Uncertain knowledge graph embedding: an effective method combining multi-relation and multi-path

doi:10.1007/s11704-023-2427-z

Front. Comput. Sci.

2024, Vol. 18

Issue (3) : 183311 https://doi.org/10.1007/s11704-023-2427-z

RESEARCH ARTICLE

Uncertain knowledge graph embedding: an effective method combining multi-relation and multi-path

Qi LIU^1,^2,³, Qinghua ZHANG^1,^2,³(

), Fan ZHAO^1,^2,³, Guoyin WANG^1,^2,³

¹. Key Laboratory of Tourism Multisource Data Perception and Decision, Ministry of Culture and Tourism, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
². Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
³. Chongqing Key Laboratory of Big Data Intelligent Computing, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

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Abstract

Uncertain Knowledge Graphs (UKGs) are used to characterize the inherent uncertainty of knowledge and have a richer semantic structure than deterministic knowledge graphs. The research on the embedding of UKG has only recently begun, Uncertain Knowledge Graph Embedding (UKGE) model has a certain effect on solving this problem. However, there are still unresolved issues. On the one hand, when reasoning the confidence of unseen relation facts, the introduced probabilistic soft logic cannot be used to combine multi-path and multi-step global information, leading to information loss. On the other hand, the existing UKG embedding model can only model symmetric relation facts, but the embedding problem of asymmetric relation facts has not be addressed. To address the above issues, a Multiplex Uncertain Knowledge Graph Embedding (MUKGE) model is proposed in this paper. First, to combine multiple information and achieve more accurate results in confidence reasoning, the Uncertain ResourceRank (URR) reasoning algorithm is introduced. Second, the asymmetry in the UKG is defined. To embed asymmetric relation facts of UKG, a multi-relation embedding model is proposed. Finally, experiments are carried out on different datasets via 4 tasks to verify the effectiveness of MUKGE. The results of experiments demonstrate that MUKGE can obtain better overall performance than the baselines, and it helps advance the research on UKG embedding.

Keywords knowledge representation uncertain knowledge graph multi-relation embedding uncertain reasoning

Corresponding Author(s): Qinghua ZHANG

Just Accepted Date: 02 March 2023 Issue Date: 27 April 2023

Cite this article:

Qi LIU,Qinghua ZHANG,Fan ZHAO, et al. Uncertain knowledge graph embedding: an effective method combining multi-relation and multi-path[J]. Front. Comput. Sci., 2024, 18(3): 183311.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-023-2427-z
https://academic.hep.com.cn/fcs/EN/Y2024/V18/I3/183311

Fig.1 The inference example of URR

Fig.2 The computation of circular correlation [48]

Fig.3 Global reasoning for unseen relation facts in MUKGE

Fig.4 The resource flow in the URR algorithm

Tab.1 The computation of an inference example by URR

Fig.5 The overall framework of MUKGE

Dataset	$\| E \|$	$\| R \|$	$\| Δ + \|$	$\| Δ ? \|$	$\| Δ a s y + \|$	Avg(s)	Std(s)
CN15k	15,000	36	241,158	7,927	1,940	0.629	0.232
NL27k	27,221	404	175,412	32,513	2,478	0.797	0.242
PPI5k	4,999	7	271,666	85,299	38,836	0.415	0.213
CN15k_ASY	15,000	36	241,158	7,927	41,190	0.606	0.321
NL27k_ASY	27,221	404	175,412	32,513	98,712	0.687	0.34
PPI5k_ASY	4,999	7	271,666	85,299	226,395	0.268	0.241

