Ziwei Zhang

Zeyang Zhang, Ziwei Zhang, Xin Wang et al. · tsinghua

Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are independent and identically distributed. However, the existing literature fails to solve TSP instances when training and testing data have different distributions. Concretely, we find that different training and testing distribution will result in more difficult TSP instances, i.e., the solution obtained by the model has a large gap from the optimal solution. To tackle this problem, in this work, we study learning-based TSP methods when training and testing data have different distributions using adaptive-hardness, i.e., how difficult a TSP instance can be for a solver. This problem is challenging because it is non-trivial to (1) define hardness measurement quantitatively; (2) efficiently and continuously generate sufficiently hard TSP instances upon model training; (3) fully utilize instances with different levels of hardness to learn a more powerful TSP solver. To solve these challenges, we first propose a principled hardness measurement to quantify the hardness of TSP instances. Then, we propose a hardness-adaptive generator to generate instances with different hardness. We further propose a curriculum learner fully utilizing these instances to train the TSP solver. Experiments show that our hardness-adaptive generator can generate instances ten times harder than the existing methods, and our proposed method achieves significant improvement over state-of-the-art models in terms of the optimality gap.

Yijian Qin, Ziwei Zhang, Xin Wang et al. · tsinghua

Graph neural architecture search (GraphNAS) has recently aroused considerable attention in both academia and industry. However, two key challenges seriously hinder the further research of GraphNAS. First, since there is no consensus for the experimental setting, the empirical results in different research papers are often not comparable and even not reproducible, leading to unfair comparisons. Secondly, GraphNAS often needs extensive computations, which makes it highly inefficient and inaccessible to researchers without access to large-scale computation. To solve these challenges, we propose NAS-Bench-Graph, a tailored benchmark that supports unified, reproducible, and efficient evaluations for GraphNAS. Specifically, we construct a unified, expressive yet compact search space, covering 26,206 unique graph neural network (GNN) architectures and propose a principled evaluation protocol. To avoid unnecessary repetitive training, we have trained and evaluated all of these architectures on nine representative graph datasets, recording detailed metrics including train, validation, and test performance in each epoch, the latency, the number of parameters, etc. Based on our proposed benchmark, the performance of GNN architectures can be directly obtained by a look-up table without any further computation, which enables fair, fully reproducible, and efficient comparisons. To demonstrate its usage, we make in-depth analyses of our proposed NAS-Bench-Graph, revealing several interesting findings for GraphNAS. We also showcase how the benchmark can be easily compatible with GraphNAS open libraries such as AutoGL and NNI. To the best of our knowledge, our work is the first benchmark for graph neural architecture search.

Beini Xie, Heng Chang, Ziwei Zhang et al. · tsinghua

Graph Neural Networks (GNNs) obtain tremendous success in modeling relational data. Still, they are prone to adversarial attacks, which are massive threats to applying GNNs to risk-sensitive domains. Existing defensive methods neither guarantee performance facing new data/tasks or adversarial attacks nor provide insights to understand GNN robustness from an architectural perspective. Neural Architecture Search (NAS) has the potential to solve this problem by automating GNN architecture designs. Nevertheless, current graph NAS approaches lack robust design and are vulnerable to adversarial attacks. To tackle these challenges, we propose a novel Robust Neural Architecture search framework for GNNs (G-RNA). Specifically, we design a robust search space for the message-passing mechanism by adding graph structure mask operations into the search space, which comprises various defensive operation candidates and allows us to search for defensive GNNs. Furthermore, we define a robustness metric to guide the search procedure, which helps to filter robust architectures. In this way, G-RNA helps understand GNN robustness from an architectural perspective and effectively searches for optimal adversarial robust GNNs. Extensive experimental results on benchmark datasets show that G-RNA significantly outperforms manually designed robust GNNs and vanilla graph NAS baselines by 12.1% to 23.4% under adversarial attacks.

