rich information for the user profile prediction. We conduct experiments on two real-world e-commerce datasets and observe a significant performance boost of our approach.
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.
Recent advancements in Graph Neural Networks have led to state-of-the-art performance on graph representation learning. However, the majority of existing works process directed graphs by symmetrization, which causes loss of directional information. To address this issue, we introduce the magnetic Laplacian, a discrete Schr\"odinger operator with magnetic field, which preserves edge directionality by encoding it into a complex phase with an electric charge parameter. By adopting a truncated variant of PageRank named Linear- Rank, we design and build a low-pass filter for homogeneous graphs and a high-pass filter for heterogeneous graphs. In this work, we propose a complex-valued graph convolutional network named Magnetic Graph Convolutional network (MGC). With the corresponding complex-valued techniques, we ensure our model will be degenerated into real-valued when the charge parameter is in specific values. We test our model on several graph datasets including directed homogeneous and heterogeneous graphs. The experimental results demonstrate that MGC is fast, powerful, and widely applicable.
Graph Representation Learning (GRL) methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are beyond the capabilities of current methods and software implementations. We present GRAPE, a software resource for graph processing and embedding that can scale with big graphs by using specialized and smart data structures, algorithms, and a fast parallel implementation of random walk-based methods. Compared with state-of-the-art software resources, GRAPE shows an improvement of orders of magnitude in empirical space and time complexity, as well as a competitive edge and node label prediction performance. GRAPE comprises about 1.7 million well-documented lines of Python and Rust code and provides 69 node embedding methods, 25 inference models, a collection of efficient graph processing utilities and over 80,000 graphs from the literature and other sources. Standardized interfaces allow seamless integration of third-party libraries, while ready-to-use and modular pipelines permit an easy-to-use evaluation of GRL methods, therefore also positioning GRAPE as a software resource to perform a fair comparison between methods and libraries for graph processing and embedding.
The class imbalance problem, as an important issue in learning node representations, has drawn increasing attention from the community. Although the imbalance considered by existing studies roots from the unequal quantity of labeled examples in different classes (quantity imbalance), we argue that graph data expose a unique source of imbalance from the asymmetric topological properties of the labeled nodes, i.e., labeled nodes are not equal in terms of their structural role in the graph (topology imbalance). In this work, we first probe the previously unknown topology-imbalance issue, including its characteristics, causes, and threats to semi-supervised node classification learning. We then provide a unified view to jointly analyzing the quantity- and topology- imbalance issues by considering the node influence shift phenomenon with the Label Propagation algorithm. In light of our analysis, we devise an influence conflict detection -- based metric Totoro to measure the degree of graph topology imbalance and propose a model-agnostic method ReNode to address the topology-imbalance issue by re-weighting the influence of labeled nodes adaptively based on their relative positions to class boundaries. Systematic experiments demonstrate the effectiveness and generalizability of our method in relieving topology-imbalance issue and promoting semi-supervised node classification. The further analysis unveils varied sensitivity of different graph neural networks (GNNs) to topology imbalance, which may serve as a new perspective in evaluating GNN architectures.
Graph convolutional neural networks (GCNNs) are popular deep learning architectures that, upon replacing regular convolutions with graph filters (GFs), generalize CNNs to irregular domains. However, classical GFs are prone to numerical errors since they consist of high-order polynomials. This problem is aggravated when several filters are applied in cascade, limiting the practical depth of GCNNs. To tackle this issue, we present the neighborhood graph filters (NGFs), a family of GFs that replaces the powers of the graph shift operator with $k$-hop neighborhood adjacency matrices. NGFs help to alleviate the numerical issues of traditional GFs, allow for the design of deeper GCNNs, and enhance the robustness to errors in the topology of the graph. To illustrate the advantage over traditional GFs in practical applications, we use NGFs in the design of deep neighborhood GCNNs to solve graph signal denoising and node classification problems over both synthetic and real-world data.
