We study the classic k-center clustering problem under the additional constraint that each cluster should be fair. In this setting, each point is marked with one or more colors, which can be used to model protected attributes (e.g., gender or ethnicity). A cluster is deemed fair if, for every color, the fraction of its points marked with that color is within some prespecified range. We present a coreset-based approach to fair k-center clustering for general metric spaces which attains almost the best approximation quality of the current state of the art solutions, while featuring running times which can be orders of magnitude faster for large datasets of low doubling dimension. We devise sequential, streaming and MapReduce implementations of our approach and conduct a thorough experimental analysis to provide evidence of their practicality, scalability, and effectiveness.
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Graph neural networks (GNNs) have gained popularity in modeling various complex networks, e.g., social network and webpage network. Despite the promising accuracy, the confidences of GNNs are shown to be miscalibrated, indicating limited awareness of prediction uncertainty and harming the reliability of model decisions. Existing calibration methods primarily focus on improving GNN models, e.g., adding regularization during training or introducing temperature scaling after training. In this paper, we argue that the miscalibration of GNNs may stem from the graph data and can be alleviated through topology modification. To support this motivation, we conduct data observations by examining the impacts ofdecisive andhomophilic edges on calibration performance, where decisive edges play a critical role in GNN predictions and homophilic edges connect nodes of the same class. By assigning larger weights to these edges in the adjacency matrix, we observe an improvement in calibration performance without sacrificing classification accuracy. This suggests the potential of a data-centric approach for calibrating GNNs. Motivated by our observations, we propose Data-centric Graph Calibration (DCGC), which uses two edge weighting modules to adjust the input graph for GNN calibration. The first module learns the weights of decisive edges by parameterizing the adjacency matrix and enabling backpropagation of the prediction loss to edge weights. This emphasizes critical edges that fit the prediction needs. The second module computes weights for homophilic edges based on predicted label distributions, assigning larger weights to edges with stronger homophily. These modifications operate at the data level and can be easily integrated with temperature scaling-based methods for better calibration. Experimental results on 8 benchmark datasets demonstrate that DCGC achieves state-of-the-art calibration performance, with an average relative improvement of 36.4% in ECE, while maintaining or even slightly improving classification accuracy. Ablation studies and hyper-parameter analysis further validate the effectiveness and robustness of our proposed method DCGC. Code and data are available at https://github.com/BUPT-GAMMA/DCGC.
We investigate the replay buffer in rehearsal-based approaches for graph continual learning (GCL) methods. Existing rehearsal-based GCL methods select the most representative nodes for each class and store them in a replay buffer for later use in training subsequent tasks. However, we discovered that considering only the class representativeness of each replayed node makes the replayed nodes to be concentrated around the center of each class, incurring a potential risk of overfitting to nodes residing in those regions, which aggravates catastrophic forgetting. Moreover, as the rehearsal-based approach heavily relies on a few replayed nodes to retain knowledge obtained from previous tasks, involving the replayed nodes that have irrelevant neighbors in the model training may have a significant detrimental impact on model performance. In this paper, we propose a GCL model named DSLR, specifically, we devise a coverage-based diversity (CD) approach to consider both the class representativeness and the diversity within each class of the replayed nodes. Moreover, we adopt graph structure learning (GSL) to ensure that the replayed nodes are connected to truly informative neighbors. Extensive experimental results demonstrate the effectiveness and efficiency of DSLR. Our source code is available at https://github.com/seungyoon-Choi/DSLR_official.