Yijian Qin, Xin Wang, Ziwei Zhang et al.

Text-attributed graphs (TAGs) are prevalent on the web and research over TAGs such as citation networks, e-commerce networks and social networks has attracted considerable attention in the web community. Recently, large language models (LLMs) have demonstrated exceptional capabilities across a wide range of tasks. However, the existing works focus on harnessing the potential of LLMs solely relying on prompts to convey graph structure information to LLMs, thus suffering from insufficient understanding of the complex structural relationships within TAGs. To address this problem, in this paper we present the Disentangled Graph-Text Learner (DGTL) model, which is able to enhance the reasoning and predicting capabilities of LLMs for TAGs. Our proposed DGTL model incorporates graph structure information through tailored disentangled graph neural network (GNN) layers, enabling LLMs to capture the intricate relationships hidden in text-attributed graphs from multiple structural factors. Furthermore, DGTL operates with frozen pre-trained LLMs, reducing computational costs and allowing much more flexibility in combining with different LLM models. Experimental evaluations demonstrate the effectiveness of the proposed DGTL model on achieving superior or comparable performance over state-of-the-art baselines. Additionally, we also demonstrate that our DGTL model can offer natural language explanations for predictions, thereby significantly enhancing model interpretability.

Haonan Yuan, Qingyun Sun, Xingcheng Fu et al.

Dynamic graph neural networks (DGNNs) are increasingly pervasive in exploiting spatio-temporal patterns on dynamic graphs. However, existing works fail to generalize under distribution shifts, which are common in real-world scenarios. As the generation of dynamic graphs is heavily influenced by latent environments, investigating their impacts on the out-of-distribution (OOD) generalization is critical. However, it remains unexplored with the following two major challenges: (1) How to properly model and infer the complex environments on dynamic graphs with distribution shifts? (2) How to discover invariant patterns given inferred spatio-temporal environments? To solve these challenges, we propose a novel Environment-Aware dynamic Graph LEarning (EAGLE) framework for OOD generalization by modeling complex coupled environments and exploiting spatio-temporal invariant patterns. Specifically, we first design the environment-aware EA-DGNN to model environments by multi-channel environments disentangling. Then, we propose an environment instantiation mechanism for environment diversification with inferred distributions. Finally, we discriminate spatio-temporal invariant patterns for out-of-distribution prediction by the invariant pattern recognition mechanism and perform fine-grained causal interventions node-wisely with a mixture of instantiated environment samples. Experiments on real-world and synthetic dynamic graph datasets demonstrate the superiority of our method against state-of-the-art baselines under distribution shifts. To the best of our knowledge, we are the first to study OOD generalization on dynamic graphs from the environment learning perspective.

Zeyang Zhang, Xin Wang, Ziwei Zhang et al.

Dynamic graph neural networks (DyGNNs) have demonstrated powerful predictive abilities by exploiting graph structural and temporal dynamics. However, the existing DyGNNs fail to handle distribution shifts, which naturally exist in dynamic graphs, mainly because the patterns exploited by DyGNNs may be variant with respect to labels under distribution shifts. In this paper, we propose Disentangled Intervention-based Dynamic graph Attention networks with Invariance Promotion (I-DIDA) to handle spatio-temporal distribution shifts in dynamic graphs by discovering and utilizing invariant patterns, i.e., structures and features whose predictive abilities are stable across distribution shifts. Specifically, we first propose a disentangled spatio-temporal attention network to capture the variant and invariant patterns. By utilizing the disentangled patterns, we design a spatio-temporal intervention mechanism to create multiple interventional distributions and an environment inference module to infer the latent spatio-temporal environments, and minimize the variance of predictions among these intervened distributions and environments, so that our model can make predictions based on invariant patterns with stable predictive abilities under distribution shifts. Extensive experiments demonstrate the superiority of our method over state-of-the-art baselines under distribution shifts. Our work is the first study of spatio-temporal distribution shifts in dynamic graphs, to the best of our knowledge.

