Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.
Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.
Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.
Graph Neural Networks (GNNs), a type of neural network that can learn from graph-structured data through neighborhood information aggregation, have shown superior performance in various downstream tasks. However, as the number of layers increases, node representations become indistinguishable, which is known as over-smoothing. To address this issue, many residual methods have emerged. In this paper, we focus on the over-smoothing issue and related residual methods. Firstly, we revisit over-smoothing from the perspective of overlapping neighborhood subgraphs, and based on this, we explain how residual methods can alleviate over-smoothing by integrating multiple orders neighborhood subgraphs to avoid the indistinguishability of the single high-order neighborhood subgraphs. Additionally, we reveal the drawbacks of previous residual methods, such as the lack of node adaptability and severe loss of high-order neighborhood subgraph information, and propose a \textbf{Posterior-Sampling-based, Node-Adaptive Residual module (PSNR)}. We theoretically demonstrate that PSNR can alleviate the drawbacks of previous residual methods. Furthermore, extensive experiments verify the superiority of the PSNR module in fully observed node classification and missing feature scenarios. Our code is available at https://github.com/jingbo02/PSNR-GNN.
Heterophily has been considered as an issue that hurts the performance of Graph Neural Networks (GNNs). To address this issue, some existing work uses a graph-level weighted fusion of the information of multi-hop neighbors to include more nodes with homophily. However, the heterophily might differ among nodes, which requires to consider the local topology. Motivated by it, we propose to use the local similarity (LocalSim) to learn node-level weighted fusion, which can also serve as a plug-and-play module. For better fusion, we propose a novel and efficient Initial Residual Difference Connection (IRDC) to extract more informative multi-hop information. Moreover, we provide theoretical analysis on the effectiveness of LocalSim representing node homophily on synthetic graphs. Extensive evaluations over real benchmark datasets show that our proposed method, namely Local Similarity Graph Neural Network (LSGNN), can offer comparable or superior state-of-the-art performance on both homophilic and heterophilic graphs. Meanwhile, the plug-and-play model can significantly boost the performance of existing GNNs. Our code is provided at https://github.com/draym28/LSGNN.
Attribute graphs are ubiquitous in multimedia applications, and graph representation learning (GRL) has been successful in analyzing attribute graph data. However, incomplete graph data and missing node attributes can have a negative impact on media knowledge discovery. Existing methods for handling attribute missing graph have limited assumptions or fail to capture complex attribute-graph dependencies. To address these challenges, we propose Attribute missing Graph Contrastive Learning (AmGCL), a framework for handling missing node attributes in attribute graph data. AmGCL leverages Dirichlet energy minimization-based feature precoding to encode in missing attributes and a self-supervised Graph Augmentation Contrastive Learning Structure (GACLS) to learn latent variables from the encoded-in data. Specifically, AmGCL utilizies feature reconstruction based on structure-attribute energy minimization while maximizes the lower bound of evidence for latent representation mutual information. Our experimental results on multiple real-world datasets demonstrate that AmGCL outperforms state-of-the-art methods in both feature imputation and node classification tasks, indicating the effectiveness of our proposed method in real-world attribute graph analysis tasks.
Graph Contrastive Learning (GCL) is an effective way to learn generalized graph representations in a self-supervised manner, and has grown rapidly in recent years. However, the underlying community semantics has not been well explored by most previous GCL methods. Research that attempts to leverage communities in GCL regards them as having the same influence on the graph, leading to extra representation errors. To tackle this issue, we define ''community strength'' to measure the difference of influence among communities. Under this premise, we propose a Community-Strength-enhanced Graph Contrastive Learning (CSGCL) framework to preserve community strength throughout the learning process. Firstly, we present two novel graph augmentation methods, Communal Attribute Voting (CAV) and Communal Edge Dropping (CED), where the perturbations of node attributes and edges are guided by community strength. Secondly, we propose a dynamic ''Team-up'' contrastive learning scheme, where community strength is used to progressively fine-tune the contrastive objective. We report extensive experiment results on three downstream tasks: node classification, node clustering, and link prediction. CSGCL achieves state-of-the-art performance compared with other GCL methods, validating that community strength brings effectiveness and generality to graph representations. Our code is available at https://github.com/HanChen-HUST/CSGCL.
