Network embedding has been widely used in social recommendation and network analysis, such as recommendation systems and anomaly detection with graphs. However, most of previous approaches cannot handle large graphs efficiently, due to that (i) computation on graphs is often costly and (ii) the size of graph or the intermediate results of vectors could be prohibitively large, rendering it difficult to be processed on a single machine. In this paper, we propose an efficient and effective distributed algorithm for network embedding on large graphs using Apache Spark, which recursively partitions a graph into several small-sized subgraphs to capture the internal and external structural information of nodes, and then computes the network embedding for each subgraph in parallel. Finally, by aggregating the outputs on all subgraphs, we obtain the embeddings of nodes in a linear cost. After that, we demonstrate in various experiments that our proposed approach is able to handle graphs with billions of edges within a few hours and is at least 4 times faster than the state-of-the-art approaches. Besides, it achieves up to $4.25\%$ and $4.27\%$ improvements on link prediction and node classification tasks respectively. In the end, we deploy the proposed algorithms in two online games of Tencent with the applications of friend recommendation and item recommendation, which improve the competitors by up to $91.11\%$ in running time and up to $12.80\%$ in the corresponding evaluation metrics.
Graph Neural Networks (GNNs) have been extensively used for mining graph-structured data with impressive performance. However, because these traditional GNNs do not distinguish among various downstream tasks, embeddings embedded by them are not always effective. Intuitively, paths in a graph imply different semantics for different downstream tasks. Inspired by this, we design a novel GNN solution, namely Customized Graph Neural Network with Path Reweighting (CustomGNN for short). Specifically, the proposed CustomGNN can automatically learn the high-level semantics for specific downstream tasks to highlight semantically relevant paths as well to filter out task-irrelevant noises in a graph. Furthermore, we empirically analyze the semantics learned by CustomGNN and demonstrate its ability to avoid the three inherent problems in traditional GNNs, i.e., over-smoothing, poor robustness, and overfitting. In experiments with the node classification task, CustomGNN achieves state-of-the-art accuracies on three standard graph datasets and four large graph datasets. The source code of the proposed CustomGNN is available at \url{https://github.com/cjpcool/CustomGNN}.
Recent years have witnessed great success in handling node classification tasks with Graph Neural Networks (GNNs). However, most existing GNNs are based on the assumption that node samples for different classes are balanced, while for many real-world graphs, there exists the problem of class imbalance, i.e., some classes may have much fewer samples than others. In this case, directly training a GNN classifier with raw data would under-represent samples from those minority classes and result in sub-optimal performance. This paper presents GraphMixup, a novel mixup-based framework for improving class-imbalanced node classification on graphs. However, directly performing mixup in the input space or embedding space may produce out-of-domain samples due to the extreme sparsity of minority classes; hence we construct semantic relation spaces that allows the Feature Mixup to be performed at the semantic level. Moreover, we apply two context-based self-supervised techniques to capture both local and global information in the graph structure and then propose Edge Mixup specifically for graph data. Finally, we develop a \emph{Reinforcement Mixup} mechanism to adaptively determine how many samples are to be generated by mixup for those minority classes. Extensive experiments on three real-world datasets show that GraphMixup yields truly encouraging results for class-imbalanced node classification tasks.
Many representative graph neural networks, e.g., GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints, which may lead to oversimplified or ill-posed filters. To overcome these issues, we propose BernNet, a novel graph neural network with theoretical support that provides a simple but effective scheme for designing and learning arbitrary graph spectral filters. In particular, for any filter over the normalized Laplacian spectrum of a graph, our BernNet estimates it by an order-$K$ Bernstein polynomial approximation and designs its spectral property by setting the coefficients of the Bernstein basis. Moreover, we can learn the coefficients (and the corresponding filter weights) based on observed graphs and their associated signals and thus achieve the BernNet specialized for the data. Our experiments demonstrate that BernNet can learn arbitrary spectral filters, including complicated band-rejection and comb filters, and it achieves superior performance in real-world graph modeling tasks. Code is available at https://github.com/ivam-he/BernNet.