Graph representation learning on vast datasets, like web data, has made significant strides. However, the associated computational and storage overheads raise concerns. In sight of this, Graph condensation (GCond) has been introduced to distill these large real datasets into a more concise yet information-rich synthetic graph. Despite acceleration efforts, existing GCond methods mainly grapple with efficiency, especially on expansive web data graphs. Hence, in this work, we pinpoint two major inefficiencies of current paradigms: (1) the concurrent updating of a vast parameter set, and (2) pronounced parameter redundancy. To counteract these two limitations correspondingly, we first (1) employ the Mean-Field variational approximation for convergence acceleration, and then (2) propose the objective of Gradient Information Bottleneck (GDIB) to prune redundancy. By incorporating the leading explanation techniques (e.g., GNNExplainer and GSAT) to instantiate the GDIB, our EXGC, the Efficient and eXplainable Graph Condensation method is proposed, which can markedly boost efficiency and inject explainability. Our extensive evaluations across eight datasets underscore EXGC's superiority and relevance. Code is available at https://github.com/MangoKiller/EXGC.
Recent works have introduced GNN-to-MLP knowledge distillation (KD) frameworks to combine both GNN's superior performance and MLP's fast inference speed. However, existing KD frameworks are primarily designed for node classification within single graphs, leaving their applicability to graph classification largely unexplored. Two main challenges arise when extending KD for node classification to graph classification: (1) The inherent sparsity of learning signals due to soft labels being generated at the graph level; (2) The limited expressiveness of student MLPs, especially in datasets with limited input feature spaces. To overcome these challenges, we introduce MuGSI, a novel KD framework that employs Multi-granularity Structural Information for graph classification. Specifically, we propose multi-granularity distillation loss in MuGSI to tackle the first challenge. This loss function is composed of three distinct components: graph-level distillation, subgraph-level distillation, and node-level distillation. Each component targets a specific granularity of the graph structure, ensuring a comprehensive transfer of structural knowledge from the teacher model to the student model. To tackle the second challenge, MuGSI proposes to incorporate a node feature augmentation component, thereby enhancing the expressiveness of the student MLPs and making them more capable learners. We perform extensive experiments across a variety of datasets and different teacher/student model architectures. The experiment results demonstrate the effectiveness, efficiency, and robustness of MuGSI. Codes are publicly available at: https://github.com/tianyao-aka/MuGSI.
Recent studies have revealed that GNNs are vulnerable to adversarial attacks. To defend against such attacks, robust graph structure refinement (GSR) methods aim at minimizing the effect of adversarial edges based on node features, graph structure, or external information. However, we have discovered that existing GSR methods are limited by narrowassumptions, such as assuming clean node features, moderate structural attacks, and the availability of external clean graphs, resulting in the restricted applicability in real-world scenarios. In this paper, we propose a self-guided GSR framework (SG-GSR), which utilizes a clean sub-graph found within the given attacked graph itself. Furthermore, we propose a novel graph augmentation and a group-training strategy to handle the two technical challenges in the clean sub-graph extraction: 1) loss of structural information, and 2) imbalanced node degree distribution. Extensive experiments demonstrate the effectiveness of SG-GSR under various scenarios including non-targeted attacks, targeted attacks, feature attacks, e-commerce fraud, and noisy node labels. Our code is available at https://github.com/yeonjun-in/torch-SG-GSR.
Heterogeneous Graph Neural Networks (HGNNs) have gained significant popularity in various heterogeneous graph learning tasks. However, most existing HGNNs rely on spatial domain-based methods to aggregate information, i.e., manually selected meta-paths or some heuristic modules, lacking theoretical guarantees. Furthermore, these methods cannot learn arbitrary valid heterogeneous graph filters within the spectral domain, which have limited expressiveness. To tackle these issues, we present a positive spectral heterogeneous graph convolution via positive noncommutative polynomials. Then, using this convolution, we propose PSHGCN, a novel Positive Spectral Heterogeneous Graph Convolutional Network. PSHGCN offers a simple yet effective method for learning valid heterogeneous graph filters. Moreover, we demonstrate the rationale of PSHGCN in the graph optimization framework. We conducted an extensive experimental study to show that PSHGCN can learn diverse heterogeneous graph filters and outperform all baselines on open benchmarks. Notably, PSHGCN exhibits remarkable scalability, efficiently handling large real-world graphs comprising millions of nodes and edges. Our codes are available at https://github.com/ivam-he/PSHGCN.
