Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding additional layers -- which in turn leads to over-smoothing and increased time and space complexity. Further, the complex dependencies between nodes make mini-batching challenging, limiting their applicability to large graphs. We propose a Scalable Multi-resolution Graph Representation Learning (SMGRL) framework that enables us to learn multi-resolution node embeddings efficiently. Our framework is model-agnostic and can be applied to any existing GCN model. We dramatically reduce training costs by training only on a reduced-dimension coarsening of the original graph, then exploit self-similarity to apply the resulting algorithm at multiple resolutions. The resulting multi-resolution embeddings can be aggregated to yield high-quality node embeddings that capture both long- and short-range dependencies. Our experiments show that this leads to improved classification accuracy, without incurring high computational costs.
We propose a novel positional encoding for learning graph on Transformer architecture. Existing approaches either linearize a graph to encode absolute position in the sequence of nodes, or encode relative position with another node using bias terms. The former loses preciseness of relative position from linearization, while the latter loses a tight integration of node-edge and node-topology interaction. To overcome the weakness of the previous approaches, our method encodes a graph without linearization and considers both node-topology and node-edge interaction. We name our method Graph Relative Positional Encoding dedicated to graph representation learning. Experiments conducted on various graph datasets show that the proposed method outperforms previous approaches significantly. Our code is publicly available at https://github.com/lenscloth/GRPE.
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and can be a serious bottleneck for the learning pipeline. Inspired by recent success in neural algorithmic reasoning, we propose a novel graph neural network to estimate extended persistence diagrams (EPDs) on graphs efficiently. Our model is built on algorithmic insights, and benefits from better supervision and closer alignment with the EPD computation algorithm. We validate our method with convincing empirical results on approximating EPDs and downstream graph representation learning tasks. Our method is also efficient; on large and dense graphs, we accelerate the computation by nearly 100 times.
Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques with a graph representation learning substrate based on the versatile Random Dot Product Graph (RDPG) model. We consider efficient, online updates of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal RDPG. This reference distribution is inferred via spectral embeddings of the first few graphs in the sequence. We characterize the distribution of this running statistic to select thresholds that guarantee error-rate control, and under simplifying approximations we offer insights on the algorithm's detection resolution and delay. The end result is a lightweight online CPD algorithm, that is also explainable by virtue of the well-appreciated interpretability of RDPG embeddings. This is in stark contrast with most existing graph CPD approaches, which either rely on extensive computation, or they store and process the entire observed time series. An apparent limitation of the RDPG model is its suitability for undirected and unweighted graphs only, a gap we aim to close here to broaden the scope of the CPD framework. Unlike previous proposals, our non-parametric RDPG model for weighted graphs does not require a priori specification of the weights' distribution to perform inference and estimation. This network modeling contribution is of independent interest beyond CPD. We offer an open-source implementation of the novel online CPD algorithm for weighted and direct graphs, whose effectiveness and efficiency are demonstrated via (reproducible) synthetic and real network data experiments.
The recent works proposing transformer-based models for graphs have proven the inadequacy of Vanilla Transformer for graph representation learning. To understand this inadequacy, there is a need to investigate if spectral analysis of the transformer will reveal insights into its expressive power. Similar studies already established that spectral analysis of Graph neural networks (GNNs) provides extra perspectives on their expressiveness. In this work, we systematically study and establish the link between the spatial and spectral domain in the realm of the transformer. We further provide a theoretical analysis and prove that the spatial attention mechanism in the transformer cannot effectively capture the desired frequency response, thus, inherently limiting its expressiveness in spectral space. Therefore, we propose FeTA, a framework that aims to perform attention over the entire graph spectrum (i.e., actual frequency components of the graphs) analogous to the attention in spatial space. Empirical results suggest that FeTA provides homogeneous performance gain against vanilla transformer across all tasks on standard benchmarks and can easily be extended to GNN-based models with low-pass characteristics (e.g., GAT).
