Graph Neural Networks (GNNs) are vulnerable to data poisoning attacks, which will generate a poisoned graph as the input to the GNN models. We present FocusedCleaner as a poisoned graph sanitizer to effectively identify the poison injected by attackers. Specifically, FocusedCleaner provides a sanitation framework consisting of two modules: bi-level structural learning and victim node detection. In particular, the structural learning module will reverse the attack process to steadily sanitize the graph while the detection module provides ``the focus" -- a narrowed and more accurate search region -- to structural learning. These two modules will operate in iterations and reinforce each other to sanitize a poisoned graph step by step. As an important application, we show that the adversarial robustness of GNNs trained over the sanitized graph for the node classification task is significantly improved. Extensive experiments demonstrate that FocusedCleaner outperforms the state-of-the-art baselines both on poisoned graph sanitation and improving robustness.
We consider the problem of finding the smallest or largest entry of a tensor of order N that is specified via its rank decomposition. Stated in a different way, we are given N sets of R-dimensional vectors and we wish to select one vector from each set such that the sum of the Hadamard product of the selected vectors is minimized or maximized. We show that this fundamental tensor problem is NP-hard for any tensor rank higher than one, and polynomial-time solvable in the rank-one case. We also propose a continuous relaxation and prove that it is tight for any rank. For low-enough ranks, the proposed continuous reformulation is amenable to low-complexity gradient-based optimization, and we propose a suite of gradient-based optimization algorithms drawing from projected gradient descent, Frank-Wolfe, or explicit parametrization of the relaxed constraints. We also show that our core results remain valid no matter what kind of polyadic tensor model is used to represent the tensor of interest, including Tucker, HOSVD/MLSVD, tensor train, or tensor ring. Next, we consider the class of problems that can be posed as special instances of the problem of interest. We show that this class includes the partition problem (and thus all NP-complete problems via polynomial-time transformation), integer least squares, integer linear programming, integer quadratic programming, sign retrieval (a special kind of mixed integer programming / restricted version of phase retrieval), and maximum likelihood decoding of parity check codes. We demonstrate promising experimental results on a number of hard problems, including state-of-art performance in decoding low density parity check codes and general parity check codes.
Overlapping community detection is a key problem in graph mining. Some research has considered applying graph convolutional networks (GCN) to tackle the problem. However, it is still challenging to incorporate deep graph convolutional networks in the case of general irregular graphs. In this study, we design a deep dynamic residual graph convolutional network (DynaResGCN) based on our novel dynamic dilated aggregation mechanisms and a unified end-to-end encoder-decoder-based framework to detect overlapping communities in networks. The deep DynaResGCN model is used as the encoder, whereas we incorporate the Bernoulli-Poisson (BP) model as the decoder. Consequently, we apply our overlapping community detection framework in a research topics dataset without having ground truth, a set of networks from Facebook having a reliable (hand-labeled) ground truth, and in a set of very large co-authorship networks having empirical (not hand-labeled) ground truth. Our experimentation on these datasets shows significantly superior performance over many state-of-the-art methods for the detection of overlapping communities in networks.
Open Source Software (OSS) is forming the spines of technology infrastructures, attracting millions of talents to contribute. Notably, it is challenging and critical to consider both the developers' interests and the semantic features of the project code to recommend appropriate development tasks to OSS developers. In this paper, we formulate the novel problem of code recommendation, whose purpose is to predict the future contribution behaviors of developers given their interaction history, the semantic features of source code, and the hierarchical file structures of projects. Considering the complex interactions among multiple parties within the system, we propose CODER, a novel graph-based code recommendation framework for open source software developers. CODER jointly models microscopic user-code interactions and macroscopic user-project interactions via a heterogeneous graph and further bridges the two levels of information through aggregation on file-structure graphs that reflect the project hierarchy. Moreover, due to the lack of reliable benchmarks, we construct three large-scale datasets to facilitate future research in this direction. Extensive experiments show that our CODER framework achieves superior performance under various experimental settings, including intra-project, cross-project, and cold-start recommendation. We will release all the datasets, code, and utilities for data retrieval upon the acceptance of this work.
