The Euclidean Steiner tree problem seeks the min-cost network to connect a collection of target locations, and it underlies many applications of wireless networks. In this paper, we present a study on solving the Euclidean Steiner tree problem using reinforcement learning enhanced by graph representation learning. Different from the commonly studied connectivity problems like travelling salesman problem or vehicle routing problem where the search space is finite, the Euclidean Steiner tree problem requires to search over the entire Euclidean space, thereby making the existing methods not applicable. In this paper, we design discretization methods by leveraging the unique characteristics of the Steiner tree, and propose new training schemes for handling the dynamic Steiner points emerging during the incremental construction. Our design is examined through a sanity check using experiments on a collection of datasets, with encouraging results demonstrating the utility of our method as an alternative to classic combinatorial methods.
Current graph representation learning techniques use Graph Neural Networks (GNNs) to extract features from dataset embeddings. In this work, we examine the quality of these embeddings and assess how changing them can affect the accuracy of GNNs. We explore different embedding extraction techniques for both images and texts; and find that the performance of different GNN architectures is dependent on the embedding style used. We see a prevalence of bag of words (BoW) embeddings and text classification tasks in available graph datasets. Given the impact embeddings has on GNN performance. this leads to a phenomenon that GNNs being optimised for BoW vectors.
Deep learning-based graph generation approaches have remarkable capacities for graph data modeling, allowing them to solve a wide range of real-world problems. Making these methods able to consider different conditions during the generation procedure even increases their effectiveness by empowering them to generate new graph samples that meet the desired criteria. This paper presents a conditional deep graph generation method called SCGG that considers a particular type of structural conditions. Specifically, our proposed SCGG model takes an initial subgraph and autoregressively generates new nodes and their corresponding edges on top of the given conditioning substructure. The architecture of SCGG consists of a graph representation learning network and an autoregressive generative model, which is trained end-to-end. Using this model, we can address graph completion, a rampant and inherently difficult problem of recovering missing nodes and their associated edges of partially observed graphs. Experimental results on both synthetic and real-world datasets demonstrate the superiority of our method compared with state-of-the-art baselines.
Since their introduction, graph attention networks achieved outstanding results in graph representation learning tasks. However, these networks consider only pairwise relationships among nodes and then they are not able to fully exploit higher-order interactions present in many real world data-sets. In this paper, we introduce Cell Attention Networks (CANs), a neural architecture operating on data defined over the vertices of a graph, representing the graph as the 1-skeleton of a cell complex introduced to capture higher order interactions. In particular, we exploit the lower and upper neighborhoods, as encoded in the cell complex, to design two independent masked self-attention mechanisms, thus generalizing the conventional graph attention strategy. The approach used in CANs is hierarchical and it incorporates the following steps: i) a lifting algorithm that learns {\it edge features} from {\it node features}; ii) a cell attention mechanism to find the optimal combination of edge features over both lower and upper neighbors; iii) a hierarchical {\it edge pooling} mechanism to extract a compact meaningful set of features. The experimental results show that CAN is a low complexity strategy that compares favorably with state of the art results on graph-based learning tasks.
Recent research has shown that criminal networks have complex organizational structures, but whether this can be used to predict static and dynamic properties of criminal networks remains little explored. Here, by combining graph representation learning and machine learning methods, we show that structural properties of political corruption, police intelligence, and money laundering networks can be used to recover missing criminal partnerships, distinguish among different types of criminal and legal associations, as well as predict the total amount of money exchanged among criminal agents, all with outstanding accuracy. We also show that our approach can anticipate future criminal associations during the dynamic growth of corruption networks with significant accuracy. Thus, similar to evidence found at crime scenes, we conclude that structural patterns of criminal networks carry crucial information about illegal activities, which allows machine learning methods to predict missing information and even anticipate future criminal behavior.
Graph Neural Networks (GNNs) are widely used for graph representation learning. Despite its prevalence, GNN suffers from two drawbacks in the graph classification task, the neglect of graph-level relationships, and the generalization issue. Each graph is treated separately in GNN message passing/graph pooling, and existing methods to address overfitting operate on each individual graph. This makes the graph representations learnt less effective in the downstream classification. In this paper, we propose a Class-Aware Representation rEfinement (CARE) framework for the task of graph classification. CARE computes simple yet powerful class representations and injects them to steer the learning of graph representations towards better class separability. CARE is a plug-and-play framework that is highly flexible and able to incorporate arbitrary GNN backbones without significantly increasing the computational cost. We also theoretically prove that CARE has a better generalization upper bound than its GNN backbone through Vapnik-Chervonenkis (VC) dimension analysis. Our extensive experiments with 11 well-known GNN backbones on 9 benchmark datasets validate the superiority and effectiveness of CARE over its GNN counterparts.
