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Journal of Zhejiang University (Science Edition)  2022, Vol. 49 Issue (4): 443-456    DOI: 10.3785/j.issn.1008-9497.2022.04.008
Mathematics and Computer Science     
Research progress of graph embedding algorithms
Hualing LIU(),Guoxiang ZHANG,Jun MA
School of Statistics and Information,Shanghai University of International Business and Economics,Shanghai 201600,China
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Abstract  

As an important form of expressing the relationship among entities, graph networks have been widely used in data analysis, relational reasoning, and information services. For these applications, how to reasonably represent network characteristic information is the primary task of network analysis research. Graph embedding technology solves the problem of how to efficiently and reasonably map massive, heterogeneous, and complex high-dimensional graph data to low-dimensional vector space while still retaining the original data feature information. This paper aims to survey the algorithm and research progress of graph embedding in recent years, analyze the development status of this field, and explore the direction for subsequent research. First, it reviews the principle and basic theory of graph embedding technology, then systematically investigates the current mainstream graph embedding algorithms, including graph embedding approaches based respectively on dimensionality reduction, matrix decomposition,network topology,neural network, generative adversarial network, and hypergraph. Then we show the application scenarios of graph embedding technology and introduce the commonly used test data sets and evaluation criteria. Finally, we highlight the future research trends and directions of graph embedding, such as dynamic graph embedding, graph embedding scalability and interpretability.



Key wordsgraph network      graph embedding      deep learning      neural network      representation learning     
Received: 25 February 2021      Published: 13 July 2022
CLC:  TP 311  
Cite this article:

Hualing LIU,Guoxiang ZHANG,Jun MA. Research progress of graph embedding algorithms. Journal of Zhejiang University (Science Edition), 2022, 49(4): 443-456.

URL:

https://www.zjujournals.com/sci/EN/Y2022/V49/I4/443


图嵌入算法研究进展

图嵌入算法是将高维网络信息映射至低维后用实数向量表示的一种方法,用于解决推荐系统、社区发现及节点分类等。近年来,随着科技的进步,图数据呈现海量、异构、高维、多模态等特点,机器学习等人工智能算法对高性能的图嵌入算法的需求日益增加,图嵌入已成为国内外人工智能领域的研究热点之一。对图嵌入算法的研究进展、技术原理及基础理论进行了综述,系统概述了已有的主流图嵌入算法,包括基于降维方法的图嵌入、基于矩阵分解的图嵌入、基于网络拓扑结构的图嵌入、基于神经网络的图嵌入、基于生成式对抗网络的图嵌入和基于超图网络的图嵌入,对这些算法进行了分析与比较,并给出了相应的应用场景;归纳总结了常用的测试数据集及其评价标准;最后,展望了图嵌入算法的研究趋势和方向。


关键词: 图网络,  图嵌入,  深度学习,  神经网络,  表示学习 
Fig.1 Graph embedding principle
类型年份刊物方法时间复杂度
基于降维方法1986SpringerPCA-
1994NIPSMDSO(|V|d2
2000ScienceLLEO(|E|d3
2001IEEELDAO(n3
2003IJCAIkernel methodsO(n)
基于矩阵分解2008ACMNPMF-
2013WWWGraph Laplacian EigenmapsO(|E|d)
2015CIKMGraRepO(|V|3
2016IEEEHSCA网络-
2016KDDHOPEO(|E|d2
基于网络拓扑结构信息2014KDDDeepWalkO(|V|d)
2015WWWLINEO(|E|d)
2016KDDnode2vecO(|V|d)
2017NIPSGraphSAGEO(|V|d)
基于神经网络2016KDDSDNEO(|V||E|)
2017ICLRGCNO(|E|d2
2018ACNEGES-
基于生成式对抗网络2017ArXivGraphGAN-
2018ACMNetRA-
基于超图网络2017CORRDHNE-
2018ArXivHGNN-
2021ACM WSDMHWNN-
Table 1 Embedded model overview
Fig.2 Node2vec algorithm node jump principle
Fig.3 SDNE model structure
Fig.4 NetRA model framework
表示超图
A (|V| × |V|)H (|V| × |E|)
最小割NP难NP完全
谱聚类实值优化实值优化
谱嵌入矩阵分解投影至特征空间
Table 2 Comparison of characteristics between graphs and hyper-graphs
Fig.5 Illustrations of graphs and hyper-graphs
图嵌入算法适用数据集优势不足应用
基于降维方法高维稀疏数据