Graph neural networks (GNNs) have shown remarkable performance on diverse graph mining tasks. Although different GNNs can be unified as the same message passing framework, they learn complementary knowledge from the same graph. Knowledge distillation (KD) is developed to combine the diverse knowledge from multiple models. It transfers knowledge from high-capacity teachers to a lightweight student. However, to avoid oversmoothing, GNNs are often shallow, which deviates from the setting of KD. In this context, we revisit KD by separating its benefits from model compression and emphasizing its power of transferring knowledge. To this end, we need to tackle two challenges: how to transfer knowledge from compact teachers to a student with the same capacity; and, how to exploit student GNN's own strength to learn knowledge. In this paper, we propose a novel adaptive KD framework, called BGNN, which sequentially transfers knowledge from multiple GNNs into a student GNN. We also introduce an adaptive temperature module and a weight boosting module. These modules guide the student to the appropriate knowledge for effective learning. Extensive experiments have demonstrated the effectiveness of BGNN. In particular, we achieve up to 3.05% improvement for node classification and 6.35% improvement for graph classification over vanilla GNNs.
Graph Convolutional Network (GCN) has exhibited strong empirical performance in many real-world applications. The vast majority of existing works on GCN primarily focus on the accuracy while ignoring how confident or uncertain a GCN is with respect to its predictions. Despite being a cornerstone of trustworthy graph mining, uncertainty quantification on GCN has not been well studied and the scarce existing efforts either fail to provide deterministic quantification or have to change the training procedure of GCN by introducing additional parameters or architectures. In this paper, we propose the first frequentist-based approach named JuryGCN in quantifying the uncertainty of GCN, where the key idea is to quantify the uncertainty of a node as the width of confidence interval by a jackknife estimator. Moreover, we leverage the influence functions to estimate the change in GCN parameters without re-training to scale up the computation. The proposed JuryGCN is capable of quantifying uncertainty deterministically without modifying the GCN architecture or introducing additional parameters. We perform extensive experimental evaluation on real-world datasets in the tasks of both active learning and semi-supervised node classification, which demonstrate the efficacy of the proposed method.
How can we solve semi-supervised node classification in various graphs possibly with noisy features and structures? Graph neural networks (GNNs) have succeeded in many graph mining tasks, but their generalizability to various graph scenarios is limited due to the difficulty of training, hyperparameter tuning, and the selection of a model itself. Einstein said that we should "make everything as simple as possible, but not simpler." We rephrase it into the careful simplicity principle: a carefully-designed simple model can surpass sophisticated ones in real-world graphs. Based on the principle, we propose SlimG for semi-supervised node classification, which exhibits four desirable properties: It is (a) accurate, winning or tying on 10 out of 13 real-world datasets; (b) robust, being the only one that handles all scenarios of graph data (homophily, heterophily, random structure, noisy features, etc.); (c) fast and scalable, showing up to 18 times faster training in million-scale graphs; and (d) interpretable, thanks to the linearity and sparsity. We explain the success of SlimG through a systematic study of the designs of existing GNNs, sanity checks, and comprehensive ablation studies.
Prevailing deep graph learning models often suffer from label sparsity issue. Although many graph few-shot learning (GFL) methods have been developed to avoid performance degradation in face of limited annotated data, they excessively rely on labeled data, where the distribution shift in the test phase might result in impaired generalization ability. Additionally, they lack a general purpose as their designs are coupled with task or data-specific characteristics. To this end, we propose a general and effective Contrastive Graph Few-shot Learning framework (CGFL). CGFL leverages a self-distilled contrastive learning procedure to boost GFL. Specifically, our model firstly pre-trains a graph encoder with contrastive learning using unlabeled data. Later, the trained encoder is frozen as a teacher model to distill a student model with a contrastive loss. The distilled model is finally fed to GFL. CGFL learns data representation in a self-supervised manner, thus mitigating the distribution shift impact for better generalization and making model task and data-independent for a general graph mining purpose. Furthermore, we introduce an information-based method to quantitatively measure the capability of CGFL. Comprehensive experiments demonstrate that CGFL outperforms state-of-the-art baselines on several graph mining tasks in the few-shot scenario. We also provide quantitative measurement of CGFL's success.