Networks have provided extremely successful models of data and complex systems. Yet, as combinatorial objects, networks do not have in general intrinsic coordinates and do not typically lie in an ambient space. The process of assigning an embedding space to a network has attracted lots of interest in the past few decades, and has been efficiently applied to fundamental problems in network inference, such as link prediction, node classification, and community detection. In this review, we provide a user-friendly guide to the network embedding literature and current trends in this field which will allow the reader to navigate through the complex landscape of methods and approaches emerging from the vibrant research activity on these subjects.
There has been rapid growth in biomedical literature, yet capturing the heterogeneity of the bibliographic information of these articles remains relatively understudied. Although graph mining research via heterogeneous graph neural networks has taken center stage, it remains unclear whether these approaches capture the heterogeneity of the PubMed database, a vast digital repository containing over 33 million articles. We introduce PubMed Graph Benchmark (PGB), a new benchmark dataset for evaluating heterogeneous graph embeddings for biomedical literature. The benchmark contains rich metadata including abstract, authors, citations, MeSH terms, MeSH hierarchy, and some other information. The benchmark contains three different evaluation tasks encompassing systematic reviews, node classification, and node clustering. In PGB, we aggregate the metadata associated with the biomedical articles from PubMed into a unified source and make the benchmark publicly available for any future works.
In node classification using graph neural networks (GNNs), a typical model generates logits for different class labels at each node. A softmax layer often outputs a label prediction based on the largest logit. We demonstrate that it is possible to infer hidden graph structural information from the dataset using these logits. We introduce the key notion of label non-uniformity, which is derived from the Wasserstein distance between the softmax distribution of the logits and the uniform distribution. We demonstrate that nodes with small label non-uniformity are harder to classify correctly. We theoretically analyze how the label non-uniformity varies across the graph, which provides insights into boosting the model performance: increasing training samples with high non-uniformity or dropping edges to reduce the maximal cut size of the node set of small non-uniformity. These mechanisms can be easily added to a base GNN model. Experimental results demonstrate that our approach improves the performance of many benchmark base models.
Imbalanced node classification widely exists in real-world networks where graph neural networks (GNNs) are usually highly inclined to majority classes and suffer from severe performance degradation on classifying minority class nodes. Various imbalanced node classification methods have been proposed recently which construct synthetic nodes and edges w.r.t. minority classes to balance the label and topology distribution. However, they are all based on the homophilic assumption that nodes of the same label tend to connect despite the wide existence of heterophilic edges in real-world graphs. Thus, they uniformly aggregate features from both homophilic and heterophilic neighbors and rely on feature similarity to generate synthetic edges, which cannot be applied to imbalanced graphs in high heterophily. To address this problem, we propose a novel GraphSANN for imbalanced node classification on both homophilic and heterophilic graphs. Firstly, we propose a unified feature mixer to generate synthetic nodes with both homophilic and heterophilic interpolation in a unified way. Next, by randomly sampling edges between synthetic nodes and existing nodes as candidate edges, we design an adaptive subgraph extractor to adaptively extract the contextual subgraphs of candidate edges with flexible ranges. Finally, we develop a multi-filter subgraph encoder that constructs different filter channels to discriminatively aggregate neighbor's information along the homophilic and heterophilic edges. Extensive experiments on eight datasets demonstrate the superiority of our model for imbalanced node classification on both homophilic and heterophilic graphs.
Homophily principle, i.e., nodes with the same labels are more likely to be connected, has been believed to be the main reason for the performance superiority of Graph Neural Networks (GNNs) over Neural Networks on node classification tasks. Recent research suggests that, even in the absence of homophily, the advantage of GNNs still exists as long as nodes from the same class share similar neighborhood patterns. However, this argument only considers intra-class Node Distinguishability (ND) but neglects inter-class ND, which provides incomplete understanding of homophily on GNNs. In this paper, we first demonstrate such deficiency with examples and argue that an ideal situation for ND is to have smaller intra-class ND than inter-class ND. To formulate this idea and study ND deeply, we propose Contextual Stochastic Block Model for Homophily (CSBM-H) and define two metrics, Probabilistic Bayes Error (PBE) and negative generalized Jeffreys divergence, to quantify ND. With the metrics, we visualize and analyze how graph filters, node degree distributions and class variances influence ND, and investigate the combined effect of intra- and inter-class ND. Besides, we discovered the mid-homophily pitfall, which occurs widely in graph datasets. Furthermore, we verified that, in real-work tasks, the superiority of GNNs is indeed closely related to both intra- and inter-class ND regardless of homophily levels. Grounded in this observation, we propose a new hypothesis-testing based performance metric beyond homophily, which is non-linear, feature-based and can provide statistical threshold value for GNNs' the superiority. Experiments indicate that it is significantly more effective than the existing homophily metrics on revealing the advantage and disadvantage of graph-aware modes on both synthetic and benchmark real-world datasets.