Network representation learning aims to generate an embedding for each node in a network, which facilitates downstream machine learning tasks such as node classification and link prediction. Current work mainly focuses on transductive network representation learning, i.e. generating fixed node embeddings, which is not suitable for real-world applications. Therefore, we propose a new inductive network representation learning method called MNCI by mining neighborhood and community influences in temporal networks. We propose an aggregator function that integrates neighborhood influence with community influence to generate node embeddings at any time. We conduct extensive experiments on several real-world datasets and compare MNCI with several state-of-the-art baseline methods on various tasks, including node classification and network visualization. The experimental results show that MNCI achieves better performance than baselines.
While deep neural networks have achieved great success in graph analysis, recent work has shown that they are vulnerable to adversarial attacks. Compared with adversarial attacks on image classification, performing adversarial attacks on graphs is more challenging because of the discrete and non-differential nature of the adjacent matrix for a graph. In this work, we propose Cluster Attack -- a Graph Injection Attack (GIA) on node classification, which injects fake nodes into the original graph to degenerate the performance of graph neural networks (GNNs) on certain victim nodes while affecting the other nodes as little as possible. We demonstrate that a GIA problem can be equivalently formulated as a graph clustering problem; thus, the discrete optimization problem of the adjacency matrix can be solved in the context of graph clustering. In particular, we propose to measure the similarity between victim nodes by a metric of Adversarial Vulnerability, which is related to how the victim nodes will be affected by the injected fake node, and to cluster the victim nodes accordingly. Our attack is performed in a practical and unnoticeable query-based black-box manner with only a few nodes on the graphs that can be accessed. Theoretical analysis and extensive experiments demonstrate the effectiveness of our method by fooling the node classifiers with only a small number of queries.
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.
The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCN's performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.
Graph Contrastive Learning (GCL) establishes a new paradigm for learning graph representations without human annotations. Although remarkable progress has been witnessed recently, the success behind GCL is still left somewhat mysterious. In this work, we first identify several critical design considerations within a general GCL paradigm, including augmentation functions, contrasting modes, contrastive objectives, and negative mining techniques. Then, to understand the interplay of different GCL components, we conduct extensive, controlled experiments over a set of benchmark tasks on datasets across various domains. Our empirical studies suggest a set of general receipts for effective GCL, e.g., simple topology augmentations that produce sparse graph views bring promising performance improvements; contrasting modes should be aligned with the granularities of end tasks. In addition, to foster future research and ease the implementation of GCL algorithms, we develop an easy-to-use library PyGCL, featuring modularized CL components, standardized evaluation, and experiment management. We envision this work to provide useful empirical evidence of effective GCL algorithms and offer several insights for future research.
Graph Neural Networks (GNNs), which generalize the deep neural networks to graph-structured data, have achieved great success in modeling graphs. However, as an extension of deep learning for graphs, GNNs lack explainability, which largely limits their adoption in scenarios that demand the transparency of models. Though many efforts are taken to improve the explainability of deep learning, they mainly focus on i.i.d data, which cannot be directly applied to explain the predictions of GNNs because GNNs utilize both node features and graph topology to make predictions. There are only very few work on the explainability of GNNs and they focus on post-hoc explanations. Since post-hoc explanations are not directly obtained from the GNNs, they can be biased and misrepresent the true explanations. Therefore, in this paper, we study a novel problem of self-explainable GNNs which can simultaneously give predictions and explanations. We propose a new framework which can find $K$-nearest labeled nodes for each unlabeled node to give explainable node classification, where nearest labeled nodes are found by interpretable similarity module in terms of both node similarity and local structure similarity. Extensive experiments on real-world and synthetic datasets demonstrate the effectiveness of the proposed framework for explainable node classification.