Tab.2 The statistics of datasets

Dataset	CN15k		NL27k		PPI5k
Metrics	MSE	MAE	MSE	MAE	MSE	MAE
URGE	10.32	22.72	7.48	11.35	1.44	6.00
$U K G E r e c t$	8.61	19.90	2.36	6.90	0.95	3.79
$U K G E l o g i$	9.86	20.74	3.43	7.93	0.96	4.07
$U K G s E$	7.71	21.34	6.58	17.54	0.95	5.72
$B E U r R E$	7.80	20.03	2.37	7.12	0.41	3.32
$M U K G E u r r ?$	10.35	20.65	2.65	6.16	0.50	3.61
$M U K G E n ?$	19.08	28.09	2.79	6.84	0.66	4.21
$M U K G E r e c t$	7.05	19.73	1.63	6.76	0.35	3.02
$M U K G E l o g i$	9.99	20.42	2.11	6.12	0.36	2.50

Tab.3 The results of confidence prediction

Fig.6 The MSEs (

× 10 ? 2

) and MAEs (

× 10 ? 2

) of MUKGE and its contrast models in the confidence prediction task. (a) is the MSEs of models on CN15k, NL27k and PPI5k. (b) is the MAEs of models on CN15k, NL27k and PPI5k

Dataset	CN15k		NL27k		PPI5k
Metrics	Linear	Exp.	Linear	Exp.	Linear	Exp.
TransE	0.601	0.591	0.730	0.722	0.710	0.700
DistMult	0.689	0.677	0.911	0.897	0.894	0.880
ComplEx	0.723	0.712	0.921	0.913	0.896	0.881
URGE	0.572	0.570	0.593	0.593	0.726	0.723
$U K G E r e c t$	0.773	0.775	0.939	0.942	0.946	0.946
$U K G E l o g i$	0.789	0.788	0.955	0.956	0.970	0.969
$U K G s E$	0.780	0.795	0.895	0.897	0.969	0.970
$B E U r R E$	0.796	0.795	0.942	0.942	0.951	0.952
$M U K G E u r r ?$	0.810	0.812	0.937	0.939	0.983	0.982
$M U K G E n ?$	0.748	0.749	0.914	0.918	0.973	0.971
$M U K G E r e c t$	0.832	0.835	0.877	0.882	0.959	0.958
$M U K G E l o g i$	0.849	0.850	0.945	0.947	0.991	0.990

Tab.4 The results of relation fact ranking

Fig.7 The NDCGs(Linear and Exp.) of MUKGE and UKGE as training proceeds on CN15K, NL27k and PPI5k. (a)?(c) are the NDCGs(Linear) of models on CN15k, NL27k and PPI5k; (d)?(f) are the NDCGs(Exp.) of models on CN15k, NL27k and PPI5k

Fig.8 The frequency distribution of confidence on CN15K, NL27k and PPI5k. (a) is the frequency distribution of confidence on CN15K; (b) is the frequency distribution of confidence on NL27k; (c) is the frequency distribution of confidence on PPI5k

Dataset	CN15k		NL27k		PPI5k
Metrics	F-1	Accu.	F-1	Accu.	F-1	Accu.
TransE	23.1	67.9	65.1	53.4	83.2	98.5
DistMult	27.9	71.1	72.1	70.1	86.9	97.1
ComplEx	18.9	73.2	63.3	53.4	83.2	98.9
URGE	21.2	86.0	83.6	88.7	85.2	98.6
$U K G E r e c t$	28.8	90.4	92.3	95.2	95.1	99.4
$U K G E l o g i$	25.9	90.1	88.4	93.0	94.5	99.5
$U K G s E$	28.2	88.7	91.5	93.7	94.2	98.7
$B E U r R E$	28.7	89.9	92.4	95.6	95.0	99.4
$M U K G E u r r ?$	25.3	89.7	88.3	93.0	94.6	99.5
$M U K G E n ?$	24.0	89.9	87.8	93.9	93.7	99.1
$M U K G E r e c t$	32.0	90.4	87.5	92.5	94.7	99.3
$M U K G E l o g i$	28.3	90.2	91.2	94.4	95.3	99.7

Tab.5 The results of relation fact classification

Fig.9 F-1 scores (%) and Accus. (%) of MUKGE and the contrast models of MUKGE. (a) is the F-1 scores of models on CN15k, NL27k and PPI5k; (b) is the Accus. of models on CN15k, NL27k and PPI5k