Graph representation learning models aim to represent the graph structure and its features into low-dimensional vectors in a latent space, which can benefit various downstream tasks, such as node classification and link prediction. Due to its powerful graph data modelling capabilities, various graph embedding models and libraries have been proposed to learn embeddings and help researchers ease conducting experiments. In this paper, we introduce a novel graph representation framework covering various graph embedding models, ranging from shallow to state-of-the-art models, namely Connector. First, we consider graph generation by constructing various types of graphs with different structural relations, including homogeneous, signed, heterogeneous, and knowledge graphs. Second, we introduce various graph representation learning models, ranging from shallow to deep graph embedding models. Finally, we plan to build an efficient open-source framework that can provide deep graph embedding models to represent structural relations in graphs. The framework is available at https://github.com/NSLab-CUK/Connector.
Node representation learning in a network is an important machine learning technique for encoding relational information in a continuous vector space while preserving the inherent properties and structures of the network. Recently, unsupervised node embedding methods such as DeepWalk, LINE, struc2vec, PTE, UserItem2vec, and RWJBG have emerged from the Skip-gram model and perform better performance in several downstream tasks such as node classification and link prediction than the existing relational models. However, providing post-hoc explanations of Skip-gram-based embeddings remains a challenging problem because of the lack of explanation methods and theoretical studies applicable for embeddings. In this paper, we first show that global explanations to the Skip-gram-based embeddings can be found by computing bridgeness under a spectral cluster-aware local perturbation. Moreover, a novel gradient-based explanation method, which we call GRAPH-wGD, is proposed that allows the top-q global explanations about learned graph embedding vectors more efficiently. Experiments show that the ranking of nodes by scores using GRAPH-wGD is highly correlated with true bridgeness scores. We also observe that the top-q node-level explanations selected by GRAPH-wGD have higher importance scores and produce more changes in class label prediction when perturbed, compared with the nodes selected by recent alternatives, using five real-world graphs.
Meta-structures are widely used to define which subset of neighbors to aggregate information in heterogeneous information networks (HINs). In this work, we investigate existing meta-structures, including meta-path and meta-graph, and observe that they are initially designed manually with fixed patterns and hence are insufficient to encode various rich semantic information on diverse HINs. Through reflection on their limitation, we define a new concept called meta-multigraph as a more expressive and flexible generalization of meta-graph, and propose a stable differentiable search method to automatically optimize the meta-multigraph for specific HINs and tasks. As the flexibility of meta-multigraphs may propagate redundant messages, we further introduce a complex-to-concise (C2C) meta-multigraph that propagates messages from complex to concise along the depth of meta-multigraph. Moreover, we observe that the differentiable search typically suffers from unstable search and a significant gap between the meta-structures in search and evaluation. To this end, we propose a progressive search algorithm by implicitly narrowing the search space to improve search stability and reduce inconsistency. Extensive experiments are conducted on six medium-scale benchmark datasets and one large-scale benchmark dataset over two representative tasks, i.e., node classification and recommendation. Empirical results demonstrate that our search methods can automatically find expressive meta-multigraphs and C2C meta-multigraphs, enabling our model to outperform state-of-the-art heterogeneous graph neural networks.
Public opinion is a crucial factor in shaping political decision-making. Nowadays, social media has become an essential platform for individuals to engage in political discussions and express their political views, presenting researchers with an invaluable resource for analyzing public opinion. In this paper, we focus on the 2020 US presidential election and create a large-scale dataset from Twitter. To detect political opinions in tweets, we build a user-tweet bipartite graph based on users' posting and retweeting behaviors and convert the task into a Graph Neural Network (GNN)-based node classification problem. Then, we introduce a novel skip aggregation mechanism that makes tweet nodes aggregate information from second-order neighbors, which are also tweet nodes due to the graph's bipartite nature, effectively leveraging user behavioral information. The experimental results show that our proposed model significantly outperforms several competitive baselines. Further analyses demonstrate the significance of user behavioral information and the effectiveness of skip aggregation.