Though graph representation learning (GRL) has made significant progress, it is still a challenge to extract and embed the rich topological structure and feature information in an adequate way. Most existing methods focus on local structure and fail to fully incorporate the global topological structure. To this end, we propose a novel Structure-Preserving Graph Representation Learning (SPGRL) method, to fully capture the structure information of graphs. Specifically, to reduce the uncertainty and misinformation of the original graph, we construct a feature graph as a complementary view via k-Nearest Neighbor method. The feature graph can be used to contrast at node-level to capture the local relation. Besides, we retain the global topological structure information by maximizing the mutual information (MI) of the whole graph and feature embeddings, which is theoretically reduced to exchanging the feature embeddings of the feature and the original graphs to reconstruct themselves. Extensive experiments show that our method has quite superior performance on semi-supervised node classification task and excellent robustness under noise perturbation on graph structure or node features.
Representation learning on temporal graphs has drawn considerable research attention owing to its fundamental importance in a wide spectrum of real-world applications. Though a number of studies succeed in obtaining time-dependent representations, it still faces significant challenges. On the one hand, most of the existing methods restrict the embedding space with a certain curvature. However, the underlying geometry in fact shifts among the positive curvature hyperspherical, zero curvature Euclidean and negative curvature hyperbolic spaces in the evolvement over time. On the other hand, these methods usually require abundant labels to learn temporal representations, and thereby notably limit their wide use in the unlabeled graphs of the real applications. To bridge this gap, we make the first attempt to study the problem of self-supervised temporal graph representation learning in the general Riemannian space, supporting the time-varying curvature to shift among hyperspherical, Euclidean and hyperbolic spaces. In this paper, we present a novel self-supervised Riemannian graph neural network (SelfRGNN). Specifically, we design a curvature-varying Riemannian GNN with a theoretically grounded time encoding, and formulate a functional curvature over time to model the evolvement shifting among the positive, zero and negative curvature spaces. To enable the self-supervised learning, we propose a novel reweighting self-contrastive approach, exploring the Riemannian space itself without augmentation, and propose an edge-based self-supervised curvature learning with the Ricci curvature. Extensive experiments show the superiority of SelfRGNN, and moreover, the case study shows the time-varying curvature of temporal graph in reality.
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond the work related to static graphs in terms of their generative modeling and representation learning. In this survey, we comprehensively review the neural time dependent graph representation learning and generative modeling approaches proposed in recent times for handling temporal graphs. Finally, we identify the weaknesses of existing approaches and discuss the research proposal of our recently published paper TIGGER[24].
Over the past few years, graph representation learning (GRL) has been a powerful strategy for analyzing graph-structured data. Recently, GRL methods have shown promising results by adopting self-supervised learning methods developed for learning representations of images. Despite their success, existing GRL methods tend to overlook an inherent distinction between images and graphs, i.e., images are assumed to be independently and identically distributed, whereas graphs exhibit relational information among data instances, i.e., nodes. To fully benefit from the relational information inherent in the graph-structured data, we propose a novel GRL method, called RGRL, that learns from the relational information generated from the graph itself. RGRL learns node representations such that the relationship among nodes is invariant to augmentations, i.e., augmentation-invariant relationship, which allows the node representations to vary as long as the relationship among the nodes is preserved. By considering the relationship among nodes in both global and local perspectives, RGRL overcomes limitations of previous contrastive and non-contrastive methods, and achieves the best of both worlds. Extensive experiments on fourteen benchmark datasets over various downstream tasks demonstrate the superiority of RGRL over state-of-the-art baselines. The source code for RGRL is available at https://github.com/Namkyeong/RGRL.
Recent years have seen a surge in research on dynamic graph representation learning, which aims to model temporal graphs that are dynamic and evolving constantly over time. However, current work typically models graph dynamics with recurrent neural networks (RNNs), making them suffer seriously from computation and memory overheads on large temporal graphs. So far, scalability of dynamic graph representation learning on large temporal graphs remains one of the major challenges. In this paper, we present a scalable framework, namely SpikeNet, to efficiently capture the temporal and structural patterns of temporal graphs. We explore a new direction in that we can capture the evolving dynamics of temporal graphs with spiking neural networks (SNNs) instead of RNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics as spike trains of neuron populations and enable spike-based propagation in an efficient way. Experiments on three large real-world temporal graph datasets demonstrate that SpikeNet outperforms strong baselines on the temporal node classification task with lower computational costs. Particularly, SpikeNet generalizes to a large temporal graph (2.7M nodes and 13.9M edges) with significantly fewer parameters and computation overheads.Our code is publicly available at \url{https://github.com/EdisonLeeeee/SpikeNet}.
