Graph Embedding Models: A Survey

doi:10.3778/j.issn.1673-9418.2104020

Journal of Frontiers of Computer Science and Technology ›› 2022, Vol. 16 ›› Issue (1): 59-87.DOI: 10.3778/j.issn.1673-9418.2104020

• Surveys and Frontiers • Previous Articles Next Articles

Graph Embedding Models: A Survey

YUAN Lining¹, LI Xin², WANG Xiaodong³, LIU Zhao⁴^,⁺()

1. School of Information Network Security, People's Public Security University of China, Beijing 100038, China
2. Science and Informatization Division, Hexi Branch of Tianjin Public Security Bureau, Tianjin 300202, China
3. Science and Informatization Division, Hedong Branch of Tianjin Public Security Bureau, Tianjin 300171, China
4. Research Center for New Crimes, People's Public Security University of China, Beijing 100038, China

Received:2021-04-08 Revised:2021-09-07 Online:2022-01-01 Published:2021-09-13
About author:YUAN Lining, born in 1995, M.S. candidate, student member of CCF. His research interests include machine learning, graph neural network, etc.
LI Xin, born in 1987, M.S. His research interests include machine learning, policing information system, etc.
WANG Xiaodong, born in 1980, intermediate engineer. His research interests include police big data, technical investigation, etc.
xml:lang="en"LIU Zhao, born in 1981, Ph.D., lecturer. His research interests include machine learning and computer vision.
Supported by:
Fundamental Research Funds for the Central Universities of China(2019JKF425);National Key Research and Development Program of China(2018YFC0809800)

图嵌入模型综述

袁立宁¹, 李欣², 王晓冬³, 刘钊⁴^,⁺()

1.中国人民公安大学信息网络安全学院,北京 100038
2.天津市公安局河西分局科技信息化支队,天津 300202
3.天津市公安局河东分局科技信息化支队,天津 300171
4.中国人民公安大学新型犯罪研究中心,北京 100038

通讯作者: + E-mail: liuzhao@ppsuc.edu.cn
作者简介:袁立宁(1995—),男,硕士研究生,CCF学生会员,主要研究方向为机器学习、图神经网络等。
李欣(1987—),男,硕士,主要研究方向为机器学习、公安信息化等。
王晓冬(1980—),男,中级工程师,主要研究方向为警务大数据、技术侦查等。
刘钊(1981—),男,博士,讲师, 主要研究方向为机器学习、计算机视觉。
基金资助:
中央高校基本科研业务费专项资金(2019JKF425);国家重点研发计划(2018YFC0809800)

Abstract

Abstract:

Effective graph analysis methods can reveal the intrinsic characteristics of graph data. However, graph is non-Euclidean data, which leads to high computation and space cost while applying traditional methods. Graph embedding is an efficient method for graph analysis. It converts original graph data into a low-dimensional space and retains key information to improve the performance of downstream tasks such as node classification, link prediction, and node clustering. Different from previous studies, this paper focuses on both static and dynamic graph embedding. Firstly, this paper proposes a universal taxonomy of static and dynamic methods, including matrix factorization based methods, random walk based methods, autoencoder based methods, graph neural networks (GNN) based methods and other embedding methods. Secondly, this paper analyzes the theoretical relevance of static and dynamic methods, and comprehensively summarizes the core strategy, downstream tasks and datasets. Finally, this paper proposes four potential research directions of graph embedding.