How can we learn effective node representations on textual graphs? Graph Neural Networks (GNNs) that use Language Models (LMs) to encode textual information of graphs achieve state-of-the-art performance in many node classification tasks. Yet, combining GNNs with LMs has not been widely explored for practical deployments due to its scalability issues. In this work, we tackle this challenge by developing a Graph-Aware Distillation framework (GRAD) to encode graph structures into an LM for graph-free, fast inference. Different from conventional knowledge distillation, GRAD jointly optimizes a GNN teacher and a graph-free student over the graph's nodes via a shared LM. This encourages the graph-free student to exploit graph information encoded by the GNN teacher while at the same time, enables the GNN teacher to better leverage textual information from unlabeled nodes. As a result, the teacher and the student models learn from each other to improve their overall performance. Experiments in eight node classification benchmarks in both transductive and inductive settings showcase GRAD's superiority over existing distillation approaches for textual graphs.
Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open research problem. Recent works have proposed extensions to standard GNN architectures to improve performance on heterophilous graphs, trading off model simplicity for prediction accuracy. However, these models fail to capture basic graph properties, such as neighborhood label distribution, which are fundamental for learning. In this work, we propose GCN for Heterophily (GCNH), a simple yet effective GNN architecture applicable to both heterophilous and homophilous scenarios. GCNH learns and combines separate representations for a node and its neighbors, using one learned importance coefficient per layer to balance the contributions of center nodes and neighborhoods. We conduct extensive experiments on eight real-world graphs and a set of synthetic graphs with varying degrees of heterophily to demonstrate how the design choices for GCNH lead to a sizable improvement over a vanilla GCN. Moreover, GCNH outperforms state-of-the-art models of much higher complexity on four out of eight benchmarks, while producing comparable results on the remaining datasets. Finally, we discuss and analyze the lower complexity of GCNH, which results in fewer trainable parameters and faster training times than other methods, and show how GCNH mitigates the oversmoothing problem.
Graph Neural Networks (GNNs) have shown state-of-the-art improvements in node classification tasks on graphs. While these improvements have been largely demonstrated in a multi-class classification scenario, a more general and realistic scenario in which each node could have multiple labels has so far received little attention. The first challenge in conducting focused studies on multi-label node classification is the limited number of publicly available multi-label graph datasets. Therefore, as our first contribution, we collect and release three real-world biological datasets and develop a multi-label graph generator to generate datasets with tunable properties. While high label similarity (high homophily) is usually attributed to the success of GNNs, we argue that a multi-label scenario does not follow the usual semantics of homophily and heterophily so far defined for a multi-class scenario. As our second contribution, we define homophily and Cross-Class Neighborhood Similarity for the multi-label scenario and provide a thorough analyses of the collected $9$ multi-label datasets. Finally, we perform a large-scale comparative study with $8$ methods and $9$ datasets and analyse the performances of the methods to assess the progress made by current state of the art in the multi-label node classification scenario. We release our benchmark at https://github.com/Tianqi-py/MLGNC.
Graph contrastive learning (GCL) has recently achieved substantial advancements. Existing GCL approaches compare two different ``views'' of the same graph in order to learn node/graph representations. The underlying assumption of these studies is that the graph augmentation strategy is capable of generating several different graph views such that the graph views are structurally different but semantically similar to the original graphs, and thus the ground-truth labels of the original and augmented graph/nodes can be regarded identical in contrastive learning. However, we observe that this assumption does not always hold. For instance, the deletion of a super-node within a social network can exert a substantial influence on the partitioning of communities for other nodes. Similarly, any perturbation to nodes or edges in a molecular graph will change the labels of the graph. Therefore, we believe that augmenting the graph, accompanied by an adaptation of the labels used for the contrastive loss, will facilitate the encoder to learn a better representation. Based on this idea, we propose ID-MixGCL, which allows the simultaneous interpolation of input nodes and corresponding identity labels to obtain soft-confidence samples, with a controllable degree of change, leading to the capture of fine-grained representations from self-supervised training on unlabeled graphs. Experimental results demonstrate that ID-MixGCL improves performance on graph classification and node classification tasks, as demonstrated by significant improvements on the Cora, IMDB-B, IMDB-M, and PROTEINS datasets compared to state-of-the-art techniques, by 3-29% absolute points.