Homophily principle, \ie{} nodes with the same labels or similar attributes are more likely to be connected, has been commonly believed to be the main reason for the superiority of Graph Neural Networks (GNNs) over traditional Neural Networks (NNs) on graph-structured data, especially on node-level tasks. However, recent work has identified a non-trivial set of datasets where GNN's performance compared to the NN's is not satisfactory. Heterophily, i.e. low homophily, has been considered the main cause of this empirical observation. People have begun to revisit and re-evaluate most existing graph models, including graph transformer and its variants, in the heterophily scenario across various kinds of graphs, e.g. heterogeneous graphs, temporal graphs and hypergraphs. Moreover, numerous graph-related applications are found to be closely related to the heterophily problem. In the past few years, considerable effort has been devoted to studying and addressing the heterophily issue. In this survey, we provide a comprehensive review of the latest progress on heterophilic graph learning, including an extensive summary of benchmark datasets and evaluation of homophily metrics on synthetic graphs, meticulous classification of the most updated supervised and unsupervised learning methods, thorough digestion of the theoretical analysis on homophily/heterophily, and broad exploration of the heterophily-related applications. Notably, through detailed experiments, we are the first to categorize benchmark heterophilic datasets into three sub-categories: malignant, benign and ambiguous heterophily. Malignant and ambiguous datasets are identified as the real challenging datasets to test the effectiveness of new models on the heterophily challenge. Finally, we propose several challenges and future directions for heterophilic graph representation learning.
Combining the message-passing paradigm with the global attention mechanism has emerged as an effective framework for learning over graphs. The message-passing paradigm and the global attention mechanism fundamentally generate node embeddings based on information aggregated from a node's local neighborhood or from the whole graph. The most basic and commonly used aggregation approach is to take the sum of information from a node's local neighbourhood or from the whole graph. However, it is unknown if the dominant information is from a node itself or from the node's neighbours (or the rest of the graph nodes). Therefore, there exists information lost at each layer of embedding generation, and this information lost could be accumulated and become more serious when more layers are used in the model. In this paper, we present a differential encoding method to address the issue of information lost. The idea of our method is to encode the differential representation between the information from a node's neighbours (or the rest of the graph nodes) and that from the node itself. The obtained differential encoding is then combined with the original aggregated local or global representation to generate the updated node embedding. By integrating differential encodings, the representational ability of generated node embeddings is improved. The differential encoding method is empirically evaluated on different graph tasks on seven benchmark datasets. The results show that it is a general method that improves the message-passing update and the global attention update, advancing the state-of-the-art performance for graph representation learning on these datasets.
Heterogeneous graphs can well describe the complex entity relationships in the real world. For example, online shopping networks contain multiple physical types of consumers and products, as well as multiple relationship types such as purchasing and favoriting. More and more scholars pay attention to this research because heterogeneous graph representation learning shows strong application potential in real-world scenarios. However, the existing heterogeneous graph models use data augmentation techniques to enhance the use of graph structure information, which only captures the graph structure information from the spatial topology, ignoring the information displayed in the spectrum dimension of the graph structure. To address the issue that heterogeneous graph representation learning methods fail to model spectral information, this paper introduces a spectral-enhanced graph contrastive learning model (SHCL) and proposes a spectral augmentation algorithm for the first time in heterogeneous graph neural networks. The proposed model learns an adaptive topology augmentation scheme through the heterogeneous graph itself, disrupting the structural information of the heterogeneous graph in the spectrum dimension, and ultimately improving the learning effect of the model. Experimental results on multiple real-world datasets demonstrate substantial advantages of the proposed model.