Zihao Guo, Qingyun Sun, Ziwei Zhang et al.

Graph incremental learning (GIL), which continuously updates graph models by sequential knowledge acquisition, has garnered significant interest recently. However, existing GIL approaches focus on task-incremental and class-incremental scenarios within a single domain. Graph domain-incremental learning (Domain-IL), aiming at updating models across multiple graph domains, has become critical with the development of graph foundation models (GFMs), but remains unexplored in the literature. In this paper, we propose Graph Domain-Incremental Learning via Knowledge Dientanglement and Preservation (GraphKeeper), to address catastrophic forgetting in Domain-IL scenario from the perspectives of embedding shifts and decision boundary deviations. Specifically, to prevent embedding shifts and confusion across incremental graph domains, we first propose the domain-specific parameter-efficient fine-tuning together with intra- and inter-domain disentanglement objectives. Consequently, to maintain a stable decision boundary, we introduce deviation-free knowledge preservation to continuously fit incremental domains. Additionally, for graphs with unobservable domains, we perform domain-aware distribution discrimination to obtain precise embeddings. Extensive experiments demonstrate the proposed GraphKeeper achieves state-of-the-art results with 6.5%~16.6% improvement over the runner-up with negligible forgetting. Moreover, we show GraphKeeper can be seamlessly integrated with various representative GFMs, highlighting its broad applicative potential.

Xin Wang, Ziwei Zhang, Haoyang Li et al.

Graph machine learning has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To tackle the challenge, automated graph machine learning, which aims at discovering the best hyper-parameter and neural architecture configuration for different graph tasks/data without manual design, is gaining an increasing number of attentions from the research community. In this paper, we extensively discuss automated graph machine learning approaches, covering hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We briefly overview existing libraries designed for either graph machine learning or automated machine learning respectively, and further in depth introduce AutoGL, our dedicated and the world's first open-source library for automated graph machine learning. Also, we describe a tailored benchmark that supports unified, reproducible, and efficient evaluations. Last but not least, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive discussion of approaches, libraries as well as directions for automated graph machine learning.

Ziwei Zhang, Yijian Qin, Zeyang Zhang et al.

Recent years have witnessed an upsurge in research interests and applications of machine learning on graphs. However, manually designing the optimal machine learning algorithms for different graph datasets and tasks is inflexible, labor-intensive, and requires expert knowledge, limiting its adaptivity and applicability. Automated machine learning (AutoML) on graphs, aiming to automatically design the optimal machine learning algorithm for a given graph dataset and task, has received considerable attention. However, none of the existing libraries can fully support AutoML on graphs. To fill this gap, we present Automated Graph Learning (AutoGL), the first dedicated library for automated machine learning on graphs. AutoGL is open-source, easy to use, and flexible to be extended. Specifically, we propose a three-layer architecture, consisting of backends to interface with devices, a complete automated graph learning pipeline, and supported graph applications. The automated machine learning pipeline further contains five functional modules: auto feature engineering, neural architecture search, hyper-parameter optimization, model training, and auto ensemble, covering the majority of existing AutoML methods on graphs. For each module, we provide numerous state-of-the-art methods and flexible base classes and APIs, which allow easy usage and customization. We further provide experimental results to showcase the usage of our AutoGL library. We also present AutoGL-light, a lightweight version of AutoGL to facilitate customizing pipelines and enriching applications, as well as benchmarks for graph neural architecture search. The codes of AutoGL are publicly available at https://github.com/THUMNLab/AutoGL.

Ziwei Zhang, Xin Wang, Wenwu Zhu

Machine learning on graphs has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To solve this critical challenge, automated machine learning (AutoML) on graphs which combines the strength of graph machine learning and AutoML together, is gaining attention from the research community. Therefore, we comprehensively survey AutoML on graphs in this paper, primarily focusing on hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We further overview libraries related to automated graph machine learning and in-depth discuss AutoGL, the first dedicated open-source library for AutoML on graphs. In the end, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive review of automated machine learning on graphs to the best of our knowledge.