As special information carriers containing both structure and feature information, graphs are widely used in graph mining, e.g., Graph Neural Networks (GNNs). However, in some practical scenarios, graph data are stored separately in multiple distributed parties, which may not be directly shared due to conflicts of interest. Hence, federated graph neural networks are proposed to address such data silo problems while preserving the privacy of each party (or client). Nevertheless, different graph data distributions among various parties, which is known as the statistical heterogeneity, may degrade the performance of naive federated learning algorithms like FedAvg. In this paper, we propose FedEgo, a federated graph learning framework based on ego-graphs to tackle the challenges above, where each client will train their local models while also contributing to the training of a global model. FedEgo applies GraphSAGE over ego-graphs to make full use of the structure information and utilizes Mixup for privacy concerns. To deal with the statistical heterogeneity, we integrate personalization into learning and propose an adaptive mixing coefficient strategy that enables clients to achieve their optimal personalization. Extensive experimental results and in-depth analysis demonstrate the effectiveness of FedEgo.
Graph pre-training strategies have been attracting a surge of attention in the graph mining community, due to their flexibility in parameterizing graph neural networks (GNNs) without any label information. The key idea lies in encoding valuable information into the backbone GNNs, by predicting the masked graph signals extracted from the input graphs. In order to balance the importance of diverse graph signals (e.g., nodes, edges, subgraphs), the existing approaches are mostly hand-engineered by introducing hyperparameters to re-weight the importance of graph signals. However, human interventions with sub-optimal hyperparameters often inject additional bias and deteriorate the generalization performance in the downstream applications. This paper addresses these limitations from a new perspective, i.e., deriving curriculum for pre-training GNNs. We propose an end-to-end model named MentorGNN that aims to supervise the pre-training process of GNNs across graphs with diverse structures and disparate feature spaces. To comprehend heterogeneous graph signals at different granularities, we propose a curriculum learning paradigm that automatically re-weighs graph signals in order to ensure a good generalization in the target domain. Moreover, we shed new light on the problem of domain adaption on relational data (i.e., graphs) by deriving a natural and interpretable upper bound on the generalization error of the pre-trained GNNs. Extensive experiments on a wealth of real graphs validate and verify the performance of MentorGNN.
Network science established itself as a prominent tool for modeling time series and complex systems. This modeling process consists of transforming a set or a single time series into a network. Nodes may represent complete time series, segments, or single values, while links define associations or similarities between the represented parts. R is one of the main programming languages used in data science, statistics, and machine learning, with many packages available. However, no single package provides the necessary methods to transform time series into networks. This paper presents ts2net, an R package for modeling one or multiple time series into networks. The package provides the time series distance functions that can be easily computed in parallel and in supercomputers to process larger data sets and methods to transform distance matrices into networks. Ts2net also provides methods to transform a single time series into a network, such as recurrence networks, visibility graphs, and transition networks. Together with other packages, ts2net permits using network science and graph mining tools to extract information from time series.