The modelling of temporal patterns in dynamic graphs is an important current research issue in the development of time-aware GNNs. Whether or not a specific sequence of events in a temporal graph constitutes a temporal pattern not only depends on the frequency of its occurrence. We consider whether it deviates from what is expected in a temporal graph where timestamps are randomly shuffled. While accounting for such a random baseline is important to model temporal patterns, it has mostly been ignored by current temporal graph neural networks. To address this issue we propose HYPA-DBGNN, a novel two-step approach that combines (i) the inference of anomalous sequential patterns in time series data on graphs based on a statistically principled null model, with (ii) a neural message passing approach that utilizes a higher-order De Bruijn graph whose edges capture overrepresented sequential patterns. Our method leverages hypergeometric graph ensembles to identify anomalous edges within both first- and higher-order De Bruijn graphs, which encode the temporal ordering of events. The model introduces an inductive bias that enhances model interpretability. We evaluate our approach for static node classification using benchmark datasets and a synthetic dataset that showcases its ability to incorporate the observed inductive bias regarding over- and under-represented temporal edges. We demonstrate the framework's effectiveness in detecting similar patterns within empirical datasets, resulting in superior performance compared to baseline methods in node classification tasks. To the best of our knowledge, our work is the first to introduce statistically informed GNNs that leverage temporal and causal sequence anomalies. HYPA-DBGNN represents a path for bridging the gap between statistical graph inference and neural graph representation learning, with potential applications to static GNNs.
The recent past has witnessed a notable surge in on-demand food delivery (OFD) services, offering delivery fulfillment within dozens of minutes after an order is placed. In OFD, pooling multiple orders for simultaneous delivery in real-time order assignment is a pivotal efficiency source, which may in turn extend delivery time. Constructing high-quality order pooling to harmonize platform efficiency with the experiences of consumers and couriers, is crucial to OFD platforms. However, the complexity and real-time nature of order assignment, making extensive calculations impractical, significantly limit the potential for order consolidation. Moreover, offline environment is frequently riddled with unknown factors, posing challenges for the platform's perceptibility and pooling decisions. Nevertheless, delivery behaviors of skilled couriers (SCs) who know the environment well, can improve system awareness and effectively inform decisions. Hence a SC delivery network (SCDN) is constructed, based on an enhanced attributed heterogeneous network embedding approach tailored for OFD. It aims to extract features from rich temporal and spatial information, and uncover the latent potential for order combinations embedded within SC trajectories. Accordingly, the vast search space of order assignment can be effectively pruned through scalable similarity calculations of low-dimensional vectors, making comprehensive and high-quality pooling outcomes more easily identified in real time. SCDN has now been deployed in Meituan dispatch system. Online tests reveal that with SCDN, the pooling quality and extent have been greatly improved. And our system can boost couriers'efficiency by 45-55% during noon peak hours, while upholding the timely delivery commitment.
Graph representation learning (GRL) is to encode graph elements into informative vector representations, which can be used in downstream tasks for analyzing graph-structured data and has seen extensive applications in various domains. However, the majority of extant studies on GRL are geared towards generating node representations, which cannot be readily employed to perform edge-based analytics tasks in edge-attributed bipartite graphs (EABGs) that pervade the real world, e.g., spam review detection in customer-product reviews and identifying fraudulent transactions in user-merchant networks. Compared to node-wise GRL, learning edge representations (ERL) on such graphs is challenging due to the need to incorporate the structure and attribute semantics from the perspective of edges while considering the separate influence of two heterogeneous node sets U and V in bipartite graphs. To our knowledge, despite its importance, limited research has been devoted to this frontier, and existing workarounds all suffer from sub-par results. Motivated by this, this paper designs EAGLE, an effective ERL method for EABGs. Building on an in-depth and rigorous theoretical analysis, we propose the factorized feature propagation (FFP) scheme for edge representations with adequate incorporation of long-range dependencies of edges/features without incurring tremendous computation overheads. We further ameliorate FFP as a dual-view FFP by taking into account the influences from nodes in U and V severally in ERL. Extensive experiments on 5 real datasets showcase the effectiveness of the proposed EAGLE models in semi-supervised edge classification tasks. In particular, EAGLE can attain a considerable gain of at most 38.11% in AP and 1.86% in AUC when compared to the best baselines.