Yang Yao, Xin Wang, Zeyang Zhang et al. · tsinghua

Large language models (LLMs) have achieved great success in many fields, and recent works have studied exploring LLMs for graph discriminative tasks such as node classification. However, the abilities of LLMs for graph generation remain unexplored in the literature. Graph generation requires the LLM to generate graphs with given properties, which has valuable real-world applications such as drug discovery, while tends to be more challenging. In this paper, we propose LLM4GraphGen to explore the ability of LLMs for graph generation with systematical task designs and extensive experiments. Specifically, we propose several tasks tailored with comprehensive experiments to address key questions regarding LLMs' understanding of different graph structure rules, their ability to capture structural type distributions, and their utilization of domain knowledge for property-based graph generation. Our evaluations demonstrate that LLMs, particularly GPT-4, exhibit preliminary abilities in graph generation tasks, including rule-based and distribution-based generation. We also observe that popular prompting methods, such as few-shot and chain-of-thought prompting, do not consistently enhance performance. Besides, LLMs show potential in generating molecules with specific properties. These findings may serve as foundations for designing good LLMs based models for graph generation and provide valuable insights and further research.

Zeyang Zhang, Xin Wang, Ziwei Zhang et al. · tsinghua

The existing graph neural architecture search (GNAS) methods heavily rely on supervised labels during the search process, failing to handle ubiquitous scenarios where supervisions are not available. In this paper, we study the problem of unsupervised graph neural architecture search, which remains unexplored in the literature. The key problem is to discover the latent graph factors that drive the formation of graph data as well as the underlying relations between the factors and the optimal neural architectures. Handling this problem is challenging given that the latent graph factors together with architectures are highly entangled due to the nature of the graph and the complexity of the neural architecture search process. To address the challenge, we propose a novel Disentangled Self-supervised Graph Neural Architecture Search (DSGAS) model, which is able to discover the optimal architectures capturing various latent graph factors in a self-supervised fashion based on unlabeled graph data. Specifically, we first design a disentangled graph super-network capable of incorporating multiple architectures with factor-wise disentanglement, which are optimized simultaneously. Then, we estimate the performance of architectures under different factors by our proposed self-supervised training with joint architecture-graph disentanglement. Finally, we propose a contrastive search with architecture augmentations to discover architectures with factor-specific expertise. Extensive experiments on 11 real-world datasets demonstrate that the proposed model is able to achieve state-of-the-art performance against several baseline methods in an unsupervised manner.

Chuanyue Yu, Kuo Zhao, Yuhan Li et al.

Graph Retrieval-Augmented Generation (GraphRAG) has shown great effectiveness in enhancing the reasoning abilities of LLMs by leveraging graph structures for knowledge representation and modeling complex real-world relationships. However, existing GraphRAG methods still face significant bottlenecks when handling complex problems that require multi-hop reasoning, as their query and retrieval phases are largely based on pre-defined heuristics and do not fully utilize the reasoning potentials of LLMs. To address this problem, we propose GraphRAG-R1, an adaptive GraphRAG framework by training LLMs with process-constrained outcome-based reinforcement learning (RL) to enhance the multi-hop reasoning ability. Our method can decompose complex problems, autonomously invoke retrieval tools to acquire necessary information, and perform effective reasoning. Specifically, we utilize a modified version of Group Relative Policy Optimization (GRPO) that supports rollout-with-thinking capability. Next, we design two process-constrained reward functions. To handle the shallow retrieval problem, we design a Progressive Retrieval Attenuation (PRA) reward to encourage essential retrievals. Then, to handle the over-thinking problem, we design Cost-Aware F1 (CAF) reward to balance the model performance with computational costs. We further design a phase-dependent training strategy, containing three training stages corresponding to cold start and these two rewards. Lastly, our method adopts a hybrid graph-textual retrieval to improve the reasoning capacity. Extensive experimental results demonstrate that GraphRAG-R1 boosts LLM capabilities in solving complex reasoning problems compared to state-of-the-art GraphRAG methods on both in-domain and out-of-domain datasets. Furthermore, our framework can be flexibly integrated with various existing retrieval methods, consistently delivering performance improvements.