Key words: graph embedding, static graph embedding, dynamic graph embedding, random walk, graph neural networks (GNN)

摘要：

图分析用于深入挖掘图数据的内在特征,然而图作为非欧几里德数据,传统的数据分析方法普遍存在较高的计算量和空间开销。图嵌入是一种解决图分析问题的有效方法,其将原始图数据转换到低维空间并保留关键信息,从而提升节点分类、链接预测、节点聚类等下游任务的性能。与以往的研究不同,同时对静态图和动态图嵌入文献进行全面回顾,提出一种静态图嵌入和动态图嵌入通用分类方法,即基于矩阵分解的图嵌入、基于随机游走的图嵌入、基于自编码器的图嵌入、基于图神经网络（GNN）的图嵌入和基于其他方法的图嵌入。其次,对静态图和动态图方法的理论相关性进行分析,对模型核心策略、下游任务和数据集进行全面总结。最后,提出了四个图嵌入的潜在研究方向。

关键词: 图嵌入, 静态图嵌入, 动态图嵌入, 随机游走, 图神经网络（GNN）

CLC Number:

TP391

YUAN Lining, LI Xin, WANG Xiaodong, LIU Zhao. Graph Embedding Models: A Survey[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(1): 59-87.

袁立宁, 李欣, 王晓冬, 刘钊. 图嵌入模型综述[J]. 计算机科学与探索, 2022, 16(1): 59-87.

Figures/Tables 35

Fig.1 Snapshot and continuous-time dynamic graphs

Fig.2 General framework for graph embedding

Table 1 Symbols and definitions

符号	说明
A	邻接矩阵
D	顶点度矩阵
L	拉普拉斯矩阵
X	特征矩阵
S	相似度矩阵
W	系数矩阵
G	静态图
$\mathcal{G}$	动态图
V	节点集
E	边集
d	嵌入维度
Y	嵌入表示

Fig.3 Content system of graph embedding

Fig.4 Categorization and summary of graph embedding models

Fig.5 Framework of eigenvalue factorization in static graph embedding

Fig.6 Steps of LLE

Fig.7 Framework of HOPE

Fig.8 Framework of matrix factorization in dynamic graph embedding

Fig.9 Framework of DANE

Fig.10 Framework of Deepwalk

Fig.11 Random walk procedure in node2vec

Fig.12 Architecture of TriDNR model

Fig.13 Framework of SDNE

Fig.14 Framework of DynGEM

Fig.15 Variations of dyngraph2vec

Fig.16 Workflow of NetWalk for anomaly detection

Fig.17 Framework of multi-layer GCN

Fig.18 Visual illustration of GraphSAGE sampling and aggregation approach

Fig.19 Framework of MF-GCN

Fig.20 Framework of DySAT

Fig.21 Framework of TemporalGAT

Fig.22 Framework of DRNE

Fig.23 Framework of Graphormer

Table 2 Strategies of static graph embedding

模型分类	模型	时间	模型策略
矩阵分解	LLE^[24]	2000	构造邻域保持映射,最小化重建损失函数
	GF^[13]	2013	分解邻接矩阵,利用向量内积捕捉边的存在
	GraRep^[25]	2015	使用SVD分解k步对数转移概率矩阵
	HOPE^[27]	2016	GSVD分解相似度矩阵,L2范数保持高阶相似度
	NGE^[30]	2013	使用NMF将输入分解为系数矩阵和嵌入矩阵
	LE^[32]	2001	保持相连节点在嵌入空间尽可能靠近
	CGE^[33]	2011	修改LE损失函数,保持低权值节点对相似性
	SPE^[34]	2009	利用核矩阵生成关系矩阵 $A ˜$ ,最小化 $A$ 和 $A ˜$ 的差异
随机游走	Deepwalk^[49]	2014	使用随机游走采样节点,Skip-Gram最大化节点共现概率
	node2vec^[50]	2016	在Deepwalk的基础上引入有偏的随机游走
	HARP^[51]	2017	利用原始图生成保留全局结构的压缩图
	Walklets^[52]	2016	改进Deepwalk,捕获节点与社区的从属关系并建模
	TriDNR^[54]	2016	最大化节点标签、节点邻域、节点内容的共现概率
自编码器	GraphEncoder^[63]	2014	利用L2损失函数重构图相似度矩阵
	SDNE^[64]	2016	使用有监督和无监督组件分别保持一阶和二阶相似度
	DNGR^[65]	2016	随机冲浪捕获图结构,生成PPMI矩阵输入SDAE
	DNE-APP^[67]	2017	使用PPMI度量和k步转移矩阵构建相似度聚合矩阵
	VGAE^[69]	2016	引入VAE,使用GCN编码器,使用内积解码器
	GALA^[73]	2020	编码器执行拉普拉斯平滑,解码器执行拉普拉斯锐化
	ANE^[76]	2018	施加对抗性正则化避免流形断裂
图神经网络	GCN^[70]	2016	利用谱卷积一阶近似提高层间传播效率
	GraphSAGE^[85]	2017	采样和聚合节点的局部邻域特征训练聚合器函数
	GAT^[95]	2017	在GCN的基础上引入self-attention和multi-head attention
	GIN^[98]	2018	利用GNN和WL图同构测试保留图结构信息
	MF-GCN^[100]	2020	使用多个局部GCN滤波器提取节点特征
	GraphAIR^[102]	2020	邻域聚合模块融合节点特征表示,邻域交互模块通过乘法运算显示建模
	SDGNN^[103]	2021	在GNN的基础引入地位理论和平衡理论
其他	LINE^[116]	2015	分别优化一阶和二阶相似度,将嵌入向量进行拼接
	DNRE^[117]	2018	直接使用LSTM聚合邻域信息重建节点嵌入
	Graphormer^[119]	2021	在标准Transformer基础上,引入有中心性编码、空间编码和边编码