Graph neural networks (GNNs) have attracted widespread attention for their impressive capability of graph representation learning. However, the increasing prevalence of large-scale graphs presents a significant challenge for GNN training due to their computational demands, limiting the applicability of GNNs in various scenarios. In response to this challenge, graph condensation (GC) is proposed as a promising acceleration solution, focusing on generating an informative compact graph that enables efficient training of GNNs while retaining performance. Despite the potential to accelerate GNN training, existing GC methods overlook the quality of large training graphs during both the training and inference stages. They indiscriminately emulate the training graph distributions, making the condensed graphs susceptible to noises within the training graph and significantly impeding the application of GC in intricate real-world scenarios. To address this issue, we propose robust graph condensation (RobGC), a plug-and-play approach for GC to extend the robustness and applicability of condensed graphs in noisy graph structure environments. Specifically, RobGC leverages the condensed graph as a feedback signal to guide the denoising process on the original training graph. A label propagation-based alternating optimization strategy is in place for the condensation and denoising processes, contributing to the mutual purification of the condensed graph and training graph. Additionally, as a GC method designed for inductive graph inference, RobGC facilitates test-time graph denoising by leveraging the noise-free condensed graph to calibrate the structure of the test graph. Extensive experiments show that RobGC is compatible with various GC methods, significantly boosting their robustness under different types and levels of graph structural noises.
Omics data analysis is crucial for studying complex diseases, but its high dimensionality and heterogeneity challenge classical statistical and machine learning methods. Graph neural networks have emerged as promising alternatives, yet the optimal strategies for their design and optimization in real-world biomedical challenges remain unclear. This study evaluates various graph representation learning models for case-control classification using high-throughput biological data from Parkinson's disease and control samples. We compare topologies derived from sample similarity networks and molecular interaction networks, including protein-protein and metabolite-metabolite interactions (PPI, MMI). Graph Convolutional Network (GCNs), Chebyshev spectral graph convolution (ChebyNet), and Graph Attention Network (GAT), are evaluated alongside advanced architectures like graph transformers, the graph U-net, and simpler models like multilayer perceptron (MLP). These models are systematically applied to transcriptomics and metabolomics data independently. Our comparative analysis highlights the benefits and limitations of various architectures in extracting patterns from omics data, paving the way for more accurate and interpretable models in biomedical research.
Graph Neural Networks (GNNs) have shown impressive performance in graph representation learning, but they face challenges in capturing long-range dependencies due to their limited expressive power. To address this, Graph Transformers (GTs) were introduced, utilizing self-attention mechanism to effectively model pairwise node relationships. Despite their advantages, GTs suffer from quadratic complexity w.r.t. the number of nodes in the graph, hindering their applicability to large graphs. In this work, we present Graph-Enhanced Contextual Operator (GECO), a scalable and effective alternative to GTs that leverages neighborhood propagation and global convolutions to effectively capture local and global dependencies in quasilinear time. Our study on synthetic datasets reveals that GECO reaches 169x speedup on a graph with 2M nodes w.r.t. optimized attention. Further evaluations on diverse range of benchmarks showcase that GECO scales to large graphs where traditional GTs often face memory and time limitations. Notably, GECO consistently achieves comparable or superior quality compared to baselines, improving the SOTA up to 4.5%, and offering a scalable and effective solution for large-scale graph learning.