Graph neural networks (GNNs) have achieved remarkable performance on graph-structured data. However, GNNs may inherit prejudice from the training data and make discriminatory predictions based on sensitive attributes, such as gender and race. Recently, there has been an increasing interest in ensuring fairness on GNNs, but all of them are under the assumption that the training and testing data are under the same distribution, i.e., training data and testing data are from the same graph. Will graph fairness performance decrease under distribution shifts? How does distribution shifts affect graph fairness learning? All these open questions are largely unexplored from a theoretical perspective. To answer these questions, we first theoretically identify the factors that determine bias on a graph. Subsequently, we explore the factors influencing fairness on testing graphs, with a noteworthy factor being the representation distances of certain groups between the training and testing graph. Motivated by our theoretical analysis, we propose our framework FatraGNN. Specifically, to guarantee fairness performance on unknown testing graphs, we propose a graph generator to produce numerous graphs with significant bias and under different distributions. Then we minimize the representation distances for each certain group between the training graph and generated graphs. This empowers our model to achieve high classification and fairness performance even on generated graphs with significant bias, thereby effectively handling unknown testing graphs. Experiments on real-world and semi-synthetic datasets demonstrate the effectiveness of our model in terms of both accuracy and fairness.
Unsupervised Graph Domain Adaptation (UGDA) has emerged as a practical solution to transfer knowledge from a label-rich source graph to a completely unlabelled target graph. However, most methods require a labelled source graph to provide supervision signals, which might not be accessible in the real-world settings due to regulations and privacy concerns. In this paper, we explore the scenario of source-free unsupervised graph domain adaptation, which tries to address the domain adaptation problem without accessing the labelled source graph. Specifically, we present a novel paradigm called GraphCTA, which performs model adaptation and graph adaptation collaboratively through a series of procedures: (1) conduct model adaptation based on node's neighborhood predictions in target graph considering both local and global information; (2) perform graph adaptation by updating graph structure and node attributes via neighborhood contrastive learning; and (3) the updated graph serves as an input to facilitate the subsequent iteration of model adaptation, thereby establishing a collaborative loop between model adaptation and graph adaptation. Comprehensive experiments are conducted on various public datasets. The experimental results demonstrate that our proposed model outperforms recent source-free baselines by large margins.
Graph neural networks (GNNs) have emerged as the state of the art for a variety of graph-related tasks and have been widely commercialized in real-world scenarios. Behind its revolutionary representation capability, the huge training costs also expose GNNs to the risks of potential model piracy attacks which threaten the intellectual property (IP) of GNNs. In this work, we design a novel and effective ownership verification framework for GNNs called GNNFingers to safeguard the IP of GNNs. The key design of the proposed framework is two-fold: graph fingerprint construction and robust verification module. With GNNFingers, a GNN model owner can verify if a deployed model is stolen from the source GNN simply by querying with graph inputs. Besides, GNNFingers could be applied to various GNN models and graph-related tasks. We extensively evaluate the proposed framework on various GNNs designed for multiple graph-related tasks including graph classification, graph matching, node classification, and link prediction. Our results show that GNNFingers can robustly distinguish post-processed surrogate GNNs from irrelevant GNNs, e.g., GNNFingers achieves 100% true positives and 100% true negatives on the test of 200 suspect GNNs of both graph classification and node classification tasks.