In recent years, phishing scams have become the crime type with the largest money involved on Ethereum, the second-largest blockchain platform. Meanwhile, graph neural network (GNN) has shown promising performance in various node classification tasks. However, for Ethereum transaction data, which could be naturally abstracted to a real-world complex graph, the scarcity of labels and the huge volume of transaction data make it difficult to take advantage of GNN methods. Here in this paper, to address the two challenges, we propose a Self-supervised Incremental deep Graph learning model (SIEGE), for the phishing scam detection problem on Ethereum. In our model, two pretext tasks designed from spatial and temporal perspectives help us effectively learn useful node embedding from the huge amount of unlabelled transaction data. And the incremental paradigm allows us to efficiently handle large-scale transaction data and help the model maintain good performance when the data distribution is drastically changing. We collect transaction records about half a year from Ethereum and our extensive experiments show that our model consistently outperforms strong baselines in both transductive and inductive settings.
The attention mechanism enables graph neural networks (GNNs) to learn the attention weights between the target node and its one-hop neighbors, thereby improving the performance further. However, most existing GNNs are oriented toward homogeneous graphs, and in which each layer can only aggregate the information of one-hop neighbors. Stacking multilayer networks introduces considerable noise and easily leads to over smoothing. We propose here a multihop heterogeneous neighborhood information fusion graph representation learning method (MHNF). Specifically, we propose a hybrid metapath autonomous extraction model to efficiently extract multihop hybrid neighbors. Then, we formulate a hop-level heterogeneous information aggregation model, which selectively aggregates different-hop neighborhood information within the same hybrid metapath. Finally, a hierarchical semantic attention fusion model (HSAF) is constructed, which can efficiently integrate different-hop and different-path neighborhood information. In this fashion, this paper solves the problem of aggregating multihop neighborhood information and learning hybrid metapaths for target tasks. This mitigates the limitation of manually specifying metapaths. In addition, HSAF can extract the internal node information of the metapaths and better integrate the semantic information present at different levels. Experimental results on real datasets show that MHNF achieves the best or competitive performance against state-of-the-art baselines with only a fraction of 1/10 ~ 1/100 parameters and computational budgets. Our code is publicly available at https://github.com/PHD-lanyu/MHNF.
Data augmentation aims to generate new and synthetic features from the original data, which can identify a better representation of data and improve the performance and generalizability of downstream tasks. However, data augmentation for graph-based models remains a challenging problem, as graph data is more complex than traditional data, which consists of two features with different properties: graph topology and node attributes. In this paper, we study the problem of graph data augmentation for Graph Convolutional Network (GCN) in the context of improving the node embeddings for semi-supervised node classification. Specifically, we conduct cosine similarity based cross operation on the original features to create new graph features, including new node attributes and new graph topologies, and we combine them as new pairwise inputs for specific GCNs. Then, we propose an attentional integrating model to weighted sum the hidden node embeddings encoded by these GCNs into the final node embeddings. We also conduct a disparity constraint on these hidden node embeddings when training to ensure that non-redundant information is captured from different features. Experimental results on five real-world datasets show that our method improves the classification accuracy with a clear margin (+2.5% - +84.2%) than the original GCN model.
Explaining the foundations for predictions obtained from graph neural networks (GNNs) is critical for credible use of GNN models for real-world problems. Owing to the rapid growth of GNN applications, recent progress in explaining predictions from GNNs, such as sensitivity analysis, perturbation methods, and attribution methods, showed great opportunities and possibilities for explaining GNN predictions. In this study, we propose a method to improve the explanation quality of node classification tasks that can be applied in a post hoc manner through aggregation of auxiliary explanations from important neighboring nodes, named SEEN. Applying SEEN does not require modification of a graph and can be used with diverse explainability techniques due to its independent mechanism. Experiments on matching motif-participating nodes from a given graph show great improvement in explanation accuracy of up to 12.71% and demonstrate the correlation between the auxiliary explanations and the enhanced explanation accuracy through leveraging their contributions. SEEN provides a simple but effective method to enhance the explanation quality of GNN model outputs, and this method is applicable in combination with most explainability techniques.
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.
Nowadays, Graph Neural Networks (GNNs) following the Message Passing paradigm become the dominant way to learn on graphic data. Models in this paradigm have to spend extra space to look up adjacent nodes with adjacency matrices and extra time to aggregate multiple messages from adjacent nodes. To address this issue, we develop a method called LinkDist that distils self-knowledge from connected node pairs into a Multi-Layer Perceptron (MLP) without the need to aggregate messages. Experiment with 8 real-world datasets shows the MLP derived from LinkDist can predict the label of a node without knowing its adjacencies but achieve comparable accuracy against GNNs in the contexts of semi- and full-supervised node classification. Moreover, LinkDist benefits from its Non-Message Passing paradigm that we can also distil self-knowledge from arbitrarily sampled node pairs in a contrastive way to further boost the performance of LinkDist.
