Improving Temporal Knowledge Graph Completion via Tensor

Decomposition with Relation-Time Context and Multi-Time Perspective

Nam Le

1,2 a

, Thanh Le

1,2 b

and Bac Le

1,2 c

Faculty of Information Technology, University of Science, Ho Chi Minh City, Vietnam

Vietnam National University, Ho Chi Minh City, Vietnam

{lnnam, lnthanh, lhbac}@ﬁt.hcmus.edu.vn

Keywords:

Knowledge Graph Completion, Temporal Knowledge Graph, Tensor Decomposition, Relation-Time Context,

Fusion Feature Embedding.

Abstract:

Knowledge graphs have progressively incorporated temporal dimensions to effectively mirror the dynamism

of real-world data, proving instrumental in applications ranging from question answering to event predic-

tion. While the ubiquity of data incompleteness and well-established challenges of traditional knowledge

graph embedding techniques remain acknowledged, this paper propels the frontier of this research area.

We introduce Multi-Time Perspective Relation-Time Context ComplEx Embedding (MPComplEx), a ten-

sor decomposition-based completion temporal knowledge graph model that not only assimilates temporal and

relational interactions speciﬁc to timestamps but also integrates advanced time perspective features from the

recent TPComplEx models. Our experimental evaluations illustrate dramatic enhancements over conventional

models, achieving state-of-the-art performance on benchmark datasets with notable increments: 4.30%/4.79%

on ICEWS-14, 11.70%/11.48% on ICEWS-05-15, 21.50%/31.20% on YAGO15k, and 26.90%/66.09% on

GDELT in term of absolute/relative performance gains on mean reciprocal rank (MMR).

1 INTRODUCTION

In the contemporary era of information proliferation,

many applications are swiftly emerging, leveraging

the robust framework of Knowledge Graphs (KGs).

These applications range from recommendation sys-

tems (Chen et al., 2022) to temporal question answer-

ing (Mavromatis et al., 2022). KGs act as repositories

of real-world knowledge, encapsulating this informa-

tion in the structured form of tuples (subject, relation,

object). To continue mining how events are involved

in the timeline, Temporal Knowledge Graphs (TKGs),

which extend KG, are constructed by introducing a

temporal dimension to the representation of evolution

knowledge. They facilitate the meticulous tracking of

the evolution of events, encoding events as quadruples

(subject, relation, object, timestamp), with timestamp

denoted by either time point or time interval. For ex-

ample, a depicted TKG in Fig.1 illustrates Albert Ein-

stein’s tenure at ETH Zurich from 1912 to 1914.

Temporal Knowledge Graph completion (TKGC)

is a reasoning task that aims to make the prediction for

https://orcid.org/0000-0002-2273-5089

https://orcid.org/0000-0002-2180-4222

https://orcid.org/0000-0002-4306-6945

Figure 1: An example of a TKG is illustrated, with the task

of predicting a missing event depicted as a dashed line.

the missing events that have a high probability of oc-

curring, e.g., (Albert Einstein, collaborated, J. Robert

Oppenheimer, 1947-1955) shown in Fig. 1. Re-

cently, literature on this research ﬁeld has divided into

two main categories: (1) extrapolation-based model,

which aims to predict future events based on histor-

ical fact records such as RE-GCN (Li et al., 2021)

and DaeMon (Dong et al., 2023). (2) the remaining

interpolation-based model is TKG embedding models

(TKGE), which aim to predict missing events based

on evaluating the plausibility of potential events via

a scoring function with embedding vectors of enti-

326

Le, N., Le, T. and Le, B.

Improving Temporal Knowledge Graph Completion via Tensor Decomposition with Relation-Time Context and Multi-Time Perspective.

DOI: 10.5220/0013130500003890

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2025) - Volume 3, pages 326-333

ISBN: 978-989-758-737-5; ISSN: 2184-433X

ties, relations and their associated timestamps, includ-

ing TTransE (Leblay and Chekol, 2018), HyTE (Das-

gupta et al., 2018), and TA-DistMult (Garc

ıa-Dur

et al., 2018). This approach focuses on events that

have no constraint on the occurring order. This work

focuses on designing a TKGE model to tackle issues

of existing interpolation-based models.