Real-world graphs exhibit diverse structures, including homophilic and heterophilic patterns, necessitating the development of a universal Graph Contrastive Learning (GCL) framework. Nonetheless, the existing GCLs, especially those with a local focus, lack universality due to the mismatch between the input graph structure and the homophily assumption for two primary components of GCLs. Firstly, the encoder, commonly Graph Convolution Network (GCN), operates as a low-pass filter, which assumes the input graph to be homophilic. This makes it challenging to aggregate features from neighbor nodes of the same class on heterophilic graphs. Secondly, the local positive sampling regards neighbor nodes as positive samples, which is inspired by the homophily assumption. This results in feature similarity amplification for the samples from the different classes (i.e., FALSE positive samples). Therefore, it is crucial to feed the encoder and positive sampling of GCLs with homophilic graph structures. This paper presents a novel GCL framework, named gRaph cOntraStive Exploring uNiversality (ROSEN), designed to achieve this objective. Specifically, ROSEN equips a local graph structure inference module, utilizing the Block Diagonal Property (BDP) of the affinity matrix extracted from node ego networks. This module can generate the homophilic graph structure by selectively removing disassortative edges. Extensive evaluations validate the effectiveness and universality of ROSEN across node classification and node clustering tasks.
Graph contrastive learning (GCL) has emerged as a state-of-the-art strategy for learning representations of diverse graphs including social and biomedical networks. GCL widely uses stochastic graph topology augmentation, such as uniform node dropping, to generate augmented graphs. However, such stochastic augmentations may severely damage the intrinsic properties of a graph and deteriorate the following representation learning process. We argue that incorporating an awareness of cohesive subgraphs during the graph augmentation and learning processes has the potential to enhance GCL performance. To this end, we propose a novel unified framework called CTAug, to seamlessly integrate cohesion awareness into various existing GCL mechanisms. In particular, CTAug comprises two specialized modules: topology augmentation enhancement and graph learning enhancement. The former module generates augmented graphs that carefully preserve cohesion properties, while the latter module bolsters the graph encoder's ability to discern subgraph patterns. Theoretical analysis shows that CTAug can strictly improve existing GCL mechanisms. Empirical experiments verify that CTAug can achieve state-of-the-art performance for graph representation learning, especially for graphs with high degrees. The code is available at https://doi.org/10.5281/zenodo.10594093, or https://github.com/wuyucheng2002/CTAug.
Graph few-shot learning (GFSL) has achieved great success in node classification tasks with rare labels. However, graph few-shot classification (GFSC) models often encounter the problem of classifying test samples with unobserved (or unknown) classes due to the rareness of labels. We formulate this problem as out-of-distribution (OOD) sample detection in inductive graph few-shot learning. This paper presents SMUG, a novel GFSL framework that can detect unobserved classes. Since we have no ground-truth OOD samples in a practical training dataset, it is challenging for the GFSC model to retrieve knowledge about unknown classes from labeled samples. To address this difficulty, we propose a sand mixing scheme to introduce observed classes as artificial OOD samples into meta-tasks. We also develop two unsupervised OOD discriminators to identify OOD samples. Thus, we can assess the performance of OOD discriminators since we know the true classes of these artificial OOD samples. Subsequently, we design a novel training procedure to optimize the encoder based on the performance of the OOD discriminators and the GFSC model. It not only enables the GFSL model to distinguish OOD samples but also promotes the classification accuracy of normal samples. We conduct extensive experiments to evaluate the effectiveness of SMUG based on four benchmark datasets. Experimental results demonstrate that SMUG achieves superior performance over state-of-the-art approaches in OOD detection and node classification. The source code of this paper is available at https://github.com/Memepp/SMUG.
Network resilience is a critical ability of a network to maintain its functionality against disturbances. A network is resilient/robust when a large portion of the nodes are to be better engaged in the network, i.e., they are less likely to leave given the changes on the network. Existing studies validate that the engagement of a node can be well captured by its coreness on network topology. Therefore, it is promising to maximize the number of nodes with increasing coreness values. In this paper, we propose and study thefollower maximization problem: maximizing the resilience gain (the number of coreness-increased vertices) via anchoring a set of vertices within a given budget. We prove that the problem is NP-hard and W[2]-hard, and it is NP-hard to approximate within an O(n^1-ε ) factor. We first propose an advanced greedy approach, followed by a time-dependent framework designed to quickly find high-quality results. The framework is initialized by the advanced greedy algorithm and incorporates novel techniques for optimizing the search space. The effectiveness and efficiency of our solution are verified with extensive experiments on 8 real-life datasets. Our source codes are available at https://github.com/Tsyxxxka/Follower-Maximization.
