Gradient orthogonal projection based continual embedding method for dynamic knowledge graph

doi:10.11772/j.issn.1001-9081.2025060737

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (6): 1776-1784.DOI: 10.11772/j.issn.1001-9081.2025060737

• Artificial intelligence • Previous Articles

Gradient orthogonal projection based continual embedding method for dynamic knowledge graph

Meihua WANG¹, Jie HUANG¹, Wen WEN²(), Ruichu CAI², Peijie HUANG¹, Yuhong XU¹, Xinlong LIN¹

^1.College of Mathematics and Informatics，South China Agricultural University，Guangzhou Guangdong 510640，China
^2.School of Computer Science and Technology，Guangdong University of Technology，Guangzhou Guangdong 510006，China

Received:2025-07-05 Revised:2026-01-08 Accepted:2026-01-14 Online:2026-02-05 Published:2026-06-10
Contact: Wen WEN
About author:WANG Meihua， born in 1970， M. S.， associate professor. Her research interests include machine learning， knowledge graph and continuous learning， data mining.
HUANG Jie， born in 1999， M. S. His research interests include machine learning， knowledge graph and continuous learning.
CAI Ruichu， born in 1983， Ph. D.， professor. His research interests include causal discovery， machine learning.
HUANG Peijie， born in 1980， Ph. D.， associate professor. His research interests include artificial intelligence， natural language processing， spoken dialogue system.
XU Yuhong， born in 1994， Ph. D.， associate professor. His research interests include causal discovery， machine learning， ensemble learning， unbalanced learning.
LIN Xinlong， born in 2000， M. S. His research interests include machine learning， time series data mining.
First author contact:WEN wen， born in 1983， Ph. D.， professor. Her research interests include machine learning， time series data mining.
Supported by:
Natural Science Foundation of Guangdong Province(2024A1515011380);Research Project on Key Areas of Universities in Guangdong Province(2024ZDZX4032)

基于梯度正交投影的动态知识图谱持续嵌入方法

王美华¹, 黄杰¹, 温雯²(), 蔡瑞初², 黄沛杰¹, 徐禹洪¹, 林新龙¹

^1.华南农业大学数学与信息学院，广州 510640
^2.广东工业大学计算机学院，广州 510006

通讯作者: 温雯
作者简介:王美华（1970—），女，江苏常州人，副教授，硕士，主要研究方向：机器学习、知识图谱与持续学习、数据挖掘
黄杰（1999—），男，广东河源人，硕士，主要研究方向：机器学习、知识图谱与持续学习
蔡瑞初（1983—），男，浙江温州人，教授，博士，CCF会员，主要研究方向：因果发现、机器学习
黄沛杰（1980—），男，广东潮州人，副教授，博士，CCF会员，主演研究方向：人工智能、自然语言处理、口语对话系统
徐禹洪（1994—），男，广东佛山人，副教授，博士，CCF会员，主要研究方向：因果发现、机器学习、集成学习、不平衡学习
林新龙（2000—）男，广东佛山人，硕士，主要研究方向：机器学习、时序数据挖掘。
第一联系人：温雯（1983—），女，江西赣州人，教授，博士，CCF会员，主要研究方向：机器学习、时序数据挖掘
基金资助:
广东省自然科学基金资助项目(2024A1515011380);广东省普通高校重点领域研究项目(2024ZDZX4032)

Abstract

Abstract:

To address the issue that the existing Knowledge Graph （KG） embedding models cannot adapt to the increasing KG， a dynamic KG continual embedding method based on gradient orthogonal projection， named GOPemb （Gradient Orthogonal Projection embedding）， was proposed. Firstly， the Core Gradient Spaces （CGSs） of old entities and old relationships were stored in historical snapshots during the training process. Secondly， when learning new triples， the gradient update directions for old entities and old relationships were constrained to align with the orthogonal directions of their respective CGSs， thereby learning new knowledge efficiently while preserving historical knowledge effectively. Finally， the CGSs of old entities and old relationships were updated to prepare for the next learning iteration. Experimental results show that compared to the best method in the comparison group， IncDE （Incremental Distillation Embedding）， GOPemb method achieves average improvements of 9.2%， 14.0%， and 8.0% in MRR （Mean Reciprocal Rank）， H@3 （Top-3 Hit Rate）， and H@10 （Top-10 Hit Rate）， respectively， on the selected datasets ICEWS05-15-CL、ICEWS18-CL and GDELT-CL. Furthermore， experimental results on learning efficiency confirm the time efficiency of GOPemb method， indicating that the method has efficient continual embedding capability.