The recent development in interpolation-based

models has signiﬁcantly improved performance for

this prediction task. Almost state-of-the-art mod-

els are based on tensor decomposition frame-

work (Trouillon et al., 2016) such as TCom-

plEx (Lacroix et al., 2019), TNTComplEx (Lacroix

et al., 2019), TPComplEx (Yang et al., 2024) and Mv-

TuckER (Wang et al., 2024). However, these mod-

els still face several challenges: (1) The ﬂexibility of

these models is limited; (2) Not utilizing temporal in-

formation to improve the quality of learning embed-

ding during model training; (3) The connection be-

tween relations and the timestamps attached to them

has not been fully exploited. To our best knowledge,

TPComplEx (Yang et al., 2024) is the ﬁrst model

to incorporate temporal information into the learning

model. Still, it does not consider the contribution of

this information to the score function. Furthermore,

temporal embedding and its additional are not linked

with relation embedding.

To address the challenges outlined above, we in-

troduce the Multi-Time Perspective Relation-Time

Context ComplEx Embedding (MPComplEx), a

novel model speciﬁcally designed to enhance the ﬂex-

ibility and performance of TKGC tasks within the ten-

sor decomposition framework. The signiﬁcance of

this model lies in its ability to capture the dynamic

nature of relations in knowledge graphs over differ-

ent periods, thereby improving the accuracy of tem-

poral knowledge graph completion tasks. We mainly

introduce adjustable weights for entities and addi-

tional time embeddings to obtain a more ﬂexible scor-

ing function, thereby increasing the model’s ﬂexibil-

ity in learning from any dataset and adapting to var-

ious tensor decomposition models. Furthermore, the

connection between temporal and relation embedding

is investigated and modeled as relation-time embed-

ding and incorporated with relation embedding via

weighted combination action, thus allowing the time

evolution information to join the decision process.

Compared to TPComplEx, our proposed model has

better generalization with the adjustable contribution

of time information for head and tail entities. More-

over, the new fusion representation for relation helps

enhance the embedded representation quality. The

main contributions of our work are summarized as

follows:

• We propose a novel temporal knowledge graph

completion model, MPComplEx, based on tensor

decomposition frameworks with weighted feature

combination strategy and incorporating the fea-

ture of connection between relation and its asso-

ciated timestamp.

• In the proposed model, we introduce weights as-

sociated with head and tail entities for control-

ling their behaviors. Besides that, the participants

of additional temporal embeddings are also con-

trolled similarly to capture multiple time perspec-

tives. Furthermore, the correlation of relation -

timestamp is modeled via a dot product and is

combined and weighted with relational embed-

ding to enhance the quality of learned embedding.

• Our experimental results on standard benchmark

datasets of TKGs show signiﬁcant improvements

over conventional models across all link predic-

tion metrics.

The remainder of our paper is organized as follows:

Section 2 introduces related works, focusing mainly

on TKGC models based on tensor decomposition.

Section 3 details our proposed model. Section 4 dis-

cusses the experimental setup, primary ﬁndings, and

ablation studies. Finally, Section 5 summarizes our

ﬁndings and outlines potential exciting directions for

future research.

2 RELATED WORK

Conventional KGE models, such as TransE (Bordes

et al., 2013) and ComplEx (Trouillon et al., 2016), try

to forecast connections by acquiring embeddings for

entities and predicates, hence evaluating the credibil-

ity of facts. These models have developed to effec-

tively process intricate relational patterns, with recent

innovations such as RotatE (Sun et al., 2019) specif-

ically designed to handle various relational patterns

such as symmetric and anti-symmetric relation pat-

terns.

Building upon this paradigm, TKGE models in-

tegrate temporal events to capture evolving relation-

ships. For instance, TTransE (Leblay and Chekol,

2018) incorporates relations and timestamps into a

uniﬁed space, enhancing the original TransE model.