In recent years, graph prompt learning/tuning has garnered increasing attention in adapting pre-trained models for graph representation learning. As a kind of universal graph prompt learning method, Graph Prompt Feature (GPF) has achieved remarkable success in adapting pre-trained models for Graph Neural Networks (GNNs). By fixing the parameters of a pre-trained GNN model, the aim of GPF is to modify the input graph data by adding some (learnable) prompt vectors into graph node features to better align with the downstream tasks on the smaller dataset. However, existing GPFs generally suffer from two main limitations. First, GPFs generally focus on node prompt learning which ignore the prompting for graph edges. Second, existing GPFs generally conduct the prompt learning on all nodes equally which fails to capture the importances of different nodes and may perform sensitively w.r.t noisy nodes in aligning with the downstream tasks. To address these issues, in this paper, we propose a new unified Graph Selective Prompt Feature learning (GSPF) for GNN fine-tuning. The proposed GSPF integrates the prompt learning on both graph node and edge together, which thus provides a unified prompt model for the graph data. Moreover, it conducts prompt learning selectively on nodes and edges by concentrating on the important nodes and edges for prompting which thus make our model be more reliable and compact. Experimental results on many benchmark datasets demonstrate the effectiveness and advantages of the proposed GSPF method.
One-class learning (OCL) comprises a set of techniques applied when real-world problems have a single class of interest. The usual procedure for OCL is learning a hypersphere that comprises instances of this class and, ideally, repels unseen instances from any other classes. Besides, several OCL algorithms for graphs have been proposed since graph representation learning has succeeded in various fields. These methods may use a two-step strategy, initially representing the graph and, in a second step, classifying its nodes. On the other hand, end-to-end methods learn the node representations while classifying the nodes in one learning process. We highlight three main gaps in the literature on OCL for graphs: (i) non-customized representations for OCL; (ii) the lack of constraints on hypersphere parameters learning; and (iii) the methods' lack of interpretability and visualization. We propose One-cLass Graph Autoencoder (OLGA). OLGA is end-to-end and learns the representations for the graph nodes while encapsulating the interest instances by combining two loss functions. We propose a new hypersphere loss function to encapsulate the interest instances. OLGA combines this new hypersphere loss with the graph autoencoder reconstruction loss to improve model learning. OLGA achieved state-of-the-art results and outperformed six other methods with a statistically significant difference from five methods. Moreover, OLGA learns low-dimensional representations maintaining the classification performance with an interpretable model representation learning and results.
When engaging in end-to-end graph representation learning with Graph Neural Networks (GNNs), the intricate causal relationships and rules inherent in graph data pose a formidable challenge for the model in accurately capturing authentic data relationships. A proposed mitigating strategy involves the direct integration of rules or relationships corresponding to the graph data into the model. However, within the domain of graph representation learning, the inherent complexity of graph data obstructs the derivation of a comprehensive causal structure that encapsulates universal rules or relationships governing the entire dataset. Instead, only specialized diminutive causal structures, delineating specific causal relationships within constrained subsets of graph data, emerge as discernible. Motivated by empirical insights, it is observed that GNN models exhibit a tendency to converge towards such specialized causal structures during the training process. Consequently, we posit that the introduction of these specific causal structures is advantageous for the training of GNN models. Building upon this proposition, we introduce a novel method that enables GNN models to glean insights from these specialized diminutive causal structures, thereby enhancing overall performance. Our method specifically extracts causal knowledge from the model representation of these diminutive causal structures and incorporates interchange intervention to optimize the learning process. Theoretical analysis serves to corroborate the efficacy of our proposed method. Furthermore, empirical experiments consistently demonstrate significant performance improvements across diverse datasets.
Major depressive disorder (MDD) is a common mental disorder that typically affects a person's mood, cognition, behavior, and physical health. Resting-state functional magnetic resonance imaging (rs-fMRI) data are widely used for computer-aided diagnosis of MDD. While multi-site fMRI data can provide more data for training reliable diagnostic models, significant cross-site data heterogeneity would result in poor model generalizability. Many domain adaptation methods are designed to reduce the distributional differences between sites to some extent, but usually ignore overfitting problem of the model on the source domain. Intuitively, target data augmentation can alleviate the overfitting problem by forcing the model to learn more generalized features and reduce the dependence on source domain data. In this work, we propose a new augmentation-based unsupervised cross-domain fMRI adaptation (AUFA) framework for automatic diagnosis of MDD. The AUFA consists of 1) a graph representation learning module for extracting rs-fMRI features with spatial attention, 2) a domain adaptation module for feature alignment between source and target data, 3) an augmentation-based self-optimization module for alleviating model overfitting on the source domain, and 4) a classification module. Experimental results on 1,089 subjects suggest that AUFA outperforms several state-of-the-art methods in MDD identification. Our approach not only reduces data heterogeneity between different sites, but also localizes disease-related functional connectivity abnormalities and provides interpretability for the model.