Table 2 Strategies of static graph embedding

模型分类	模型	时间	模型策略
矩阵分解	LLE^[24]	2000	构造邻域保持映射,最小化重建损失函数
	GF^[13]	2013	分解邻接矩阵,利用向量内积捕捉边的存在
	GraRep^[25]	2015	使用SVD分解k步对数转移概率矩阵
	HOPE^[27]	2016	GSVD分解相似度矩阵,L2范数保持高阶相似度
	NGE^[30]	2013	使用NMF将输入分解为系数矩阵和嵌入矩阵
	LE^[32]	2001	保持相连节点在嵌入空间尽可能靠近
	CGE^[33]	2011	修改LE损失函数,保持低权值节点对相似性
	SPE^[34]	2009	利用核矩阵生成关系矩阵 $A ˜$ ,最小化 $A$ 和 $A ˜$ 的差异
随机游走	Deepwalk^[49]	2014	使用随机游走采样节点,Skip-Gram最大化节点共现概率
	node2vec^[50]	2016	在Deepwalk的基础上引入有偏的随机游走
	HARP^[51]	2017	利用原始图生成保留全局结构的压缩图
	Walklets^[52]	2016	改进Deepwalk,捕获节点与社区的从属关系并建模
	TriDNR^[54]	2016	最大化节点标签、节点邻域、节点内容的共现概率
自编码器	GraphEncoder^[63]	2014	利用L2损失函数重构图相似度矩阵
	SDNE^[64]	2016	使用有监督和无监督组件分别保持一阶和二阶相似度
	DNGR^[65]	2016	随机冲浪捕获图结构,生成PPMI矩阵输入SDAE
	DNE-APP^[67]	2017	使用PPMI度量和k步转移矩阵构建相似度聚合矩阵
	VGAE^[69]	2016	引入VAE,使用GCN编码器,使用内积解码器
	GALA^[73]	2020	编码器执行拉普拉斯平滑,解码器执行拉普拉斯锐化
	ANE^[76]	2018	施加对抗性正则化避免流形断裂
图神经网络	GCN^[70]	2016	利用谱卷积一阶近似提高层间传播效率
	GraphSAGE^[85]	2017	采样和聚合节点的局部邻域特征训练聚合器函数
	GAT^[95]	2017	在GCN的基础上引入self-attention和multi-head attention
	GIN^[98]	2018	利用GNN和WL图同构测试保留图结构信息
	MF-GCN^[100]	2020	使用多个局部GCN滤波器提取节点特征
	GraphAIR^[102]	2020	邻域聚合模块融合节点特征表示,邻域交互模块通过乘法运算显示建模
	SDGNN^[103]	2021	在GNN的基础引入地位理论和平衡理论
其他	LINE^[116]	2015	分别优化一阶和二阶相似度,将嵌入向量进行拼接
	DNRE^[117]	2018	直接使用LSTM聚合邻域信息重建节点嵌入
	Graphormer^[119]	2021	在标准Transformer基础上,引入有中心性编码、空间编码和边编码