Graph Neural Networks (GNNs) have achieved significant success in learning better representations by performing feature propagation and transformation iteratively to leverage neighborhood information. Nevertheless, iterative propagation restricts the information of higher-layer neighborhoods to be transported through and fused with the lower-layer neighborhoods', which unavoidably results in feature smoothing between neighborhoods in different layers and can thus compromise the performance, especially on heterophily networks. Furthermore, most deep GNNs only recognize the importance of higher-layer neighborhoods while yet to fully explore the importance of multi-hop dependency within the context of different layer neighborhoods in learning better representations. In this work, we first theoretically analyze the feature smoothing between neighborhoods in different layers and empirically demonstrate the variance of the homophily level across neighborhoods at different layers. Motivated by these analyses, we further propose a tree decomposition method to disentangle neighborhoods in different layers to alleviate feature smoothing among these layers. Moreover, we characterize the multi-hop dependency via graph diffusion within our tree decomposition formulation to construct Tree Decomposed Graph Neural Network (TDGNN), which can flexibly incorporate information from large receptive fields and aggregate this information utilizing the multi-hop dependency. Comprehensive experiments demonstrate the superior performance of TDGNN on both homophily and heterophily networks under a variety of node classification settings. Extensive parameter analysis highlights the ability of TDGNN to prevent over-smoothing and incorporate features from shallow layers with deeper multi-hop dependencies, which provides new insights towards deeper graph neural networks. Code of TDGNN: http://github.com/YuWVandy/TDGNN
Self-supervised Learning (SSL) aims at learning representations of objects without relying on manual labeling. Recently, a number of SSL methods for graph representation learning have achieved performance comparable to SOTA semi-supervised GNNs. A Siamese network, which relies on data augmentation, is the popular architecture used in these methods. However, these methods rely on heuristically crafted data augmentation techniques. Furthermore, they use either contrastive terms or other tricks (e.g., asymmetry) to avoid trivial solutions that can occur in Siamese networks. In this study, we propose, GraphSurgeon, a novel SSL method for GNNs with the following features. First, instead of heuristics we propose a learnable data augmentation method that is jointly learned with the embeddings by leveraging the inherent signal encoded in the graph. In addition, we take advantage of the flexibility of the learnable data augmentation and introduce a new strategy that augments in the embedding space, called post augmentation. This strategy has a significantly lower memory overhead and run-time cost. Second, as it is difficult to sample truly contrastive terms, we avoid explicit negative sampling. Third, instead of relying on engineering tricks, we use a scalable constrained optimization objective motivated by Laplacian Eigenmaps to avoid trivial solutions. To validate the practical use of GraphSurgeon, we perform empirical evaluation using 14 public datasets across a number of domains and ranging from small to large scale graphs with hundreds of millions of edges. Our finding shows that GraphSurgeon is comparable to six SOTA semi-supervised and on par with five SOTA self-supervised baselines in node classification tasks. The source code is available at https://github.com/zekarias-tilahun/graph-surgeon.
Many tasks in graph machine learning, such as link prediction and node classification, are typically solved by using representation learning, in which each node or edge in the network is encoded via an embedding. Though there exists a lot of network embeddings for static graphs, the task becomes much more complicated when the dynamic (i.e. temporal) network is analyzed. In this paper, we propose a novel approach for dynamic network representation learning based on Temporal Graph Network by using a highly custom message generating function by extracting Causal Anonymous Walks. For evaluation, we provide a benchmark pipeline for the evaluation of temporal network embeddings. This work provides the first comprehensive comparison framework for temporal network representation learning in every available setting for graph machine learning problems involving node classification and link prediction. The proposed model outperforms state-of-the-art baseline models. The work also justifies the difference between them based on evaluation in various transductive/inductive edge/node classification tasks. In addition, we show the applicability and superior performance of our model in the real-world downstream graph machine learning task provided by one of the top European banks, involving credit scoring based on transaction data.