Key words: knowledge graph, knowledge graph embedding, representation learning, Continual Learning (CL), incremental learning

摘要：

针对现有的知识图谱（KG）嵌入模型无法适应不断增长的KG的问题，提出一种基于梯度正交投影的动态KG持续嵌入方法GOPemb （Gradient Orthogonal Projection embedding）。首先，在训练过程中将旧实体和旧关系的核心梯度空间（CGS）存储于历史快照；其次，在学习新三元组时，旧实体和旧关系的梯度更新方向被约束为与它们各自CGS的正交方向一致，从而在有效保留历史知识的同时高效地学习新知识；最后，更新旧实体和旧关系的CGS，从而为下一次的学习迭代作准备。实验结果显示，相较于对比方法中最优的IncDE （Incremental Distillation Embedding），GOPemb方法在数据集ICEWS05-15-CL、ICEWS18-CL和GDELT-CL上的MRR （Mean Reciprocal Rank）、H@3 （Top-3 Hit Rate）和H@10 （Top-10 Hit Rate）分别平均提升了9.2%、14.0%和8.0%。此外，学习效率的实验结果也验证了GOPemb方法的时间高效性，表明该方法具备高效的持续嵌入能力。

关键词: 知识图谱, 知识图谱嵌入, 表示学习, 持续学习, 增量学习

CLC Number:

TP391.1

Meihua WANG, Jie HUANG, Wen WEN, Ruichu CAI, Peijie HUANG, Yuhong XU, Xinlong LIN. Gradient orthogonal projection based continual embedding method for dynamic knowledge graph[J]. Journal of Computer Applications, 2026, 46(6): 1776-1784.

王美华, 黄杰, 温雯, 蔡瑞初, 黄沛杰, 徐禹洪, 林新龙. 基于梯度正交投影的动态知识图谱持续嵌入方法[J]. 《计算机应用》唯一官方网站, 2026, 46(6): 1776-1784.

Figures/Tables 10

Tab. 1 Mathematical symbols and their descriptions

数学符号	具体含义
$K$	动态KG
$K t$	动态KG中的第 $t$ 个KG快照
$E t$	快照 $K t$ 中的实体集合
$R t$	快照 $K t$ 中的关系集合
$O$	实体和关系的总集合
$o$	对象 $o$ 表示任意一个实体或关系
$W$	存储所有对象的CGS
$ε$	阈值
$τ$	训练的迭代次数
$d$	模型的嵌入维度

Tab. 1 Mathematical symbols and their descriptions

数学符号	具体含义
$K$	动态KG
$K t$	动态KG中的第 $t$ 个KG快照
$E t$	快照 $K t$ 中的实体集合
$R t$	快照 $K t$ 中的关系集合
$O$	实体和关系的总集合
$o$	对象 $o$ 表示任意一个实体或关系
$W$	存储所有对象的CGS
$ε$	阈值
$τ$	训练的迭代次数
$d$	模型的嵌入维度

Fig. 1 Overall framework of GOPemb

Tab. 2 Statistical information of benchmark datasets

数据集	快照1			快照2			快照3			快照4			快照5
数据集	$Δ K 1$	$E 1$	$R 1$	$Δ K 2$	$E 2$	$R 2$	$Δ K 3$	$E 3$	$R 3$	$Δ K 4$	$E 4$	$R 4$	$Δ K 5$	$E 5$	$R 5$
ICEWS05-15-CL	13 500	2 192	177	11 800	3 202	195	11 800	3 960	205	11 800	4 626	220	11 800	5 160	228
ICEWS18-CL	17 000	4 030	174	17 000	6 246	204	17 000	7 860	215	17 000	9 398	220	17 000	10 543	224
GDELT-CL	40 000	2 250	184	40 000	2 928	196	40 000	3 326	208	40 000	3 677	211	40 000	3 945	214

Tab. 2 Statistical information of benchmark datasets

数据集	快照1			快照2			快照3			快照4			快照5
数据集	$Δ K 1$	$E 1$	$R 1$	$Δ K 2$	$E 2$	$R 2$	$Δ K 3$	$E 3$	$R 3$	$Δ K 4$	$E 4$	$R 4$	$Δ K 5$	$E 5$	$R 5$
ICEWS05-15-CL	13 500	2 192	177	11 800	3 202	195	11 800	3 960	205	11 800	4 626	220	11 800	5 160	228
ICEWS18-CL	17 000	4 030	174	17 000	6 246	204	17 000	7 860	215	17 000	9 398	220	17 000	10 543	224
GDELT-CL	40 000	2 250	184	40 000	2 928	196	40 000	3 326	208	40 000	3 677	211	40 000	3 945	214