Group interactions arise in various scenarios in real-world systems: collaborations of researchers, co-purchases of products, and discussions in online Q&A sites, to name a few. Such higher-order relations are naturally modeled as hypergraphs, which consist of hyperedges (i.e., any-sized subsets of nodes). For hypergraphs, the challenge to learn node representation when features or labels are not available is imminent, given that (a) most real-world hypergraphs are not equipped with external features while (b) most existing approaches for hypergraph learning resort to additional information. Thus, in this work, we propose VilLain, a novel self-supervised hypergraph representation learning method based on the propagation of virtual labels (v-labels). Specifically, we learn for each node a sparse probability distribution over v-labels as its feature vector, and we propagate the vectors to construct the final node embeddings. Inspired by higher-order label homogeneity, which we discover in real-world hypergraphs, we design novel self-supervised loss functions for the v-labels to reproduce the higher-order structure-label pattern. We demonstrate that VilLain is: (a) Requirement-free: learning node embeddings without relying on node labels and features, (b) Versatile: giving embeddings that are not specialized to specific tasks but generalizable to diverse downstream tasks, and (c) Accurate: more accurate than its competitors for node classification, hyperedge prediction, node clustering, and node retrieval tasks. Our code and dataset are available at https://github.com/geon0325/VilLain.
To make Graph Neural Networks (GNNs) meet the requirements of the Web, the universality and the generalization become two important research directions. On one hand, many universal GNNs are presented for semi-supervised tasks on both homophilic and non-homophilic graphs by distinguishing homophilic and heterophilic edges with the help of labels. On the other hand, self-supervised learning (SSL) algorithms on graphs are presented by leveraging the self-supervised learning schemes from computer vision and natural language processing. Unfortunately, graph universal self-supervised learning remains resolved. Most existing SSL methods on graphs, which often employ two-layer GCN as the encoder and train the mapping functions, can't alter the low-passing filtering characteristic of GCN. Therefore, to be universal, SSL must becustomized for the graph, i.e., learning the graph. However, learning the graph via universal GNNs is disabled in SSL, since their distinguishability on homophilic and heterophilic edges disappears without the labels. To overcome this difficulty, this paper proposes novel GrAph-customized Universal Self-Supervised Learning (GAUSS) by exploiting local attribute distribution. The main idea is to replace the global parameters with locally learnable propagation. To make the propagation matrix demonstrate the affinity between the nodes, the self-representative learning framework is employed with k-block diagonal regularization. Extensive experiments on synthetic and real-world datasets demonstrate its effectiveness, universality and robustness to noises.
Due to the ubiquity of graph data on the web, web graph mining has become a hot research spot. Nonetheless, the prevalence of largescale web graphs in real applications poses significant challenges to storage, computational capacity and graph model design. Despite numerous studies to enhance the scalability of graph models, a noticeable gap remains between academic research and practical web graph mining applications. One major cause is that in most industrial scenarios, only a small part of nodes in a web graph are actually required to be analyzed, where we term these nodes as target nodes, while others as background nodes. In this paper, we argue that properly fetching and condensing the background nodes from massive web graph data might be a more economical shortcut to tackle the obstacles fundamentally. To this end, we make the first attempt to study the problem of massive background nodes compression for target nodes classification. Through extensive experiments, we reveal two critical roles played by the background nodes in target node classification: enhancing structural connectivity between target nodes, and feature correlation with target nodes. Following this, we propose a novel Graph-Skeleton model, which properly fetches the background nodes, and further condenses the semantic and topological information of background nodes within similar target-background local structures. Extensive experiments on various web graph datasets demonstrate the effectiveness and efficiency of the proposed method. In particular, for MAG240M dataset with 0.24 billion nodes, our generated skeleton graph achieves highly comparable performance while only containing 1.8% nodes of the original graph.
