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Learning Context-based Embeddings for Knowledge Graph Completion

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| Apr 25, 2022

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Journal of Data and Information Science

Volume 7 (2022): Issue 2 (April 2022)

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Article Category: Research Paper

Published Online: Apr 25, 2022

Page range: 84 - 106

Received: Nov 03, 2021

Accepted: Mar 10, 2022

DOI: https://doi.org/10.2478/jdis-2022-0009

Keywords
Full expressiveness, Relational contexts, Knowledge graph embedding, Relation patterns, Link prediction

© 2022 Fei Pu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Testing the ability of inferring relation patterns on UMLS.

	UMLS

	Symmetry	Antisymmetry	Inversion	Composition
ComplEx	-	0.8806	0.8615	0.8732
Rotate	-	0.9065	0.9069	0.9141
HAKE	-	0.8558	0.8650	0.8723
LineaRE	-	0.9446	0.9441	0.9490
ContE	-	0.9644	0.9622	0.9645

Experimental results for Nations.

	Nations

	MRR	Hits@N

		1	3	10
TransE (Antoine et al., 2013)	0.4813	0.2189	0.6667	0.9801
DistMult (Yang et al., 2015)	0.7131	0.5970	0.7761	0.9776
ComplEx (Trouillon et al., 2016)	0.6677	0.5274	0.7413	0.9776
ConvE (Dettmers et al., 2018)	0.5616	0.3470	0.7155	0.9946
Rotate (Sun et al., 2019)	0.7155	0.5796	0.7985	1.0
HAKE (Zhang et al., 2020)	0.7157	0.5945	0.7786	0.9851
LineaRE (Peng & Zhang, 2020)	0.8146	0.7114	0.8881	0.9975
ContE	0.8412	0.7587	0.9179	1.0

Comparison of SOTA baselines and ContE model in terms of time complexity and number of parameters.

Models	#Parameters	Time Complexity
TransE	O(n_ed + n_rd)	O(d)
NTN	O(n_ed + n_rd²k)	O(d³)
ComplEx	O(n_ed + n_rd)	O(d)
TransR	O(n_ed + n_rdk)	O(dk)
SimplE	O(n_ed + n_rd)	O(d)
ContE	O(n_ed + 2n_rd)	O(d)

Summary on datasets.

Dataset	\|E\|	\|R\|	\|training\|	\|validation\|	\|test\|
FB15K-237	14,541	237	272,115	17,535	20,466
UMLS	135	46	5,216	652	661
Nations	14	55	1,592	199	201
Countries_S1	271	2	1,111	24	24
Countries_S2	271	2	1,063	24	24
Countries_S3	271	2	985	24	24

Experimental results for FB15K-237.

	FB15K-237

	MRR	Hits@N

		1	3	10
TransE (Antoine et al., 2013)	0.279	0.198	0.376	0.441
DistMult (Yang et al., 2015)	0.281	0.199	0.301	0.446
ComplEx (Trouillon et al., 2016)	0.278	0.194	0.297	0.45
ConvE (Dettmers et al., 2018)	0.312	0.225	0.341	0.497
ConvKB (Nguyen et al., 2018)	0.289	0.198	0.324	0.471
R-GCN (Schlichtkrull et al., 2018)	0.164	0.10	0.181	0.30
SimplE (Seyed & David, 2018)	0.169	0.095	0.179	0.327
CapsE (Nguyen et al., 2019)	0.150	-	-	0.356
Rotate (Sun et al., 2019)	0.338	0.241	0.375	0.533
ContE	0.3445	0.2454	0.3823	0.5383

Experimental results for UMLS.

	UMLS

	MRR	Hits@N

		1	3	10
TransE (Antoine et al., 2013)	0.7966	0.6452	0.9418	0.9841
DistMult (Yang et al., 2015)	0.868	0.821	-	0.967
ComplEx (Trouillon et al., 2016)	0.8753	0.7942	0.9531	0.9713
ConvE (Dettmers et al., 2018)	0.957	0.932	-	0.994
NeuralLP (Yang, Zhang, & Cohen, 2017)	0.778	0.643	-	0.962
NTP-λ (Rocktaschel et al., 2017)	0.912	0.843	-	1.0
MINERVA (Das et al., 2018)	0.825	0.728	-	0.968
KGRRS+ComplEx (Lin et al., 2018)	0.929	0.887	-	0.985
KGRRS+ConvE (Lin et al., 2018)	0.940	0.902	-	0.992
Rotate (Sun et al., 2019)	0.9274	0.8744	0.9788	0.9947
HAKE (Zhang et al., 2020)	0.8928	0.8366	0.9387	0.9849
LineaRE (Peng & Zhang, 2020)	0.9508	0.9145	0.9856	0.9992
ContE	0.9677	0.9501	0.9811	1.0

Parameters and scoring functions in SOTA baselines and in ContE model.