Heterogeneous graphs, which contain nodes and edges of multiple types, are prevalent in various domains, including bibliographic networks, social media, and knowledge graphs. As a fundamental task in analyzing heterogeneous graphs, relevance measure aims to calculate the relevance between two objects of different types, which has been used in many applications such as web search, recommendation, and community detection. Most of existing relevance measures focus on homogeneous networks where objects are of the same type, and a few measures are developed for heterogeneous graphs, but they often need the pre-defined meta-path. Defining meaningful meta-paths requires much domain knowledge, which largely limits their applications, especially on schema-rich heterogeneous graphs like knowledge graphs. Recently, the Graph Neural Network (GNN) has been widely applied in many graph mining tasks, but it has not been applied for measuring relevance yet. To address the aforementioned problems, we propose a novel GNN-based relevance measure, namely GSim. Specifically, we first theoretically analyze and show that GNN is effective for measuring the relevance of nodes in the graph. We then propose a context path-based graph neural network (CP-GNN) to automatically leverage the semantics in heterogeneous graphs. Moreover, we exploit CP-GNN to support relevance measures between two objects of any type. Extensive experiments demonstrate that GSim outperforms existing measures.
Admittedly, Graph Convolution Network (GCN) has achieved excellent results on graph datasets such as social networks, citation networks, etc. However, softmax used as the decision layer in these frameworks is generally optimized with thousands of iterations via gradient descent. Furthermore, due to ignoring the inner distribution of the graph nodes, the decision layer might lead to an unsatisfactory performance in semi-supervised learning with less label support. To address the referred issues, we propose a novel graph deep model with a non-gradient decision layer for graph mining. Firstly, manifold learning is unified with label local-structure preservation to capture the topological information of the nodes. Moreover, owing to the non-gradient property, closed-form solutions is achieved to be employed as the decision layer for GCN. Particularly, a joint optimization method is designed for this graph model, which extremely accelerates the convergence of the model. Finally, extensive experiments show that the proposed model has achieved state-of-the-art performance compared to the current models.
Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn embeddings on a smaller summary graph, and then restore the node embeddings of the original graph. However, all existing works depend on heuristic designs and lack theoretical analysis. Different from existing works, we contribute an in-depth theoretical analysis of three specific embedding learning methods based on introduced kernel matrix, and reveal that learning embeddings via graph summarization is actually learning embeddings on a approximate graph constructed by the configuration model. We also give analysis about approximation error. To the best of our knowledge, this is the first work to give theoretical analysis of this approach. Furthermore, our analysis framework gives interpretation of some existing methods and provides great insights for future work on this problem.
Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes within the vertex connections, neglecting the crucial asynchronous nature of such dynamics where the evolution of each local structure starts at different times and lasts for various durations. To maintain asynchronous structural evolutions within the graph, we innovatively formulate dynamic graphs as temporal edge sequences associated with joining time of vertices (ToV) and timespan of edges (ToE). Then, a time-aware Transformer is proposed to embed vertices' dynamic connections and ToEs into the learned vertex representations. Meanwhile, we treat each edge sequence as a whole and embed its ToV of the first vertex to further encode the time-sensitive information. Extensive evaluations on several datasets show that our approach outperforms the state-of-the-art in a wide range of graph mining tasks. At the same time, it is very efficient and scalable for embedding large-scale dynamic graphs.
Graph Neural Networks (GNNs) have achieved tremendous success in many graph mining tasks benefitting from the message passing strategy that fuses the local structure and node features for better graph representation learning. Despite the success of GNNs, and similar to other types of deep neural networks, GNNs are found to be vulnerable to unnoticeable perturbations on both graph structure and node features. Many adversarial attacks have been proposed to disclose the fragility of GNNs under different perturbation strategies to create adversarial examples. However, vulnerability of GNNs to successful backdoor attacks was only shown recently. In this paper, we disclose the TRAP attack, a Transferable GRAPh backdoor attack. The core attack principle is to poison the training dataset with perturbation-based triggers that can lead to an effective and transferable backdoor attack. The perturbation trigger for a graph is generated by performing the perturbation actions on the graph structure via a gradient based score matrix from a surrogate model. Compared with prior works, TRAP attack is different in several ways: i) it exploits a surrogate Graph Convolutional Network (GCN) model to generate perturbation triggers for a blackbox based backdoor attack; ii) it generates sample-specific perturbation triggers which do not have a fixed pattern; and iii) the attack transfers, for the first time in the context of GNNs, to different GNN models when trained with the forged poisoned training dataset. Through extensive evaluations on four real-world datasets, we demonstrate the effectiveness of the TRAP attack to build transferable backdoors in four different popular GNNs using four real-world datasets.