HyTE (Dasgupta et al., 2018) applies a mapping

function to each timestamp, translating entities and

relations by adjusting them to a hyperplane. The

TeRo (Xu et al., 2020) model enhances entity embed-

dings by incorporating timestamps to represent tem-

poral progression. It utilizes relational rotations to

capture temporal dynamics. Recent models such as

Improving Temporal Knowledge Graph Completion via Tensor Decomposition with Relation-Time Context and Multi-Time Perspective

327

TA-DistMult (Garc

ıa-Dur

an et al., 2018) and TCom-

plEx (Lacroix et al., 2019) extended based on previ-

ous models based on tensor decomposition for static

data with more advantages to capture the time evolu-

tion. TA-DistMult decomposes timestamps into indi-

vidual tokens and incorporates them into relation rep-

resentations using Recurrent Neural Networks. Also,

TComplEx enhances the ComplEx model by utilizing

complex-valued vectors to handle relations that are

not symmetric. TimePlex (Jain et al., 2020b) lever-

ages the recurring nature of events to facilitate dy-

namic relational interactions. ChronoR (Sadeghian

et al., 2021) extends the RotatE model by connecting

timestamps with relations and seeing their combina-

tion as a rotational transformation. TPCompEx (Yang

et al., 2024) introduces modules incorporating distinct

temporal embeddings into things, considering various

time perspectives. However, dealing with events with

the same relation and co-occur takes work.

3 THE PROPOSED MODEL

Given temporal knowledge graph G = {Q ,E,R ,T },

where E, R , T , and Q respectively represent the sets

of entities, relations, timestamps, and quadruplets. A

quadruplet is denoted as (s,r,o,t), where r ∈ R rep-

resents the connection between a subject (head entity)

s ∈ E and an object (tail entity) o ∈ E at a speciﬁc

timestamp t ∈ T . In any TKG, the number of rela-

tions is much less than that of entities, so entity pre-

diction is more challenging than relation prediction.

Therefore, TKC tasks often focus on predicting miss-

ing entities in a given data set like (s,r,?,t) where ?

donates the missing element.

3.1 Baseline Models: TComplEx and

TPComplEx

This section examines two decomposition models,

TComplEx and TPComplex, for the TKC prob-

lem. In order to address the TKC problem, TCom-

plEx (Lacroix et al., 2019) is an augmented iteration

of the ComplEx decomposition model. This approach

uses complex vector embedding and Hermitian prod-

ucts to compute scores for a collection of four facts.

Its score function can be formulated as follows:

φ(s,r,o,t) = Re





(1)

where φ() denotes the scoring function, Re(.) re-

turns the real vector component for input embed-

ding; C

∈ R

2×d

denotes the complex em-

bedding with embedding rank d for subject, relation,

object, and timestamp, respectively. Recently, TP-

ComplEx (Yang et al., 2024) investigated that TCom-

plEx can not handle inversion relation on timestamp,

i.e., its temporal complex embedding will degenerate

to the real or imaginary part if this relation type ex-

ists. Introducing additional temporal complex embed-

dings shows the potential in modeling relations with

the property of simultaneousness. Its score function

can be formulated as follows:

φ(s,r,o,t) = Re





(2)

where C

is the temporal embedding, and C

are

additional temporal embedding for subject and object,

respectively.

Based on these theoretical considerations, TP-

ComplEx possesses the capability to represent rela-

tional patterns that adhere to the property of simulta-

neousness (see (Yang et al., 2024, Deﬁnition 3)). Of-

ten, the limitations obtained for temporal embedding

are excessively stringent. In addition, according to

our observations, TPComplEx fails to consider the re-

lationship between a given relation and the time com-

ponent, which might signiﬁcantly impact the ability to

reason about missing links in graph data. In the fol-

lowing section, we present a detailed and systematic

guide to implementing our proposed strategy, which

offers more signiﬁcant potential in integrating diverse

perspectives of time and the underlying connections

between relation and its associated timestamps.

3.2 Fusing Relation-Time Context and

Time Properties

Following the methodology of TPComplEx, we

incorporate additional temporal embeddings into

TComplEx with control variables α

,α

∈ R

∪ {0}

and β

,β

∈ R

∪ {0} for subject and object embed-

ding, respectively. Consequently, the score function

becomes:

(s,r,o,t) = φ

base

(s,r,o,t)+ G

)

+ G

) + G

(3)

where φ

base

(s,r,o,t) = Re



,β



, C

represents the temporal embedding, while C

denote additional temporal embeddings. The weights

{α

,β

,} are associated with the subject and object

embeddings, respectively. And {α

,β

} correspond

to the additional temporal embeddings C

, and C

respectively. For C

embedding, we will handle it

later to simplify the model structure.