Table 3 Strategies of dynamic graph embedding

模型分类	模型	时间	模型策略
矩阵分解	DANE^[36]	2017	拉普拉斯特征映射捕获t时刻的结构和属性信息,矩阵摄动理论更新动态信息
	DHPE^[38]	2018	GSVD分解各时刻Katz矩阵,矩阵摄动理论更新动态信息
	TRIP^[40]	2015	利用图中三角形个数构建特征函数,将特征对矩阵映射成嵌入向量
	TIMERS^[41]	2017	SVD最大误差界重启,消除增量更新积累的误差
	DWSF^[45]	2017	将图中有限监督信息合并为标签,并在每次迭代中更新
随机游走	CTDNE^[56]	2018	按照时间顺序对边进行遍历
	dynnode2vec^[57]	2018	node2vec初始化快照,对变化点执行随机游走,利用Skip-Gram更新动态信息
	STWalk^[59]	2017	捕捉规定时间窗内节点的变化
	tNodeEmbed^[60]	2019	模仿句子嵌入作为节点嵌入,捕捉节点角色和边的动态变化
自编码器	DynGEM^[78]	2018	提出PropSize动态调节神经元个数,同时引入L1和L2正则化
	dyngraph2vec^[79]	2019	组合AE和LSTM,构建不同的编码器和解码器组合
	NetWalk^[81]	2018	同时最小化节点距离和自编码器重构误差
	BurstGraph^[84]	2019	将动态演化分为一般演化和突发演化,RNN捕捉各时刻的图结构
	HVGNN^[92]	2021	采用基于TGNN的双曲VGAE
图神经网络	DyRep^[106]	2018	基于自我传播、外源驱动、局部嵌入传播更新节点表示
	DySAT^[108]	2020	结构注意力提取邻域特征,时间注意力捕捉多个时刻的表示
	EvolveGCN^[110]	2019	在每个时刻使用RNN调整GCN参数
	DGNN^[111]	2020	使用时态信息增强LSTM作为更新框架
	TemporalGAT^[112]	2020	集成GAT和TCN,self-attention应用于邻域,TCN用于动态信息更新
其他	HTNE^[120]	2018	Hawkes捕捉过去时刻对当前时刻邻域的影响,Skip-Gram更新动态信息
	DynamicTriad^[122]	2018	通过闭合三元组和开放三元组模拟图的动态演化
	M²DNE^[125]	2019	微观动态描述结构的形成,宏观动态描述规模的演化,利用二者交互生成嵌入
	CAW^[126]	2021	回溯多个时刻的相邻链接编码因果关系,根据特征位置计数编码相应节点标识