Tab. 3 Experimental environment configuration

软件/硬件环境名称	环境参数
GPU	4060
CPU	Intel i9-13900HX
CUDA	12.0
显存	8 GB
编程语言	Python 3.9
深度学习框架	PyTorch 2.1.0

Tab. 4 Average link prediction results of five KG snapshots

方法	ICEWS05-15-CL			ICEWS18-CL			GDELT-CL
方法	MRR	H@3	H@10	MRR	H@3	H@10	MRR	H@3	H@10
重训练	0.099	12.920	29.543	0.079	09.571	23.704	0.051	5.649	14.650
CWR	0.072	8.500	21.267	0.054	05.585	15.462	0.037	3.539	9.501
GEM	0.085	10.193	25.030	0.064	06.281	18.587	0.039	3.692	10.074
ER	0.082	09.823	24.253	0.060	05.995	17.547	0.036	3.168	9.459
SI	0.080	09.767	23.543	0.061	06.075	17.474	0.040	3.912	10.457
IncDE	0.088	10.915	27.313	0.072	07.823	21.436	0.043	4.221	11.985
LKGE	0.086	10.692	27.160	0.069	07.787	20.023	0.045	4.468	12.291
GOPemb	0.096	12.488	29.149	0.077	08.593	23.153	0.048	4.969	13.102

Fig. 2 Visualization of link prediction results for each snapshot

Fig. 3 Stability and plasticity results on three datasets

Tab. 5 Total training time for all snapshots of different methods on three datasets

方法	不同数据集上的训练时间/s
方法	ICEWS05-15-CL	ICEWS18-CL	GDELT-CL
重训练	704	1 567	720
CWR	453	607	491
GEM	344	469	427
ER	634	1 163	540
SI	243	312	361
IncDE	415	478	536
LKGE	171	332	296
GOPemb	212	313	303

Tab. 6 MRR results under different thresholds ε

$ε$	ICEWS05-15-CL			ICEWS18-CL			GDELT-CL
$ε$	MRR	BWT	FWT	MRR	BWT	FWT	MRR	BWT	FWT
0.70	0.096	0.011	0.085	0.077	0.007	0.070	0.048	0.004	0.044
0.80	0.094	0.009	0.085	0.075	0.006	0.069	0.048	0.004	0.044
0.90	0.091	0.007	0.084	0.075	0.006	0.069	0.047	0.004	0.043
0.95	0.089	0.006	0.083	0.073	0.005	0.068	0.046	0.005	0.041

Tab. 6 MRR results under different thresholds ε

$ε$	ICEWS05-15-CL			ICEWS18-CL			GDELT-CL
$ε$	MRR	BWT	FWT	MRR	BWT	FWT	MRR	BWT	FWT
0.70	0.096	0.011	0.085	0.077	0.007	0.070	0.048	0.004	0.044
0.80	0.094	0.009	0.085	0.075	0.006	0.069	0.048	0.004	0.044
0.90	0.091	0.007	0.084	0.075	0.006	0.069	0.047	0.004	0.043
0.95	0.089	0.006	0.083	0.073	0.005	0.068	0.046	0.005	0.041

Tab. 7 H@10 results under different thresholds ε

$ε$	ICEWS05-15-CL			ICEWS18-CL			GDELT-CL
$ε$	H@10	BWT	FWT	H@10	BWT	FWT	H@10	BWT	FWT
0.70	29.149	3.453	25.696	23.153	2.023	21.130	13.102	1.364	11.738
0.80	28.374	2.757	25.617	22.808	1.667	21.141	13.001	1.523	11.648
0.90	27.086	2.059	25.062	22.223	1.506	20.717	12.617	1.067	11.550
0.95	26.669	1.823	24.846	22.152	1.509	20.643	12.628	1.141	11.541

Tab. 7 H@10 results under different thresholds ε

$ε$	ICEWS05-15-CL			ICEWS18-CL			GDELT-CL
$ε$	H@10	BWT	FWT	H@10	BWT	FWT	H@10	BWT	FWT
0.70	29.149	3.453	25.696	23.153	2.023	21.130	13.102	1.364	11.738
0.80	28.374	2.757	25.617	22.808	1.667	21.141	13.001	1.523	11.648
0.90	27.086	2.059	25.062	22.223	1.506	20.717	12.617	1.067	11.550
0.95	26.669	1.823	24.846	22.152	1.509	20.643	12.628	1.141	11.541

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Gradient orthogonal projection based continual embedding method for dynamic knowledge graph

基于梯度正交投影的动态知识图谱持续嵌入方法

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