Yisen Gao, Jiaxin Bai, Tianshi Zheng et al.

Abductive reasoning in knowledge graphs aims to generate plausible logical hypotheses from observed entities, with broad applications in areas such as clinical diagnosis and scientific discovery. However, due to a lack of controllability, a single observation may yield numerous plausible but redundant or irrelevant hypotheses on large-scale knowledge graphs. To address this limitation, we introduce the task of controllable hypothesis generation to improve the practical utility of abductive reasoning. This task faces two key challenges when controlling for generating long and complex logical hypotheses: hypothesis space collapse and hypothesis oversensitivity. To address these challenges, we propose CtrlHGen, a Controllable logcial Hypothesis Generation framework for abductive reasoning over knowledge graphs, trained in a two-stage paradigm including supervised learning and subsequent reinforcement learning. To mitigate hypothesis space collapse, we design a dataset augmentation strategy based on sub-logical decomposition, enabling the model to learn complex logical structures by leveraging semantic patterns in simpler components. To address hypothesis oversensitivity, we incorporate smoothed semantic rewards including Dice and Overlap scores, and introduce a condition-adherence reward to guide the generation toward user-specified control constraints. Extensive experiments on three benchmark datasets demonstrate that our model not only better adheres to control conditions but also achieves superior semantic similarity performance compared to baselines.

Yunan Wang, Jianxin Li, Ziwei Zhang

Dynamic Text-Attribute Graphs (DyTAGs), characterized by time-evolving graph interactions and associated text attributes, are prevalent in real-world applications. Existing methods, such as Graph Neural Networks (GNNs) and Large Language Models (LLMs), mostly focus on static TAGs. Extending these existing methods to DyTAGs is challenging as they largely neglect the recent-global temporal semantics: the recent semantic dependencies among interaction texts and the global semantic evolution of nodes over time. Furthermore, applying LLMs to the abundant and evolving text in DyTAGs faces efficiency issues. To tackle these challenges, we propose Dynamic Global-Recent Adaptive Semantic Processing (DyGRASP), a novel method that leverages LLMs and temporal GNNs to efficiently and effectively reason on DyTAGs. Specifically, we first design a node-centric implicit reasoning method together with a sliding window mechanism to efficiently capture recent temporal semantics. In addition, to capture global semantic dynamics of nodes, we leverage explicit reasoning with tailored prompts and an RNN-like chain structure to infer long-term semantics. Lastly, we intricately integrate the recent and global temporal semantics as well as the dynamic graph structural information using updating and merging layers. Extensive experiments on DyTAG benchmarks demonstrate DyGRASP's superiority, achieving up to 34% improvement in Hit@10 for destination node retrieval task. Besides, DyGRASP exhibits strong generalization across different temporal GNNs and LLMs.

Beini Xie, Heng Chang, Ziwei Zhang et al.

Graph Neural Architecture Search (GNAS) has achieved superior performance on various graph-structured tasks. However, existing GNAS studies overlook the applications of GNAS in resource-constraint scenarios. This paper proposes to design a joint graph data and architecture mechanism, which identifies important sub-architectures via the valuable graph data. To search for optimal lightweight Graph Neural Networks (GNNs), we propose a Lightweight Graph Neural Architecture Search with Graph SparsIfication and Network Pruning (GASSIP) method. In particular, GASSIP comprises an operation-pruned architecture search module to enable efficient lightweight GNN search. Meanwhile, we design a novel curriculum graph data sparsification module with an architecture-aware edge-removing difficulty measurement to help select optimal sub-architectures. With the aid of two differentiable masks, we iteratively optimize these two modules to efficiently search for the optimal lightweight architecture. Extensive experiments on five benchmarks demonstrate the effectiveness of GASSIP. Particularly, our method achieves on-par or even higher node classification performance with half or fewer model parameters of searched GNNs and a sparser graph.