Node classification is a central task in graph data analysis. Scarce or even no labeled data of emerging classes is a big challenge for existing methods. A natural question arises: can we classify the nodes from those classes that have never been seen? In this paper, we study this zero-shot node classification (ZNC) problem which has a two-stage nature: (1) acquiring high-quality class semantic descriptions (CSDs) for knowledge transfer, and (2) designing a well generalized graph-based learning model. For the first stage, we give a novel quantitative CSDs evaluation strategy based on estimating the real class relationships, so as to get the "best" CSDs in a completely automatic way. For the second stage, we propose a novel Decomposed Graph Prototype Network (DGPN) method, following the principles of locality and compositionality for zero-shot model generalization. Finally, we conduct extensive experiments to demonstrate the effectiveness of our solutions.
Graphs are widely used to model the relational structure of data, and the research of graph machine learning (ML) has a wide spectrum of applications ranging from drug design in molecular graphs to friendship recommendation in social networks. Prevailing approaches for graph ML typically require abundant labeled instances in achieving satisfactory results, which is commonly infeasible in real-world scenarios since labeled data for newly emerged concepts (e.g., new categorizations of nodes) on graphs is limited. Though meta-learning has been applied to different few-shot graph learning problems, most existing efforts predominately assume that all the data from those seen classes is gold-labeled, while those methods may lose their efficacy when the seen data is weakly-labeled with severe label noise. As such, we aim to investigate a novel problem of weakly-supervised graph meta-learning for improving the model robustness in terms of knowledge transfer. To achieve this goal, we propose a new graph meta-learning framework -- Graph Hallucination Networks (Meta-GHN) in this paper. Based on a new robustness-enhanced episodic training, Meta-GHN is meta-learned to hallucinate clean node representations from weakly-labeled data and extracts highly transferable meta-knowledge, which enables the model to quickly adapt to unseen tasks with few labeled instances. Extensive experiments demonstrate the superiority of Meta-GHN over existing graph meta-learning studies on the task of weakly-supervised few-shot node classification.
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.
Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by message passing. Its prediction performance has been shown to be strongly bounded by assortative mixing in the graph, a key property wherein nodes with similar attributes mix/connect with each other. We observe that real world networks exhibit heterogeneous or diverse mixing patterns and the conventional global measurement of assortativity, such as global assortativity coefficient, may not be a representative statistic in quantifying this mixing. We adopt a generalized concept, node-level assortativity, one that is based at the node level to better represent the diverse patterns and accurately quantify the learnability of GNNs. We find that the prediction performance of a wide range of GNN models is highly correlated with the node level assortativity. To break this limit, in this work, we focus on transforming the input graph into a computation graph which contains both proximity and structural information as distinct type of edges. The resulted multi-relational graph has an enhanced level of assortativity and, more importantly, preserves rich information from the original graph. We then propose to run GNNs on this computation graph and show that adaptively choosing between structure and proximity leads to improved performance under diverse mixing. Empirically, we show the benefits of adopting our transformation framework for semi-supervised node classification task on a variety of real world graph learning benchmarks.
Teaching Graph Neural Networks (GNNs) to accurately classify nodes under severely noisy labels is an important problem in real-world graph learning applications, but is currently underexplored. Although pairwise training methods have demonstrated promise in supervised metric learning and unsupervised contrastive learning, they remain less studied on noisy graphs, where the structural pairwise interactions (PI) between nodes are abundant and thus might benefit label noise learning rather than the pointwise methods. This paper bridges the gap by proposing a pairwise framework for noisy node classification on graphs, which relies on the PI as a primary learning proxy in addition to the pointwise learning from the noisy node class labels. Our proposed framework PI-GNN contributes two novel components: (1) a confidence-aware PI estimation model that adaptively estimates the PI labels, which are defined as whether the two nodes share the same node labels, and (2) a decoupled training approach that leverages the estimated PI labels to regularize a node classification model for robust node classification. Extensive experiments on different datasets and GNN architectures demonstrate the effectiveness of PI-GNN, yielding a promising improvement over the state-of-the-art methods. Code is publicly available at https://github.com/TianBian95/pi-gnn.