Model	Scoring function ψ(e₁,r,e₂)	Parameters
TransE	\|\|ν_e₁ + ν_r − ν_e₂\|\|_{_p}	ν_e₁, ν_r, ν_e₂ ∈ ℝ^d
ComplEx	$Re (< ν_{e_{1}}, ν_{r}, {\bar{ν}}_{e_{2}} >)$ {{ Re}} \left( { < {\nu _{{e_1}}},{\nu _r},{{\bar \nu }_{{e_2}}} > } \right)	ν_e₁, ν_r, ν_e₂ ∈ ℂ^d
SimplE	$\frac{1}{2} (< h_{e_{1}}, ν_{r}, t_{e_{2}} > + < h_{e_{2}}, ν_{r^{- 1}}, t_{e_{1}} >)$ {1 \over 2}\left( { < {h_{{e_1}}},{\nu _r},{t_{{e_2}}} > + < {h_{{e_2}}},{\nu _{{r^{ - 1}}}},{t_{{e_1}}} > } \right)	h_e₁, ν_r, t_e₂, h_e₂, ν_r⁻¹, t_e₁ ∈ ℝ^d
ConvE	$g (vec (g (concat ({\hat{v}}_{e_{1}}, ν_{r}) * Ω)) W) \cdot ν_{e_{2}}$ g\left( {vec\left( {g\left( {concat\left( {{{\hat v}_{{e_1}}},{\nu _r}} \right)*\Omega } \right)} \right)W} \right) \cdot {\nu _{{e_2}}}	ν_e₁, ν_r, ν_e₂ ∈ ℝ^d
ConvKB	concat(g([ν_e₁, ν_r, ν_e₂] * Ω)) · w	ν_e₁, ν_r, ν_e₂ ∈ ℂ^d
Rotate	\|\|ν_e₁ ○ ν_r − ν_e₂\|\|	ν_e₁, ν_e₂, ν_r, ∈ C^d
HAKE	\|\|ν_{e1_m} ○ ν_{r_m} − ν_{e2_m}\|\|₂	$ν_{e 1_{m}}, ν_{e 2_{m}} \in R^{d}, ν_{r_{m}} \in R_{+}^{d}$ {\nu _{e{1_m}}},{\nu _{e{2_m}}} \in {R^d},{\nu _{{r_m}}} \in R_ + ^d
HAKE	−λ \|\|sin(ν_{e1_p} + ν_{r_p} − ν_{e2_p})\|\|₁	ν_{e1_p}, r_p, ν_{e2_p} ∈ [0, 2π)^d
ContE	< f_r + ν_e₁, b_r + ν_e₂ >	ν_e₁, ν_e₂, f_r, b_r, ∈ ℝ^d

Experimental results for Countries.S2 and Countries.S3.

	Countries_S2				Countries_S3

	MRR	Hits@N			MRR	Hits@N

		1	3	10		1	3	10
TransE	0.6997	0.50	0.9375	1.0	0.1206	0.00	0.0833	0.3542
DistMult	0.7813	0.5833	1.0	1.0	0.2496	0.0625	0.333	0.6250
ComplEx	0.7934	0.6042	0.9792	1.0	0.2731	0.0833	0.3958	0.6667
Rotate	0.6979	0.4792	0.9583	1.0	0.1299	0.00	0.0833	0.4792
HAKE	0.6667	0.4583	0.8333	0.9583	0.2472	0.0625	0.3333	0.5417
LineaRE	0.7873	0.6458	0.9583	0.9792	0.2393	0.0625	0.3542	0.5208
ContE	0.8370	0.7292	0.9583	0.9792	0.4695	0.3542	0.5	0.625

Relation pattern modeling and inference abilities of baseline models.

Model	Symmetry	Antisymmetry	Inversion	Composition
TransE (Antoine et al., 2013)	×	✓	✓	✓
DistMult (Yang et al., 2015)	✓	×	×	×
ComplEx (Trouillon et al., 2016)	✓	✓	✓	×
SimplE (Seyed & David, 2018)	✓	✓	✓	×
ConvE (Dettmers et al., 2018)	−	−	−	−
ConvKB (Nguyen et al., 2018)	−	−	−	−
RotatE (Sun et al., 2019)	✓	✓	✓	✓
HAKE (Zhang et al., 2020)	✓	✓	✓	✓
KGCR (Pu et al., 2020)	✓	✓	✓	×
LineaRE (Peng & Zhang, 2020)	✓	✓	✓	✓
ContE	✓	✓	✓	✓

Experimental results for Countries.S1.

	Countries_S1

	MRR	Hits@N

		1	3	10
TransE (Antoine et al., 2013)	0.8785	0.7708	1.0	1.0
DistMult (Yang et al., 2015)	0.9028	0.8125	1.0	1.0
ComplEx (Trouillon et al., 2016)	0.9792	0.9583	1.0	1.0
Rotate (Sun et al., 2019)	0.8750	0.7708	1.0	1.0
HAKE (Zhang et al., 2020)	0.9045	0.8333	0.9792	1.0
LineaRE (Peng & Zhang, 2020)	1.0	1.0	1.0	1.0
ContE	1.0	1.0	1.0	1.0

Testing the ability of inferring relation patterns on Nations.

	Nations

	Symmetry	Antisymmetry	Inversion	Composition
ComplEx	-	0.6499	0.6487	0.6499
Rotate	-	0.6825	0.6970	0.6907
HAKE	-	0.6953	0.6835	0.6844
LineaRE	-	0.8189	0.8240	0.8333
ContE	-	0.8256	0.8326	0.8303

eISSN:: 2543-683X
Language:: English

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