Research in machine learning for autism spectrum disorder (ASD) classification bears the promise to improve clinical diagnoses. However, recent studies in clinical imaging have shown the limited generalization of biomarkers across and beyond benchmark datasets. Despite increasing model complexity and sample size in neuroimaging, the classification performance of ASD remains far away from clinical application. This raises the question of how we can overcome these barriers to develop early biomarkers for ASD. One approach might be to rethink how we operationalize the theoretical basis of this disease in machine learning models. Here we introduced unsupervised graph representations that explicitly map the neural mechanisms of a core aspect of ASD, deficits in dyadic social interaction, as assessed by dual brain recordings, termed hyperscanning, and evaluated their predictive performance. The proposed method differs from existing approaches in that it is more suitable to capture social interaction deficits on a neural level and is applicable to young children and infants. First results from functional near-infrared spectroscopy data indicate potential predictive capacities of a task-agnostic, interpretable graph representation. This first effort to leverage interaction-related deficits on neural level to classify ASD may stimulate new approaches and methods to enhance existing models to achieve developmental ASD biomarkers in the future.
Person-job fit is the core technique of online recruitment platforms, which can improve the efficiency of recruitment by accurately matching the job positions with the job seekers. Existing works mainly focus on modeling the unidirectional process or overall matching. However, recruitment is a two-way selection process, which means that both candidate and employer involved in the interaction should meet the expectation of each other, instead of unilateral satisfaction. In this paper, we propose a dual-perspective graph representation learning approach to model directed interactions between candidates and jobs. To model the two-way selection preference from the dual-perspective of job seekers and employers, we incorporate two different nodes for each candidate (or job) and characterize both successful matching and failed matching via a unified dual-perspective interaction graph. To learn dual-perspective node representations effectively, we design an effective optimization algorithm, which involves a quadruple-based loss and a dual-perspective contrastive learning loss. Extensive experiments on three large real-world recruitment datasets have shown the effectiveness of our approach.
The prevailing graph neural network models have achieved significant progress in graph representation learning. However, in this paper, we uncover an ever-overlooked phenomenon: the pre-trained graph representation learning model tested with full graphs underperforms the model tested with well-pruned graphs. This observation reveals that there exist confounders in graphs, which may interfere with the model learning semantic information, and current graph representation learning methods have not eliminated their influence. To tackle this issue, we propose Robust Causal Graph Representation Learning (RCGRL) to learn robust graph representations against confounding effects. RCGRL introduces an active approach to generate instrumental variables under unconditional moment restrictions, which empowers the graph representation learning model to eliminate confounders, thereby capturing discriminative information that is causally related to downstream predictions. We offer theorems and proofs to guarantee the theoretical effectiveness of the proposed approach. Empirically, we conduct extensive experiments on a synthetic dataset and multiple benchmark datasets. The results demonstrate that compared with state-of-the-art methods, RCGRL achieves better prediction performance and generalization ability.
Circular trading is a form of tax evasion in Goods and Services Tax where a group of fraudulent taxpayers (traders) aims to mask illegal transactions by superimposing several fictitious transactions (where no value is added to the goods or service) among themselves in a short period. Due to the vast database of taxpayers, it is infeasible for authorities to manually identify groups of circular traders and the illegitimate transactions they are involved in. This work uses big data analytics and graph representation learning techniques to propose a framework to identify communities of circular traders and isolate the illegitimate transactions in the respective communities. Our approach is tested on real-life data provided by the Department of Commercial Taxes, Government of Telangana, India, where we uncovered several communities of circular traders.
Paper recommendation with user-generated keyword is to suggest papers that simultaneously meet user's interests and are relevant to the input keyword. This is a recommendation task with two queries, a.k.a. user ID and keyword. However, existing methods focus on recommendation according to one query, a.k.a. user ID, and are not applicable to solving this problem. In this paper, we propose a novel click-through rate (CTR) prediction model with heterogeneous graph neural network, called AMinerGNN, to recommend papers with two queries. Specifically, AMinerGNN constructs a heterogeneous graph to project user, paper, and keyword into the same embedding space by graph representation learning. To process two queries, a novel query attentive fusion layer is designed to recognize their importances dynamically and then fuse them as one query to build a unified and end-to-end recommender system. Experimental results on our proposed dataset and online A/B tests prove the superiority of AMinerGNN.