Node classification and link prediction are widely studied in graph representation learning. While both transductive node classification and link prediction operate over a single input graph, they have so far been studied separately. Node classification models take an input graph with node features and incomplete node labels, and implicitly assume that the graph is relationally complete, i.e., no edges are missing. By contrast, link prediction models are solely motivated by relational incompleteness of the input graphs, and do not typically leverage node features or classes. We propose a unifying perspective and study the problems of (i) transductive node classification over incomplete graphs and (ii) link prediction over graphs with node features, introduce a new dataset for this setting, WikiAlumni, and conduct an extensive benchmarking study.
Graph neural networks (GNNs) have shown great prowess in learning representations suitable for numerous graph-based machine learning tasks. When applied to semi-supervised node classification, GNNs are widely believed to work well due to the homophily assumption ("like attracts like"), and fail to generalize to heterophilous graphs where dissimilar nodes connect. Recent works design new architectures to overcome such heterophily-related limitations, citing poor baseline performance and new architecture improvements on a few heterophilous graph benchmark datasets as evidence for this notion. In our experiments, we empirically find that standard graph convolutional networks (GCNs) can actually achieve better performance than such carefully designed methods on some commonly used heterophilous graphs. This motivates us to reconsider whether homophily is truly necessary for good GNN performance. We find that this claim is not quite true, and in fact, GCNs can achieve strong performance on heterophilous graphs under certain conditions. Our work carefully characterizes these conditions, and provides supporting theoretical understanding and empirical observations. Finally, we examine existing heterophilous graphs benchmarks and reconcile how the GCN (under)performs on them based on this understanding.
Graph Neural Networks (GNNs) have been widely applied to various fields due to their powerful representations of graph-structured data. Despite the success of GNNs, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. To address this limitations, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which preclude noisy connections and include useful connections (e.g., meta-paths) for tasks, while learning effective node representations on the new graphs in an end-to-end fashion. We further propose enhanced version of GTNs, Fast Graph Transformer Networks (FastGTNs), that improve scalability of graph transformations. Compared to GTNs, FastGTNs are 230x faster and use 100x less memory while allowing the identical graph transformations as GTNs. In addition, we extend graph transformations to the semantic proximity of nodes allowing non-local operations beyond meta-paths. Extensive experiments on both homogeneous graphs and heterogeneous graphs show that GTNs and FastGTNs with non-local operations achieve the state-of-the-art performance for node classification tasks. The code is available: https://github.com/seongjunyun/Graph_Transformer_Networks
Node embedding learns a low-dimensional representation for each node in the graph. Recent progress on node embedding shows that proximity matrix factorization methods gain superb performance and scale to large graphs with millions of nodes. Existing approaches first define a proximity matrix and then learn the embeddings that fit the proximity by matrix factorization. Most existing matrix factorization methods adopt the same proximity for different tasks, while it is observed that different tasks and datasets may require different proximity, limiting their representation power. Motivated by this, we propose {\em Lemane}, a framework with trainable proximity measures, which can be learned to best suit the datasets and tasks at hand automatically. Our method is end-to-end, which incorporates differentiable SVD in the pipeline so that the parameters can be trained via backpropagation. However, this learning process is still expensive on large graphs. To improve the scalability, we train proximity measures only on carefully subsampled graphs, and then apply standard proximity matrix factorization on the original graph using the learned proximity. Note that, computing the learned proximities for each pair is still expensive for large graphs, and existing techniques for computing proximities are not applicable to the learned proximities. Thus, we present generalized push techniques to make our solution scalable to large graphs with millions of nodes. Extensive experiments show that our proposed solution outperforms existing solutions on both link prediction and node classification tasks on almost all datasets.
Node representation learning has demonstrated its effectiveness for various applications on graphs. Particularly, recent developments in contrastive learning have led to promising results in unsupervised node representation learning for a number of tasks. Despite the success of graph contrastive learning and consequent growing interest, fairness is largely under-explored in the field. To this end, this study addresses fairness issues in graph contrastive learning with fairness-aware graph augmentation designs, through adaptive feature masking and edge deletion. In the study, different fairness notions on graphs are introduced, which serve as guidelines for the proposed graph augmentations. Furthermore, theoretical analysis is provided to quantitatively prove that the proposed feature masking approach can reduce intrinsic bias. Experimental results on real social networks are presented to demonstrate that the proposed augmentations can enhance fairness in terms of statistical parity and equal opportunity, while providing comparable classification accuracy to state-of-the-art contrastive methods for node classification.