数学原理简单、

易于理解和实施

无法捕捉高阶相似度节点分类、节点聚类
基于矩阵分解稀疏数据可以捕捉全局结构高时间复杂度节点分类、节点聚类

基于网络拓扑

结构信息

大部分数据集

可以捕获节点间的

远距离关系

无法保留全局结构

节点分类、链接预测、

可视化、图分类

基于神经网络大部分数据集有效且健壮高计算成本

节点分类、链接预测、

三元组预测

基于生成式对抗网络复杂数据

充分利用不同来源的

结构信息,改善了嵌入精度

难以证明合理性节点分类、图分类
基于超图网络复杂数据可以处理复杂的图网络数据难以实施节点分类
Table 3 Characteristic analysis of graph embedding algorithms
名称社交网络合成网络语言网络协作网络

生物

网络

BLOGCATALOGFLICKRYOUTUBEKARATESYN-SBMWIKIPEDIACiteSeerASTRO-PHCoraPPI
节点数10 31280 5131 157 827341 0242 4053 31218 7722 7083 890
边数333 9835 899 8824 945 3827829 83317 9814 723396 1605 42938 739
平均度64.7843.748.544.5958.27-5.2731.5546.7319.92
标签数391954723196750
加权图
有向图
Table 4 Data set overview
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[8] WANG Xie, ZHANG Xiaocan, SU Cheng. Land use classification of remote sensing images based on multi-scale learning and deep convolution neural network[J]. Journal of Zhejiang University (Science Edition), 2020, 47(6): 715-723.
[9] ZENG Jindi, ZHANG Feng, WU Sensen, DU Zhenhong, LIU Renyi. Spatial interpolation based on spatial auto-regressive neural network[J]. Journal of Zhejiang University (Science Edition), 2020, 47(5): 572-581.
[10] LI Junyi, REN Tao, LU Luzheng. A comparative study of big text data mining methods on tourist emotion computing[J]. Journal of Zhejiang University (Science Edition), 2020, 47(4): 507-520.
[11] ZHOU Xiaotian, ZHANG Feng, DU Zhenhong, LIU Renyi. Optimization of typhoon track prediction based on neural network ensemble prediction[J]. Journal of Zhejiang University (Science Edition), 2020, 47(2): 196-202.
[12] LU Jiapin, LUO Yuetong, HUANG Zhaosong, ZHANG Yankong, CHEN Wei. An information fusion map matching method based on ranking learning[J]. Journal of Zhejiang University (Science Edition), 2020, 47(1): 27-35.
[13] ZHANG Beina, FENG Zhenhua, ZHANG Feng, DU Zhenhong, LIU Renyi, ZHOU Qin. Urban air quality data completion method based on spatio-temporal multi-view BP neural network[J]. Journal of Zhejiang University (Science Edition), 2019, 46(6): 737-744.
[14] PAN Shuiyang, LIU Junwei, WANG Yiming. Forecasting stock returns with artificial neural networks.[J]. Journal of Zhejiang University (Science Edition), 2019, 46(5): 550-555.
[15] Shanxiong CHEN, Xiaolong WANG, Xu HAN, Yun LIU, Minggui WANG. A recognition method of Ancient Yi character based on deep learning[J]. Journal of Zhejiang University (Science Edition), 2019, 46(3): 261-269.