Graph representation learning has demonstrated improved performance in tasks such as link prediction and node classification across a range of domains. Research has shown that many natural graphs can be organized in hierarchical communities, leading to approaches that use these communities to improve the quality of node representations. However, these approaches do not take advantage of the learned representations to also improve the quality of the discovered communities and establish an iterative and joint optimization of representation learning and community discovery. In this work, we present Mazi, an algorithm that jointly learns the hierarchical community structure and the node representations of the graph in an unsupervised fashion. To account for the structure in the node representations, Mazi generates node representations at each level of the hierarchy, and utilizes them to influence the node representations of the original graph. Further, the communities at each level are discovered by simultaneously maximizing the modularity metric and minimizing the distance between the representations of a node and its community. Using multi-label node classification and link prediction tasks, we evaluate our method on a variety of synthetic and real-world graphs and demonstrate that Mazi outperforms other hierarchical and non-hierarchical methods.
Recent studies have revealed that GNNs are vulnerable to adversarial attacks. Most existing robust graph learning methods measure model robustness based on label information, rendering them infeasible when label information is not available. A straightforward direction is to employ the widely used Infomax technique from typical Unsupervised Graph Representation Learning (UGRL) to learn robust unsupervised representations. Nonetheless, directly transplanting the Infomax technique from typical UGRL to robust UGRL may involve a biased assumption. In light of the limitation of Infomax, we propose a novel unbiased robust UGRL method called Robust Graph Information Bottleneck (RGIB), which is grounded in the Information Bottleneck (IB) principle. Our RGIB attempts to learn robust node representations against adversarial perturbations by preserving the original information in the benign graph while eliminating the adversarial information in the adversarial graph. There are mainly two challenges to optimize RGIB: 1) high complexity of adversarial attack to perturb node features and graph structure jointly in the training procedure; 2) mutual information estimation upon adversarially attacked graphs. To tackle these problems, we further propose an efficient adversarial training strategy with only feature perturbations and an effective mutual information estimator with subgraph-level summary. Moreover, we theoretically establish a connection between our proposed RGIB and the robustness of downstream classifiers, revealing that RGIB can provide a lower bound on the adversarial risk of downstream classifiers. Extensive experiments over several benchmarks and downstream tasks demonstrate the effectiveness and superiority of our proposed method.
Recently, hyperbolic space has risen as a promising alternative for semi-supervised graph representation learning. Many efforts have been made to design hyperbolic versions of neural network operations. However, the inspiring geometric properties of this unique geometry have not been fully explored yet. The potency of graph models powered by the hyperbolic space is still largely underestimated. Besides, the rich information carried by abundant unlabelled samples is also not well utilized. Inspired by the recently active and emerging self-supervised learning, in this study, we attempt to enhance the representation power of hyperbolic graph models by drawing upon the advantages of contrastive learning. More specifically, we put forward a novel Hyperbolic Graph Contrastive Learning (HGCL) framework which learns node representations through multiple hyperbolic spaces to implicitly capture the hierarchical structure shared between different views. Then, we design a hyperbolic position consistency (HPC) constraint based on hyperbolic distance and the homophily assumption to make contrastive learning fit into hyperbolic space. Experimental results on multiple real-world datasets demonstrate the superiority of the proposed HGCL as it consistently outperforms competing methods by considerable margins for the node classification task.
Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a low-dimensional vector representation (the embedding) for each node. Despite the widespread use of these embeddings for a variety of downstream transductive machine learning tasks, there is little principled analysis of the effectiveness of this approach for common tasks. In this work, we provide an empirical and theoretical analysis for the performance of a class of embeddings on the common task of pairwise community labeling. This is a binary variant of the classic community detection problem, which seeks to build a classifier to determine whether a pair of vertices participate in a community. In line with our goal of foundational understanding, we focus on a popular class of unsupervised embedding techniques that learn low rank factorizations of a vertex proximity matrix (this class includes methods like GraRep, DeepWalk, node2vec, NetMF). We perform detailed empirical analysis for community labeling over a variety of real and synthetic graphs with ground truth. In all cases we studied, the models trained from embedding features perform poorly on community labeling. In constrast, a simple logistic model with classic graph structural features handily outperforms the embedding models. For a more principled understanding, we provide a theoretical analysis for the (in)effectiveness of these embeddings in capturing the community structure. We formally prove that popular low-dimensional factorization methods either cannot produce community structure, or can only produce ``unstable" communities. These communities are inherently unstable under small perturbations.
Because of its wide application, critical nodes identification has become an important research topic at the micro level of network science. Influence maximization is one of the main problems in critical nodes mining and is usually handled with heuristics. In this paper, a deep graph learning framework IMGNN is proposed and the corresponding training sample generation scheme is designed. The framework takes centralities of nodes in a network as input and the probability that nodes in the optimal initial spreaders as output. By training on a large number of small synthetic networks, IMGNN is more efficient than human-based heuristics in minimizing the size of initial spreaders under the fixed infection scale. The experimental results on one synthetic and five real networks show that, compared with traditional non-iterative node ranking algorithms, IMGNN has the smallest proportion of initial spreaders under different infection probabilities when the final infection scale is fixed. And the reordered version of IMGNN outperforms all the latest critical nodes mining algorithms.
Graph contrastive learning is the state-of-the-art unsupervised graph representation learning framework and has shown comparable performance with supervised approaches. However, evaluating whether the graph contrastive learning is robust to adversarial attacks is still an open problem because most existing graph adversarial attacks are supervised models, which means they heavily rely on labels and can only be used to evaluate the graph contrastive learning in a specific scenario. For unsupervised graph representation methods such as graph contrastive learning, it is difficult to acquire labels in real-world scenarios, making traditional supervised graph attack methods difficult to be applied to test their robustness. In this paper, we propose a novel unsupervised gradient-based adversarial attack that does not rely on labels for graph contrastive learning. We compute the gradients of the adjacency matrices of the two views and flip the edges with gradient ascent to maximize the contrastive loss. In this way, we can fully use multiple views generated by the graph contrastive learning models and pick the most informative edges without knowing their labels, and therefore can promisingly support our model adapted to more kinds of downstream tasks. Extensive experiments show that our attack outperforms unsupervised baseline attacks and has comparable performance with supervised attacks in multiple downstream tasks including node classification and link prediction. We further show that our attack can be transferred to other graph representation models as well.
Unsupervised graph representation learning has emerged as a powerful tool to address real-world problems and achieves huge success in the graph learning domain. Graph contrastive learning is one of the unsupervised graph representation learning methods, which recently attracts attention from researchers and has achieved state-of-the-art performances on various tasks. The key to the success of graph contrastive learning is to construct proper contrasting pairs to acquire the underlying structural semantics of the graph. However, this key part is not fully explored currently, most of the ways generating contrasting pairs focus on augmenting or perturbating graph structures to obtain different views of the input graph. But such strategies could degrade the performances via adding noise into the graph, which may narrow down the field of the applications of graph contrastive learning. In this paper, we propose a novel graph contrastive learning method, namely \textbf{D}ual \textbf{S}pace \textbf{G}raph \textbf{C}ontrastive (DSGC) Learning, to conduct graph contrastive learning among views generated in different spaces including the hyperbolic space and the Euclidean space. Since both spaces have their own advantages to represent graph data in the embedding spaces, we hope to utilize graph contrastive learning to bridge the spaces and leverage advantages from both sides. The comparison experiment results show that DSGC achieves competitive or better performances among all the datasets. In addition, we conduct extensive experiments to analyze the impact of different graph encoders on DSGC, giving insights about how to better leverage the advantages of contrastive learning between different spaces.