For subject and object aggregation (see (Yang

et al., 2024, Deﬁnition 4)), we deﬁne two ﬁrst addi-

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

328

Table 1: Model parameters and embedding ranks for our baselines and proposed models.

Models Parameters ICEWS14 ICEWS05-15 YAGO15k GDELT

ComplEx 2d(|E| + 2|R |) 1820 860 1960 3820

TComplEx 2d(|E| + |T | + 2|R |) 1740 1360 1940 2270

TPComplEx 2d(|E| + 3|T | + 2|R |) 1594 886 1892 1256

MPComplEx 2d(|E| + 3|T | + 2|R |) 1500 800 1500 1200

tional embeddings as:

) = Re



,α



, (4)

) = Re



,β



. (5)

And for modelling the associated relation and times-

tamp (see (Yang et al., 2024, Deﬁnition 5)), we can

formulate G

) = Re(

⟨

⟩

). To simplify

the model structure, the additional embedding C

can

be deﬁned as C



,β



. Thus, we have:

) = Re



,α

,β



. (6)

To construct the score function, we put Eq. 4, 5

and 6 into the Eq. 3. Thus, we obtain a new score

function, which is deﬁned as:

(s,r,o,t) = φ

base

(s,r,o,t)

+ Re



,β

,α



+ Re



,β



+ Re



,α

,β



(7)

Simplifying the above expression, we have:

(s,r,o,t) = Re





(8)

where C

= α

+ α

, C

= β

+ β

. This

version is called eTPComplEx (extended TPCom-

plEx). Clearly, when α

= α

= β

= 1, Eq. 8

becomes the score function of TPComplEx.

To capture the interaction between relation em-

bedding and temporal embedding, we design a new

embedding that can model the interaction between

them. This embedding, referred to as the relation-time

context embedding, is denoted by C

⟨

⟩

. Uti-

lizing this embedding, we then construct a score func-

tion with previous deﬁned additional temporal em-

bedding C

, C

and C

as follows:

(s,r,o,t) = φ

base

(s,r,o,t)+ G

(α

)

+ G

(β

) + G

(9)

By expanding the above score function similar to

Eq. 7, we have the score function when using relation-

time context embedding as follows:

(s,r,o,t) = Re





(10)

This version is called cTPComplEx (relation-time

context TPComplEx).

By combining the weighted score functions from

Eq. 10 and Eq. 8, we derive a more generalized score

function, which is formulated as follows:

φ(s,r,o,t) = φ

(s,r,o,t)+ (1 − γ)φ

(s,r,o,t)

= Re





(11)

where the combined embedding C

is deﬁned as

= γC

+ (1 − γ)C

. Here, γ is the weight factor

that balances the percentage of features of the relation

derived from C

and the relation-time context embed-

ding C

. This version is named MPComplEx.

Clearly, when α

= α

= 1, β

= β

= 0, γ = 1, the

score function in Eq. 11 becomes the score function

of TComplEx. Moreover, in the case of α

= α

= β

= 1, γ = 1, the score function of MPComplEx

becomes the score function of TPComplEx.

3.3 Optimization

Following the methodologies outlined in (Lacroix

et al., 2019; Yang et al., 2024), we compute the in-

stantaneous multi-class loss for each training quadru-

ple (s,r,o,t) as follows:

L = −φ(s, r, o,t) + log







∑

′

̸=o

′

∈E

exp



φ(s,r,o

′



)







(12)

where φ(.) represents the score function. In addition,

we include a regularization term, L

reg

. Therefore, the

ﬁnal loss function used for training is given by:

total

= L + L

reg

. (13)

Similarly to TPComplEx (Yang et al., 2024), our

model incorporates entities with temporal bias into

the regularization process and adopts N3 regulariza-

tion as deﬁned by (Lacroix et al., 2019). The regular-

ization function is expressed as:

reg

= λ



∥



+ λ

∥

(14)

where λ

and λ

are the regularization weights for

the entity-relation and temporal embeddings, respec-

tively.