Attempting to fully exploit the rich information of topological structure and node features for attributed graph, we introduce self-supervised learning mechanism to graph representation learning and propose a novel Self-supervised Consensus Representation Learning (SCRL) framework. In contrast to most existing works that only explore one graph, our proposed SCRL method treats graph from two perspectives: topology graph and feature graph. We argue that their embeddings should share some common information, which could serve as a supervisory signal. Specifically, we construct the feature graph of node features via k-nearest neighbor algorithm. Then graph convolutional network (GCN) encoders extract features from two graphs respectively. Self-supervised loss is designed to maximize the agreement of the embeddings of the same node in the topology graph and the feature graph. Extensive experiments on real citation networks and social networks demonstrate the superiority of our proposed SCRL over the state-of-the-art methods on semi-supervised node classification task. Meanwhile, compared with its main competitors, SCRL is rather efficient.
We propose an extension to the transformer neural network architecture for general-purpose graph learning by adding a dedicated pathway for pairwise structural information, called edge channels. The resultant framework - which we call Edge-augmented Graph Transformer (EGT) - can directly accept, process and output structural information of arbitrary form, which is important for effective learning on graph-structured data. Our model exclusively uses global self-attention as an aggregation mechanism rather than static localized convolutional aggregation. This allows for unconstrained long-range dynamic interactions between nodes. Moreover, the edge channels allow the structural information to evolve from layer to layer, and prediction tasks on edges/links can be performed directly from the output embeddings of these channels. We verify the performance of EGT in a wide range of graph-learning experiments on benchmark datasets, in which it outperforms Convolutional/Message-Passing Graph Neural Networks. EGT sets a new state-of-the-art for the quantum-chemical regression task on the OGB-LSC PCQM4Mv2 dataset containing 3.8 million molecular graphs. Our findings indicate that global self-attention based aggregation can serve as a flexible, adaptive and effective replacement of graph convolution for general-purpose graph learning. Therefore, convolutional local neighborhood aggregation is not an essential inductive bias.
Graph Neural Networks (GNNs) have already been widely applied in various graph mining tasks. However, they suffer from the shallow architecture issue, which is the key impediment that hinders the model performance improvement. Although several relevant approaches have been proposed, none of the existing studies provides an in-depth understanding of the root causes of performance degradation in deep GNNs. In this paper, we conduct the first systematic experimental evaluation to present the fundamental limitations of shallow architectures. Based on the experimental results, we answer the following two essential questions: (1) what actually leads to the compromised performance of deep GNNs; (2) when we need and how to build deep GNNs. The answers to the above questions provide empirical insights and guidelines for researchers to design deep and well-performed GNNs. To show the effectiveness of our proposed guidelines, we present Deep Graph Multi-Layer Perceptron (DGMLP), a powerful approach (a paradigm in its own right) that helps guide deep GNN designs. Experimental results demonstrate three advantages of DGMLP: 1) high accuracy -- it achieves state-of-the-art node classification performance on various datasets; 2) high flexibility -- it can flexibly choose different propagation and transformation depths according to graph size and sparsity; 3) high scalability and efficiency -- it supports fast training on large-scale graphs. Our code is available in https://github.com/zwt233/DGMLP.
We propose a decentralised "local2global" approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping subgraphs (or "patches") and training local representations for each patch independently. In a second step, we combine the local representations into a globally consistent representation by estimating the set of rigid motions that best align the local representations using information from the patch overlaps, via group synchronization. A key distinguishing feature of local2global relative to existing work is that patches are trained independently without the need for the often costly parameter synchronisation during distributed training. This allows local2global to scale to large-scale industrial applications, where the input graph may not even fit into memory and may be stored in a distributed manner. Preliminary results on medium-scale data sets (up to $\sim$7K nodes and $\sim$200K edges) are promising, with a graph reconstruction performance for local2global that is comparable to that of globally trained embeddings. A thorough evaluation of local2global on large scale data and applications to downstream tasks, such as node classification and link prediction, constitutes ongoing work.