Node classification is of great importance among various graph mining tasks. In practice, real-world graphs generally follow the long-tail distribution, where a large number of classes only consist of limited labeled nodes. Although Graph Neural Networks (GNNs) have achieved significant improvements in node classification, their performance decreases substantially in such a few-shot scenario. The main reason can be attributed to the vast generalization gap between meta-training and meta-test due to the task variance caused by different node/class distributions in meta-tasks (i.e., node-level and class-level variance). Therefore, to effectively alleviate the impact of task variance, we propose a task-adaptive node classification framework under the few-shot learning setting. Specifically, we first accumulate meta-knowledge across classes with abundant labeled nodes. Then we transfer such knowledge to the classes with limited labeled nodes via our proposed task-adaptive modules. In particular, to accommodate the different node/class distributions among meta-tasks, we propose three essential modules to perform \emph{node-level}, \emph{class-level}, and \emph{task-level} adaptations in each meta-task, respectively. In this way, our framework can conduct adaptations to different meta-tasks and thus advance the model generalization performance on meta-test tasks. Extensive experiments on four prevalent node classification datasets demonstrate the superiority of our framework over the state-of-the-art baselines. Our code is provided at https://github.com/SongW-SW/TENT.
Despite the success of the Sylvester equation empowered methods on various graph mining applications, such as semi-supervised label learning and network alignment, there also exists several limitations. The Sylvester equation's inability of modeling non-linear relations and the inflexibility of tuning towards different tasks restrict its performance. In this paper, we propose an end-to-end neural framework, SYMGNN, which consists of a multi-network neural aggregation module and a prior multi-network association incorporation learning module. The proposed framework inherits the key ideas of the Sylvester equation, and meanwhile generalizes it to overcome aforementioned limitations. Empirical evaluations on real-world datasets show that the instantiations of SYMGNN overall outperform the baselines in geometric matrix completion task, and its low-rank instantiation could further reduce the memory consumption by 16.98\% on average.
We introduce Hyperbard, a dataset of diverse relational data representations derived from Shakespeare's plays. Our representations range from simple graphs capturing character co-occurrence in single scenes to hypergraphs encoding complex communication settings and character contributions as hyperedges with edge-specific node weights. By making multiple intuitive representations readily available for experimentation, we facilitate rigorous representation robustness checks in graph learning, graph mining, and network analysis, highlighting the advantages and drawbacks of specific representations. Leveraging the data released in Hyperbard, we demonstrate that many solutions to popular graph mining problems are highly dependent on the representation choice, thus calling current graph curation practices into question. As an homage to our data source, and asserting that science can also be art, we present all our points in the form of a play.
The graph Transformer emerges as a new architecture and has shown superior performance on various graph mining tasks. In this work, we observe that existing graph Transformers treat nodes as independent tokens and construct a single long sequence composed of all node tokens so as to train the Transformer model, causing it hard to scale to large graphs due to the quadratic complexity on the number of nodes for the self-attention computation. To this end, we propose a Neighborhood Aggregation Graph Transformer (NAGphormer) that treats each node as a sequence containing a series of tokens constructed by our proposed Hop2Token module. For each node, Hop2Token aggregates the neighborhood features from different hops into different representations and thereby produces a sequence of token vectors as one input. In this way, NAGphormer could be trained in a mini-batch manner and thus could scale to large graphs. Moreover, we mathematically show that as compared to a category of advanced Graph Neural Networks (GNNs), the decoupled Graph Convolutional Network, NAGphormer could learn more informative node representations from the multi-hop neighborhoods. Extensive experiments on benchmark datasets from small to large are conducted to demonstrate that NAGphormer consistently outperforms existing graph Transformers and mainstream GNNs. Code is available at https://github.com/JHL-HUST/NAGphormer.