Improving Temporal Knowledge Graph Completion via Tensor Decomposition with Relation-Time Context and Multi-Time Perspective

329

Table 2: Statistic information of four standard benchmark datasets. The ﬁrst three columns present the number of entities,

relations, and timestamps, and remain columns present the number of quadruples for each dataset.

Dataset #Entities #Relations #Timestamps #Train #Validation #Test

ICEWS14 7128 230 365 72,826 8941 8963

ICEWS05-15 10,488 251 4017 386,962 46,275 46,092

YAGO15k 15,403 34 198 110,441 13,815 13,800

GDELT 500 20 366 2,735,685 341,961 341,961

3.4 Computational Complexity

Table 1 presents the computational complexity of em-

bedding models through the number of parameters re-

quired for training and the embedding ranks or dimen-

sions. It demonstrates that our models maintain the

same parameter count as other tensor decomposition-

based TKGC models, such as TComplEx and TP-

ComplEx.

4 EXPERIMENTS AND RESULTS

4.1 Experiment Setup

4.1.1 Standard Benchmark Datasets

During the experiment process, four standard bench-

mark datasets of TKGs are used, namely ICEWS14,

ICEWS05-15, YAGO15k (Garc

ıa-Dur

an et al., 2018),

and GDELT (Trivedi et al., 2017). Table 2 summa-

rizes the details of the four datasets.

4.1.2 Baselines

We evaluate our proposed models by comparing them

to previous well-performed TKGE models that are

considered to be at the forefront of the ﬁeld, in-

clude: TTransE (Leblay and Chekol, 2018); TCom-

plEx, TNTComplEx (Lacroix et al., 2019); Time-

Plex (Jain et al., 2020a); ChronoR (Sadeghian et al.,

2021); TeLM (Xu et al., 2021); BTDG (Lai et al.,

2022); TBDRI (Yu et al., 2023); SANe (Li et al.,

2024); MTComplEx (Zhang et al., 2024); TPCom-

plEx (Yang et al., 2024); MvTuckER (Wang et al.,

2024). Our model is based on TPComplEx, are de-

signed to improve performance while maintaining the

same number of embedding parameters.

4.1.3 Metrics and Implementation Details

To evaluate our proposed model, after ranking all the

candidates according to their scores calculated by the

scoring function, we employ two metrics that are used

widely in temporal knowledge graph research includ-

ing Mean Reciprocal Rank (MRR), and Hit@k. The

higher MRR and Hits@n indicate better performance.

Our models are based on TComplEx (Lacroix et al.,

2019) and TPComplEx (Yang et al., 2024), utilizing

the PyTorch library (Paszke et al., 2019) and running

on NVIDIA GeForce RTX 3070 8Gb VRAM. Fol-

lowing the methodologies of TPComplEx, we tune

our models using grid search to optimize hyperpa-

rameters based on validation dataset performance.

Control variables for entity embeddings, such as

,α

,β

, are adjusted within {1, 1.5, 2, 2.5},

while those for relation embedding, γ, range from

{0, 0.25, 0.5, 0.75, 0.85, 0.95}. Regularization rates

and λ

are set within {0.1, 0.01, 0.001, 0.0001,

0.00001}. During training, we maintain a consistent

batch size of 1000 and employ Adagrad (Duchi et al.,

2011) to optimize our model with a ﬁxed learning rate

of 0.1 across all datasets. Our source codes is avail-

able at https://github.com/lnhutnam/MPComplEx.

4.2 Comparative Study

To evaluate the capabilities of MPComplEx, we con-

ducted a comparative assessment against the current

state-of-the-art TKGC models, with results presented

in Table 3. The performance metrics for all baseline

models were directly sourced from the original pa-

per on TPComplEx. Our ﬁndings indicate that the

proposed model consistently outperforms all baseline

models across the four evaluation datasets. Specif-

ically, compared to the top-performing model, TP-

ComplEx, our proposed approach demonstrates sig-

niﬁcant improvements across all metrics. The differ-

ences between our MPComplEx model and TPCom-

plEx are quantiﬁed through absolute performance

gains (APG) and relative performance gains (RPG).