Table 3 Strategies of dynamic graph embedding

模型分类	模型	时间	模型策略
矩阵分解	DANE^[36]	2017	拉普拉斯特征映射捕获t时刻的结构和属性信息,矩阵摄动理论更新动态信息
	DHPE^[38]	2018	GSVD分解各时刻Katz矩阵,矩阵摄动理论更新动态信息
	TRIP^[40]	2015	利用图中三角形个数构建特征函数,将特征对矩阵映射成嵌入向量
	TIMERS^[41]	2017	SVD最大误差界重启,消除增量更新积累的误差
	DWSF^[45]	2017	将图中有限监督信息合并为标签,并在每次迭代中更新
随机游走	CTDNE^[56]	2018	按照时间顺序对边进行遍历
	dynnode2vec^[57]	2018	node2vec初始化快照,对变化点执行随机游走,利用Skip-Gram更新动态信息
	STWalk^[59]	2017	捕捉规定时间窗内节点的变化
	tNodeEmbed^[60]	2019	模仿句子嵌入作为节点嵌入,捕捉节点角色和边的动态变化
自编码器	DynGEM^[78]	2018	提出PropSize动态调节神经元个数,同时引入L1和L2正则化
	dyngraph2vec^[79]	2019	组合AE和LSTM,构建不同的编码器和解码器组合
	NetWalk^[81]	2018	同时最小化节点距离和自编码器重构误差
	BurstGraph^[84]	2019	将动态演化分为一般演化和突发演化,RNN捕捉各时刻的图结构
	HVGNN^[92]	2021	采用基于TGNN的双曲VGAE
图神经网络	DyRep^[106]	2018	基于自我传播、外源驱动、局部嵌入传播更新节点表示
	DySAT^[108]	2020	结构注意力提取邻域特征,时间注意力捕捉多个时刻的表示
	EvolveGCN^[110]	2019	在每个时刻使用RNN调整GCN参数
	DGNN^[111]	2020	使用时态信息增强LSTM作为更新框架
	TemporalGAT^[112]	2020	集成GAT和TCN,self-attention应用于邻域,TCN用于动态信息更新
其他	HTNE^[120]	2018	Hawkes捕捉过去时刻对当前时刻邻域的影响,Skip-Gram更新动态信息
	DynamicTriad^[122]	2018	通过闭合三元组和开放三元组模拟图的动态演化
	M²DNE^[125]	2019	微观动态描述结构的形成,宏观动态描述规模的演化,利用二者交互生成嵌入
	CAW^[126]	2021	回溯多个时刻的相邻链接编码因果关系,根据特征位置计数编码相应节点标识

Table 4 Statistics of static graph datasets

统计项	20-NewsGroup	Flickr	DBLP	YouTube	Wikipedia	Cora	CiteSeer	Pubmed	Yelp
#Nodes	1 720,3 224,5 141	80 513	29 199	1 138 499	2 405	2 708	3 327	19 717	6 569
#Edges	Fully connected	5 899 882	133 664	2 990 443	17 981	5 429	4 732	44 338	95 361
#Features	—	—	—	—	4 973	1 433	3 703	500	—
#Labels	3,6,9	195	4	47	17	7	6	3	—

Table 5 Statistics of dynamic graph datasets

统计项	Epinions	Hep-th	AS	Enron	UCI
#Nodes	14 180	1 424~7 980	7 716	184	1 809
#Edges	227 642	2 556~21 036	10 695~26 467	63~591	16 822
#Features	9 936	—	—	—	—
#Labels	20	—	—	—	—
#Time Steps	16	60	100	128	13

Fig.24 Performance comparison of graph reconstruction

Fig.25 Performance comparison of static graph node classification

Table 6 Performance comparison of dynamic graph node classification %

Index	Deepwalk	node2vec	LINE	DANE	tNodeEmbed	CTDNE	HTNE	DynamicTriad	M²DNE
micro-F1	69.65	75.20	67.56	74.53	82.20	71.70	71.40	71.10	69.75
macro-F1	72.37	23.50	70.97	75.69	50.40	8.30	6.90	5.50	69.71

Table 7 Performance comparison of link prediction %

Index	Deepwalk	GAE	VGAE	Linear-GAE	Linear-VGAE	GALA	GraphSAGE	MF-GCN	GraphAIR
AUC	80.5	89.5	90.8	91.5	91.6	94.4	93.7	92.4	95.0
AP	83.6	89.9	92.0	92.9	93.1	94.8	—	—	—

Fig.26 Performance comparison of node clustering

Fig.27 Performance comparison of anomaly detection

Fig.28 Visualization of different models

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Graph Embedding Models: A Survey

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