Haoyang Li, Xin Wang, Ziwei Zhang et al.

Graph machine learning has been extensively studied in both academia and industry. Although booming with a vast number of emerging methods and techniques, most of the literature is built on the in-distribution hypothesis, i.e., testing and training graph data are identically distributed. However, this in-distribution hypothesis can hardly be satisfied in many real-world graph scenarios where the model performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this critical problem, out-of-distribution (OOD) generalization on graphs, which goes beyond the in-distribution hypothesis, has made great progress and attracted ever-increasing attention from the research community. In this paper, we comprehensively survey OOD generalization on graphs and present a detailed review of recent advances in this area. First, we provide a formal problem definition of OOD generalization on graphs. Second, we categorize existing methods into three classes from conceptually different perspectives, i.e., data, model, and learning strategy, based on their positions in the graph machine learning pipeline, followed by detailed discussions for each category. We also review the theories related to OOD generalization on graphs and introduce the commonly used graph datasets for thorough evaluations. Finally, we share our insights on future research directions. This paper is the first systematic and comprehensive review of OOD generalization on graphs, to the best of our knowledge.

Haoyang Li, Xin Wang, Ziwei Zhang et al.

Graph neural networks (GNNs) have achieved impressive performance when testing and training graph data come from identical distribution. However, existing GNNs lack out-of-distribution generalization abilities so that their performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this problem, in this work, we propose an out-of-distribution generalized graph neural network (OOD-GNN) for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs. Our proposed OOD-GNN employs a novel nonlinear graph representation decorrelation method utilizing random Fourier features, which encourages the model to eliminate the statistical dependence between relevant and irrelevant graph representations through iteratively optimizing the sample graph weights and graph encoder. We further present a global weight estimator to learn weights for training graphs such that variables in graph representations are forced to be independent. The learned weights help the graph encoder to get rid of spurious correlations and, in turn, concentrate more on the true connection between learned discriminative graph representations and their ground-truth labels. We conduct extensive experiments to validate the out-of-distribution generalization abilities on two synthetic and 12 real-world datasets with distribution shifts. The results demonstrate that our proposed OOD-GNN significantly outperforms state-of-the-art baselines.

Ruobing Xie, Qi Liu, Shukai Liu et al.

Recently, real-world recommendation systems need to deal with millions of candidates. It is extremely challenging to conduct sophisticated end-to-end algorithms on the entire corpus due to the tremendous computation costs. Therefore, conventional recommendation systems usually contain two modules. The matching module focuses on the coverage, which aims to efficiently retrieve hundreds of items from large corpora, while the ranking module generates specific ranks for these items. Recommendation diversity is an essential factor that impacts user experience. Most efforts have explored recommendation diversity in ranking, while the matching module should take more responsibility for diversity. In this paper, we propose a novel Heterogeneous graph neural network framework for diversified recommendation (GraphDR) in matching to improve both recommendation accuracy and diversity. Specifically, GraphDR builds a huge heterogeneous preference network to record different types of user preferences, and conduct a field-level heterogeneous graph attention network for node aggregation. We also innovatively conduct a neighbor-similarity based loss to balance both recommendation accuracy and diversity for the diversified matching task. In experiments, we conduct extensive online and offline evaluations on a real-world recommendation system with various accuracy and diversity metrics and achieve significant improvements. We also conduct model analyses and case study for a better understanding of our model. Moreover, GraphDR has been deployed on a well-known recommendation system, which affects millions of users. The source code will be released.