Graph Neural Networks (GNNs) have shown expressive performance on graph representation learning by aggregating information from neighbors. Recently, some studies have discussed the importance of modeling neighborhood distribution on the graph. However, most existing GNNs aggregate neighbors' features through single statistic (e.g., mean, max, sum), which loses the information related to neighbor's feature distribution and therefore degrades the model performance. In this paper, inspired by the method of moment in statistical theory, we propose to model neighbor's feature distribution with multi-order moments. We design a novel GNN model, namely Mix-Moment Graph Neural Network (MM-GNN), which includes a Multi-order Moment Embedding (MME) module and an Element-wise Attention-based Moment Adaptor module. MM-GNN first calculates the multi-order moments of the neighbors for each node as signatures, and then use an Element-wise Attention-based Moment Adaptor to assign larger weights to important moments for each node and update node representations. We conduct extensive experiments on 15 real-world graphs (including social networks, citation networks and web-page networks etc.) to evaluate our model, and the results demonstrate the superiority of MM-GNN over existing state-of-the-art models.
Contrastive learning is an effective unsupervised method in graph representation learning, and the key component of contrastive learning lies in the construction of positive and negative samples. Previous methods usually utilize the proximity of nodes in the graph as the principle. Recently, the data-augmentation-based contrastive learning method has advanced to show great power in the visual domain, and some works extended this method from images to graphs. However, unlike the data augmentation on images, the data augmentation on graphs is far less intuitive and much harder to provide high-quality contrastive samples, which leaves much space for improvement. In this work, by introducing an adversarial graph view for data augmentation, we propose a simple but effective method, Adversarial Graph Contrastive Learning (ARIEL), to extract informative contrastive samples within reasonable constraints. We develop a new technique called information regularization for stable training and use subgraph sampling for scalability. We generalize our method from node-level contrastive learning to the graph level by treating each graph instance as a super-node. ARIEL consistently outperforms the current graph contrastive learning methods for both node-level and graph-level classification tasks on real-world datasets. We further demonstrate that ARIEL is more robust in the face of adversarial attacks.
Graph Neural Networks (GNNs) have been successfully applied to many real-world static graphs. However, the success of static graphs has not fully translated to dynamic graphs due to the limitations in model design, evaluation settings, and training strategies. Concretely, existing dynamic GNNs do not incorporate state-of-the-art designs from static GNNs, which limits their performance. Current evaluation settings for dynamic GNNs do not fully reflect the evolving nature of dynamic graphs. Finally, commonly used training methods for dynamic GNNs are not scalable. Here we propose ROLAND, an effective graph representation learning framework for real-world dynamic graphs. At its core, the ROLAND framework can help researchers easily repurpose any static GNN to dynamic graphs. Our insight is to view the node embeddings at different GNN layers as hierarchical node states and then recurrently update them over time. We then introduce a live-update evaluation setting for dynamic graphs that mimics real-world use cases, where GNNs are making predictions and being updated on a rolling basis. Finally, we propose a scalable and efficient training approach for dynamic GNNs via incremental training and meta-learning. We conduct experiments over eight different dynamic graph datasets on future link prediction tasks. Models built using the ROLAND framework achieve on average 62.7% relative mean reciprocal rank (MRR) improvement over state-of-the-art baselines under the standard evaluation settings on three datasets. We find state-of-the-art baselines experience out-of-memory errors for larger datasets, while ROLAND can easily scale to dynamic graphs with 56 million edges. After re-implementing these baselines using the ROLAND training strategy, ROLAND models still achieve on average 15.5% relative MRR improvement over the baselines.
This work considers the task of representation learning on the attributed relational graph (ARG). Both the nodes and edges in an ARG are associated with attributes/features allowing ARGs to encode rich structural information widely observed in real applications. Existing graph neural networks offer limited ability to capture complex interactions within local structural contexts, which hinders them from taking advantage of the expression power of ARGs. We propose Motif Convolution Module (MCM), a new motif-based graph representation learning technique to better utilize local structural information. The ability to handle continuous edge and node features is one of MCM's advantages over existing motif-based models. MCM builds a motif vocabulary in an unsupervised way and deploys a novel motif convolution operation to extract the local structural context of individual nodes, which is then used to learn higher-level node representations via multilayer perceptron and/or message passing in graph neural networks. When compared with other graph learning approaches to classifying synthetic graphs, our approach is substantially better in capturing structural context. We also demonstrate the performance and explainability advantages of our approach by applying it to several molecular benchmarks.