The objective of image manipulation detection is to identify and locate the manipulated regions in the images. Recent approaches mostly adopt the sophisticated Convolutional Neural Networks (CNNs) to capture the tampering artifacts left in the images to locate the manipulated regions. However, these approaches ignore the feature correlations, i.e., feature inconsistencies, between manipulated regions and non-manipulated regions, leading to inferior detection performance. To address this issue, we propose a hierarchical Graph Convolutional Network (HGCN-Net), which consists of two parallel branches: the backbone network branch and the hierarchical graph representation learning (HGRL) branch for image manipulation detection. Specifically, the feature maps of a given image are extracted by the backbone network branch, and then the feature correlations within the feature maps are modeled as a set of fully-connected graphs for learning the hierarchical graph representation by the HGRL branch. The learned hierarchical graph representation can sufficiently capture the feature correlations across different scales, and thus it provides high discriminability for distinguishing manipulated and non-manipulated regions. Extensive experiments on four public datasets demonstrate that the proposed HGCN-Net not only provides promising detection accuracy, but also achieves strong robustness under a variety of common image attacks in the task of image manipulation detection, compared to the state-of-the-arts.
We propose a decentralised "local2global"' approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping subgraphs (or "patches") and training local representations for each patch independently. In a second step, we combine the local representations into a globally consistent representation by estimating the set of rigid motions that best align the local representations using information from the patch overlaps, via group synchronization. A key distinguishing feature of local2global relative to existing work is that patches are trained independently without the need for the often costly parameter synchronization during distributed training. This allows local2global to scale to large-scale industrial applications, where the input graph may not even fit into memory and may be stored in a distributed manner. We apply local2global on data sets of different sizes and show that our approach achieves a good trade-off between scale and accuracy on edge reconstruction and semi-supervised classification. We also consider the downstream task of anomaly detection and show how one can use local2global to highlight anomalies in cybersecurity networks.
Finding low dimensional representation of data from long-timescale trajectories of biomolecular processes such as protein-folding or ligand-receptor binding is of fundamental importance and kinetic models such as Markov modeling have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and linear dynamical model in an end-to-end manner. VAMPNet is based on variational approach to Markov processes (VAMP) and relies on neural networks to learn the coarse-grained dynamics. In this contribution, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint which is used in the VAMPNet to generate a coarse-grained representation. This type of molecular representation results in a higher resolution and more interpretable Markov model than the standard VAMPNet enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.
Graph Neural Networks (GNNs) have proven to excel in predictive modeling tasks where the underlying data is a graph. However, as GNNs are extensively used in human-centered applications, the issue of fairness has arisen. While edge deletion is a common method used to promote fairness in GNNs, it fails to consider when data is inherently missing fair connections. In this work we consider the unexplored method of edge addition, accompanied by deletion, to promote fairness. We propose two model-agnostic algorithms to perform edge editing: a brute force approach and a continuous approximation approach, FairEdit. FairEdit performs efficient edge editing by leveraging gradient information of a fairness loss to find edges that improve fairness. We find that FairEdit outperforms standard training for many data sets and GNN methods, while performing comparably to many state-of-the-art methods, demonstrating FairEdit's ability to improve fairness across many domains and models.
Graph Neural Networks (GNNs) have become the state-of-the-art method for many applications on graph structured data. GNNs are a model for graph representation learning, which aims at learning to generate low dimensional node embeddings that encapsulate structural and feature-related information. GNNs are usually trained in an end-to-end fashion, leading to highly specialized node embeddings. While this approach achieves great results in the single-task setting, the generation of node embeddings that can be used to perform multiple tasks (with performance comparable to single-task models) is still an open problem. We propose the use of meta-learning to allow the training of a GNN model capable of producing multi-task node embeddings. In particular, we exploit the properties of optimization-based meta-learning to learn GNNs that can produce general node representations by learning parameters that can quickly (i.e. with a few steps of gradient descent) adapt to multiple tasks. Our experiments show that the embeddings produced by a model trained with our purposely designed meta-learning procedure can be used to perform multiple tasks with comparable or, surprisingly, even higher performance than both single-task and multi-task end-to-end models.