Ziwei Zhang, Chenhao Niu, Peng Cui et al.

Graph neural networks (GNNs) are emerging machine learning models on graphs. Permutation-equivariance and proximity-awareness are two important properties highly desirable for GNNs. Both properties are needed to tackle some challenging graph problems, such as finding communities and leaders. In this paper, we first analytically show that the existing GNNs, mostly based on the message-passing mechanism, cannot simultaneously preserve the two properties. Then, we propose Stochastic Message Passing (SMP) model, a general and simple GNN to maintain both proximity-awareness and permutation-equivariance. In order to preserve node proximities, we augment the existing GNNs with stochastic node representations. We theoretically prove that the mechanism can enable GNNs to preserve node proximities, and at the same time, maintain permutation-equivariance with certain parametrization. We report extensive experimental results on ten datasets and demonstrate the effectiveness and efficiency of SMP for various typical graph mining tasks, including graph reconstruction, node classification, and link prediction.

Ziwei Zhang, Peng Cui, Jian Pei et al.

Graph Neural Networks (GNNs) are emerging machine learning models on graphs. Although sufficiently deep GNNs are shown theoretically capable of fully preserving graph structures, most existing GNN models in practice are shallow and essentially feature-centric. We show empirically and analytically that the existing shallow GNNs cannot preserve graph structures well. To overcome this fundamental challenge, we propose Eigen-GNN, a simple yet effective and general plug-in module to boost GNNs ability in preserving graph structures. Specifically, we integrate the eigenspace of graph structures with GNNs by treating GNNs as a type of dimensionality reduction and expanding the initial dimensionality reduction bases. Without needing to increase depths, Eigen-GNN possesses more flexibilities in handling both feature-driven and structure-driven tasks since the initial bases contain both node features and graph structures. We present extensive experimental results to demonstrate the effectiveness of Eigen-GNN for tasks including node classification, link prediction, and graph isomorphism tests.

Ziwei Zhang, Peng Cui, Wenwu Zhu

Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique characteristics of graphs. Recently, substantial research efforts have been devoted to applying deep learning methods to graphs, resulting in beneficial advances in graph analysis techniques. In this survey, we comprehensively review the different types of deep learning methods on graphs. We divide the existing methods into five categories based on their model architectures and training strategies: graph recurrent neural networks, graph convolutional networks, graph autoencoders, graph reinforcement learning, and graph adversarial methods. We then provide a comprehensive overview of these methods in a systematic manner mainly by following their development history. We also analyze the differences and compositions of different methods. Finally, we briefly outline the applications in which they have been used and discuss potential future research directions.

Ziwei Zhang

Spectral clustering and Singular Value Decomposition (SVD) are both widely used technique for analyzing graph data. In this note, I will present their connections using simple linear algebra, aiming to provide some in-depth understanding for future research.

Ziwei Zhang, Peng Cui, Haoyang Li et al.

Network embedding, which learns low-dimensional vector representation for nodes in the network, has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because they are computationally expensive and, at the same time, difficult to be accelerated by distributed computing schemes. To address these problems, we propose RandNE (Iterative Random Projection Network Embedding), a novel and simple billion-scale network embedding method. Specifically, we propose a Gaussian random projection approach to map the network into a low-dimensional embedding space while preserving the high-order proximities between nodes. To reduce the time complexity, we design an iterative projection procedure to avoid the explicit calculation of the high-order proximities. Theoretical analysis shows that our method is extremely efficient, and friendly to distributed computing schemes without any communication cost in the calculation. We also design a dynamic updating procedure which can efficiently incorporate the dynamic changes of the networks without error aggregation. Extensive experimental results demonstrate the efficiency and efficacy of RandNE over state-of-the-art methods in several tasks including network reconstruction, link prediction and node classification on multiple datasets with different scales, ranging from thousands to billions of nodes and edges.