Dataset	CN15k_ASY		NL27k_ASY		PPI5k_ASY
Metrics	MSE	MAE	MSE	MAE	MSE	MAE
$U K G E r e c t$	9.09	21.92	6.09	14.17	3.41	12.88
$U K G E l o g i$	13.49	24.90	7.44	14.50	4.85	14.97
$U K G s E$	10.25	25.18	12.06	22.42	5.30	19.87
$B E U r R E$	8.75	21.43	5.73	12.71	2.58	11.23
$M U K G E u r r ?$	13.13	23.95	3.68	8.78	2.24	8.55
$M U K G E n ?$	14.69	24.63	4.74	10.82	2.36	8.39
$M U K G E r e c t$	8.25	20.96	2.69	9.62	1.99	9.64
$M U K G E l o g i$	11.58	21.90	3.91	8.33	1.43	5.19

Tab.6 Confidence prediction of asymmetric relation fact embedding

Dataset	CN15k_ASY		NL27k_ASY		PPI5k_ASY
Metrics	Linear	Exp.	Linear	Exp.	Linear	Exp.
$U K G E r e c t$	0.683	0.683	0.773	0.769	0.783	0.773
$U K G E l o g i$	0.717	0.715	0.827	0.823	0.757	0.746
$U K G s E$	0.663	0.663	0.724	0.718	0.736	0.724
$B E U r R E$	0.721	0.722	0.876	0.872	0.849	0.834
$M U K G E u r r ?$	0.749	0.754	0.843	0.850	0.833	0.833
$M U K G E n ?$	0.732	0.733	0.837	0.840	0.812	0.813
$M U K G E r e c t$	0.796	0.799	0.882	0.886	0.839	0.835
$M U K G E l o g i$	0.813	0.813	0.935	0.939	0.906	0.903

Tab.7 Relation fact ranking of asymmetric relation fact embedding

Dataset	CN15k_ASY		NL27k_ASY		PPI5k_ASY
Metrics	F-1	Accu.	F-1	Accu.	F-1	Accu.
$U K G E r e c t$	12.3	89.9	78.4	89.7	6.4	97.5
$U K G E l o g i$	9.5	89.9	74.3	87.4	5.5	96.4
$U K G s E$	8.7	88.5	72.6	81.5	5.2	95.6
$B E U r R E$	16.7	89.8	82.9	92.6	19.8	98.6
$M U K G E u r r ?$	14.8	90.1	83.0	92.8	18.7	98.4
$M U K G E n ?$	14.9	90.0	82.0	92.4	20.0	98.0
$M U K G E r e c t$	15.7	90.4	83.5	96.3	19.5	99.2
$M U K G E l o g i$	17.0	90.3	82.7	96.1	21.3	99.0

Tab.8 Relation fact classification of asymmetric relation fact embedding

Fig.10 The MSEs (

× 10 ? 2

) and MAEs (

× 10 ? 2

) of MUKGE and UKGE in the confidence prediction task on CN15k_ASY, NL27k_ASY and PPI5k_ASY. (a) is the MSEs of models on CN15k_ASY, NL27k_ASY and PPI5k_ASY; (b) is the MAEs of models on CN15k_ASY, NL27k_ASY and PPI5k_ASY

Fig.11 The NDCGs (Linear and Exp.) of MUKGE and UKGE as training proceeds on CN15K_ASY, NL27k_ASY and PPI5k_ASY. (a)?(c) are the NDCGs(Linear) of models on CN15k_ASY, NL27k_ASY and PPI5k_ASY; (d)?(f) are the NDCGs(Exp.) of models on CN15k_ASY, NL27k_ASY and PPI5k_ASY

Fig.12 F-1 scores (%) and Accus. (%) of MUKGE and UKGE in relation fact classification on CN15k_ASY, NL27k_ASY and PPI5k_ASY. (a) is the F-1 scores of models on CN15k_ASY, NL27k_ASY and PPI5k_ASY; (b) is the Accus. of models on CN15k_ASY, NL27k_ASY and PPI5k_ASY

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