Motivated by potential financial gain, companies may hire fraudster groups to write fake reviews to either demote competitors or promote their own businesses. Such groups are considerably more successful in misleading customers, as people are more likely to be influenced by the opinion of a large group. To detect such groups, a common model is to represent fraudster groups' static networks, consequently overlooking the longitudinal behavior of a reviewer thus the dynamics of co-review relations among reviewers in a group. Hence, these approaches are incapable of excluding outlier reviewers, which are fraudsters intentionally camouflaging themselves in a group and genuine reviewers happen to co-review in fraudster groups. To address this issue, in this work, we propose to first capitalize on the effectiveness of the HIN-RNN in both reviewers' representation learning while capturing the collaboration between reviewers, we first utilize the HIN-RNN to model the co-review relations of reviewers in a group in a fixed time window of 28 days. We refer to this as spatial relation learning representation to signify the generalisability of this work to other networked scenarios. Then we use an RNN on the spatial relations to predict the spatio-temporal relations of reviewers in the group. In the third step, a Graph Convolution Network (GCN) refines the reviewers' vector representations using these predicted relations. These refined representations are then used to remove outlier reviewers. The average of the remaining reviewers' representation is then fed to a simple fully connected layer to predict if the group is a fraudster group or not. Exhaustive experiments of the proposed approach showed a 5% (4%), 12% (5%), 12% (5%) improvement over three of the most recent approaches on precision, recall, and F1-value over the Yelp (Amazon) dataset, respectively.
Biphasic face photo-sketch synthesis has significant practical value in wide-ranging fields such as digital entertainment and law enforcement. Previous approaches directly generate the photo-sketch in a global view, they always suffer from the low quality of sketches and complex photo variations, leading to unnatural and low-fidelity results. In this paper, we propose a novel Semantic-Driven Generative Adversarial Network to address the above issues, cooperating with Graph Representation Learning. Considering that human faces have distinct spatial structures, we first inject class-wise semantic layouts into the generator to provide style-based spatial information for synthesized face photos and sketches. Additionally, to enhance the authenticity of details in generated faces, we construct two types of representational graphs via semantic parsing maps upon input faces, dubbed the IntrA-class Semantic Graph (IASG) and the InteR-class Structure Graph (IRSG). Specifically, the IASG effectively models the intra-class semantic correlations of each facial semantic component, thus producing realistic facial details. To preserve the generated faces being more structure-coordinated, the IRSG models inter-class structural relations among every facial component by graph representation learning. To further enhance the perceptual quality of synthesized images, we present a biphasic interactive cycle training strategy by fully taking advantage of the multi-level feature consistency between the photo and sketch. Extensive experiments demonstrate that our method outperforms the state-of-the-art competitors on the CUFS and CUFSF datasets.
Dynamic graph neural networks have been widely used in modeling and representation learning of graph structure data. Current dynamic representation learning focuses on either discrete learning which results in temporal information loss or continuous learning that involves heavy computation. In this work, we proposed a novel dynamic graph neural network, Sparse-Dyn. It adaptively encodes temporal information into a sequence of patches with an equal amount of temporal-topological structure. Therefore, while avoiding the use of snapshots which causes information loss, it also achieves a finer time granularity, which is close to what continuous networks could provide. In addition, we also designed a lightweight module, Sparse Temporal Transformer, to compute node representations through both structural neighborhoods and temporal dynamics. Since the fully-connected attention conjunction is simplified, the computation cost is far lower than the current state-of-the-arts. Link prediction experiments are conducted on both continuous and discrete graph datasets. Through comparing with several state-of-the-art graph embedding baselines, the experimental results demonstrate that Sparse-Dyn has a faster inference speed while having competitive performance.