Scalable graph neural networks (GNNs) have emerged as a promising technique, which exhibits superior predictive performance and high running efficiency across numerous large-scale graph-based web applications. However, (i) Most scalable GNNs tend to treat all nodes with the same propagation rules, neglecting their topological uniqueness; (ii) Existing node-wise propagation optimization strategies are insufficient on web-scale graphs with intricate topology, where a full portrayal of nodes' local properties is required. Intuitively, different nodes in web-scale graphs possess distinct topological roles, and therefore propagating them indiscriminately or neglecting local contexts may compromise the quality of node representations. To address the above issues, we propose Adaptive Topology-aware Propagation (ATP), which reduces potential high-bias propagation and extracts structural patterns of each node in a scalable manner to improve running efficiency and predictive performance. Remarkably, ATP is crafted to be a plug-and-play node-wise propagation optimization strategy, allowing for offline execution independent of the graph learning process in a new perspective. Therefore, this approach can be seamlessly integrated into most scalable GNNs while remaining orthogonal to existing node-wise propagation optimization strategies. Extensive experiments on 12 datasets have demonstrated the effectiveness of ATP.
SSTKG: Simple Spatio-Temporal Knowledge Graph for Intepretable and Versatile Dynamic Information Embedding
PDF ↗Knowledge graphs (KGs) have been increasingly employed for link prediction and recommendation using real-world datasets. However, the majority of current methods rely on static data, neglecting the dynamic nature and the hidden spatio-temporal attributes of real-world scenarios. This often results in suboptimal predictions and recommendations. Although there are effective spatio-temporal inference methods, they face challenges such as scalability with large datasets and inadequate semantic understanding, which impede their performance. To address these limitations, this paper introduces a novel framework - Simple Spatio-Temporal Knowledge Graph (SSTKG), for constructing and exploring spatio-temporal KGs. To integrate spatial and temporal data into KGs, our framework exploited through a new 3-step embedding method. Output embeddings can be used for future temporal sequence prediction and spatial information recommendation, providing valuable insights for various applications such as retail sales forecasting and traffic volume prediction. Our framework offers a simple but comprehensive way to understand the underlying patterns and trends in dynamic KG, thereby enhancing the accuracy of predictions and the relevance of recommendations. This work paves the way for more effective utilization of spatio-temporal data in KGs, with potential impacts across a wide range of sectors.
Graph self-supervised algorithms have achieved significant success in acquiring generic knowledge from abundant unlabeled graph data. These pre-trained models can be applied to various downstream Web applications, saving training time and improving downstream performance. However, variations in attribute semantics across graphs pose challenges in transferring pre-trained models to downstream tasks. Concretely speaking, for example, the additional task-specific node information in downstream tasks (specificity) is usually deliberately omitted so that the pre-trained representation (transferability) can be leveraged. The trade-off as such is termed as "transferability-specificity dilemma" in this work. To address this challenge, we introduce an innovative deployment module coined as GraphControl, motivated by ControlNet, to realize better graph domain transfer learning. Specifically, by leveraging universal structural pre-trained models and GraphControl, we align the input space across various graphs and incorporate unique characteristics of target data as conditional inputs. These conditions will be progressively integrated into the model during fine-tuning or prompt tuning through ControlNet, facilitating personalized deployment. Extensive experiments show that our method significantly enhances the adaptability of pre-trained models on target attributed datasets, achieving 1.4-3x performance gain. Furthermore, it outperforms training-from-scratch methods on target data with a comparable margin and exhibits faster convergence. Our codes are available at: https://github.com/wykk00/GraphControl.