Graph anomaly detection (GAD) is increasingly crucial in various applications, ranging from financial fraud detection to fake news detection. However, current GAD methods largely overlook the fairness problem, which might result in discriminatory decisions skewed toward certain demographic groups defined on sensitive attributes (e.g., gender, religion, ethnicity, etc.). This greatly limits the applicability of these methods in real-world scenarios in light of societal and ethical restrictions. To address this critical gap, we make the first attempt to integrate fairness with utility in GAD decision-making. Specifically, we devise a novel DisEntangle-based FairnEss-aware aNomaly Detection framework on the attributed graph, named DEFEND. DEFEND first introduces disentanglement in GNNs to capture informative yet sensitive-irrelevant node representations, effectively reducing societal bias inherent in graph representation learning. Besides, to alleviate discriminatory bias in evaluating anomalous nodes, DEFEND adopts a reconstruction-based anomaly detection, which concentrates solely on node attributes without incorporating any graph structure. Additionally, given the inherent association between input and sensitive attributes, DEFEND constrains the correlation between the reconstruction error and the predicted sensitive attributes. Our empirical evaluations on real-world datasets reveal that DEFEND performs effectively in GAD and significantly enhances fairness compared to state-of-the-art baselines. To foster reproducibility, our code is available at https://github.com/AhaChang/DEFEND.
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called persistence barcodes. We introduce extended persistence into a supervised learning framework for graph classification. Global topological information, in the form of a barcode with four different types of bars and their explicit cycle representatives, is combined into the model by the readout function which is computed by extended persistence. The entire model is end-to-end differentiable. We use a link-cut tree data structure and parallelism to lower the complexity of computing extended persistence, obtaining a speedup of more than 60x over the state-of-the-art for extended persistence computation. This makes extended persistence feasible for machine learning. We show that, under certain conditions, extended persistence surpasses both the WL[1] graph isomorphism test and 0-dimensional barcodes in terms of expressivity because it adds more global (topological) information. In particular, arbitrarily long cycles can be represented, which is difficult for finite receptive field message passing graph neural networks. Furthermore, we show the effectiveness of our method on real world datasets compared to many existing recent graph representation learning methods.
Binary code similarity detection is an important problem with applications in areas such as malware analysis, vulnerability research and license violation detection. This paper proposes a novel graph neural network architecture combined with a novel graph data representation called call graphlets. A call graphlet encodes the neighborhood around each function in a binary executable, capturing the local and global context through a series of statistical features. A specialized graph neural network model operates on this graph representation, learning to map it to a feature vector that encodes semantic binary code similarities using deep-metric learning. The proposed approach is evaluated across five distinct datasets covering different architectures, compiler tool chains, and optimization levels. Experimental results show that the combination of call graphlets and the novel graph neural network architecture achieves comparable or state-of-the-art performance compared to baseline techniques across cross-architecture, mono-architecture and zero shot tasks. In addition, our proposed approach also performs well when evaluated against an out-of-domain function inlining task. The work provides a general and effective graph neural network-based solution for conducting binary code similarity detection.
Message-passing graph neural networks (GNNs) excel at capturing local relationships but struggle with long-range dependencies in graphs. In contrast, graph transformers (GTs) enable global information exchange but often oversimplify the graph structure by representing graphs as sets of fixed-length vectors. This work introduces a novel architecture that overcomes the shortcomings of both approaches by combining the long-range information of random walks with local message passing. By treating random walks as sequences, our architecture leverages recent advances in sequence models to effectively capture long-range dependencies within these walks. Based on this concept, we propose a framework that offers (1) more expressive graph representations through random walk sequences, (2) the ability to utilize any sequence model for capturing long-range dependencies, and (3) the flexibility by integrating various GNN and GT architectures. Our experimental evaluations demonstrate that our approach achieves significant performance improvements on 19 graph and node benchmark datasets, notably outperforming existing methods by up to 13\% on the PascalVoc-SP and COCO-SP datasets. The code is available at https://github.com/BorgwardtLab/NeuralWalker.
Predicting genetic mutations from whole slide images is indispensable for cancer diagnosis. However, existing work training multiple binary classification models faces two challenges: (a) Training multiple binary classifiers is inefficient and would inevitably lead to a class imbalance problem. (b) The biological relationships among genes are overlooked, which limits the prediction performance. To tackle these challenges, we innovatively design a Biological-knowledge enhanced PathGenomic multi-label Transformer to improve genetic mutation prediction performances. BPGT first establishes a novel gene encoder that constructs gene priors by two carefully designed modules: (a) A gene graph whose node features are the genes' linguistic descriptions and the cancer phenotype, with edges modeled by genes' pathway associations and mutation consistencies. (b) A knowledge association module that fuses linguistic and biomedical knowledge into gene priors by transformer-based graph representation learning, capturing the intrinsic relationships between different genes' mutations. BPGT then designs a label decoder that finally performs genetic mutation prediction by two tailored modules: (a) A modality fusion module that firstly fuses the gene priors with critical regions in WSIs and obtains gene-wise mutation logits. (b) A comparative multi-label loss that emphasizes the inherent comparisons among mutation status to enhance the discrimination capabilities. Sufficient experiments on The Cancer Genome Atlas benchmark demonstrate that BPGT outperforms the state-of-the-art.
The Transformer architecture has recently gained considerable attention in the field of graph representation learning, as it naturally overcomes several limitations of Graph Neural Networks (GNNs) with customized attention mechanisms or positional and structural encodings. Despite making some progress, existing works tend to overlook external information of graphs, specifically the correlation between graphs. Intuitively, graphs with similar structures should have similar representations. Therefore, we propose Graph External Attention (GEA) -- a novel attention mechanism that leverages multiple external node/edge key-value units to capture inter-graph correlations implicitly. On this basis, we design an effective architecture called Graph External Attention Enhanced Transformer (GEAET), which integrates local structure and global interaction information for more comprehensive graph representations. Extensive experiments on benchmark datasets demonstrate that GEAET achieves state-of-the-art empirical performance. The source code is available for reproducibility at: https://github.com/icm1018/GEAET.
Anomaly detection in continuous-time dynamic graphs is an emerging field yet under-explored in the context of learning algorithms. In this paper, we pioneer structured analyses of link-level anomalies and graph representation learning for identifying categorically anomalous graph links. First, we introduce a fine-grained taxonomy for edge-level anomalies leveraging structural, temporal, and contextual graph properties. Based on these properties, we introduce a method for generating and injecting typed anomalies into graphs. Next, we introduce a novel method to generate continuous-time dynamic graphs featuring consistencies across either or combinations of time, structure, and context. To enable temporal graph learning methods to detect specific types of anomalous links rather than the bare existence of a link, we extend the generic link prediction setting by: (1) conditioning link existence on contextual edge attributes; and (2) refining the training regime to accommodate diverse perturbations in the negative edge sampler. Comprehensive benchmarks on synthetic and real-world datasets -- featuring synthetic and labeled organic anomalies and employing six state-of-the-art link prediction methods -- validate our taxonomy and generation processes for anomalies and benign graphs, as well as our approach to adapting methods for anomaly detection. Our results reveal that different learning methods excel in capturing different aspects of graph normality and detecting different types of anomalies. We conclude with a comprehensive list of findings highlighting opportunities for future research.