In terms of APG, our model achieves improvements

of 4.3%, 11.7%, 21.5%, and 26.9% on MRR and

6.6%, 16.3%, 24.8%, and 30.1% in Hit@1 for the

ICEWS14, ICEWS05-15, YAGO15k, and GDELT

datasets, respectively. Moreover, with RPG, our

model achieves 4.79%, 11.48%, 31.20%, and 66.09%

on MRR and 7.63%, 17.38%, 38.10%, and 91.49%

on Hit@1 on these datasets.

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

330

Table 3: Experiment results on the ICEWS14, ICEWS05-15, YAGO15k, and GDELT datasets. The highest score is high-

lighted in bold, and the second-best score is underlined. The absolute performance gains (APG) and the relative performance

gain (RPG) indicate the performance improvement of our model compared with the best-performing baseline TPComplEx.

APG and RPG are calculated by APG = R

ours

− R

baseline

and RPG = (R

ours

− R

baseline

)/R

baseline

where R

ours

and R

baseline

are the results of our model and baseline TPComplEx, respectively.

Model

MRR ↑ Hit@1 ↑ Hit@10 ↑ MRR ↑ Hit@1 ↑ Hit@10 ↑

ICEWS14 ICEWS05-15

TTransE (Leblay and Chekol, 2018) 0.255 0.074 0.601 0.271 0.084 0.616

TComplEx (Lacroix et al., 2019) 0.610 0.530 0.770 0.660 0.590 0.800

ChronoR (Sadeghian et al., 2021) 0.625 0.547 0.773 0.675 0.596 0.820

TeLM (Xu et al., 2021) 0.625 0.545 0.774 0.678 0.599 0.823

BTDG (Lai et al., 2022) 0.601 0.516 0.753 0.627 0.534 0.798

TBDRI (Yu et al., 2023) 0.652 0.552 0.785 0.709 0.646 0.821

SANe (Li et al., 2024) 0.638 0.558 0.782 0.683 0.605 0.823

MTComplEx (Zhang et al., 2024) 0.629 0.548 0.782 0.675 0.592 0.822

TPComplEx (Yang et al., 2024) 0.898 0.865 0.954 0.845 0.794 0.934

MvTuckER (Wang et al., 2024) 0.654 0.577 0.797 0.698 0.618 0.841

MPComplEx (Ours) 0.941 0.931 0.957 0.962 0.957 0.974

APG (%) ↑ 4.30 6.60 0.30 11.70 16.30 4.00

RPG (%) ↑ 4.79 7.63 0.31 11.48 17.38 2.78

YAGO15k GDELT

TTransE (Leblay and Chekol, 2018) 0.321 0.230 0.510 0.115 0.000 0.318

TComplEx (Lacroix et al., 2019) 0.360 0.280 0.540 0.298 0.213 0.464

ChronoR (Sadeghian et al., 2021) 0.366 0.292 0.538 - - -

TBDRI (Yu et al., 2023) 0.368 0.301 0.554 0.269 0.164 0.441

SANe (Li et al., 2024) - - - 0.301 0.212 0.476

TPComplEx (Yang et al., 2024) 0.689 0.651 0.762 0.407 0.329 0.559

MvTuckER (Wang et al., 2024) - - - 0.549 0.477 0.682

MPComplEx (Ours) 0.904 0.899 0.914 0.676 0.630 0.762

APG (%) ↑ 21.50 24.80 15.20 26.90 30.1 20.30

RPG (%) ↑ 31.20 38.10 19.95 66.09 91.49 36.31

These experimental results demonstrate the ef-

fectiveness of incorporating weighted combinations

of additional temporal embeddings with their cor-

responding subject and object embeddings, which

signiﬁcantly enhances the ﬂexibility of our model

compared to TPComplEx. Furthermore, integrating

weighted time-relational features into relation em-

bedding has allowed the proposed model to substan-

tially improve over TPComplEx, particularly in cases

where the facts recorded by each timestamp are few

or unique, as observed in the YAGO15k dataset. Ad-

ditionally, for datasets with fewer entities and rela-

tions but a large number of facts, such as GDELT,

our model exhibits scalability with large-scale data,

requiring fewer hyperparameters than previous ten-

sor decomposition models like ComplEx, TComplEx

or TPComplEx while still delivering notable perfor-

mance across various evaluation metrics.

4.3 Ablation Study

4.3.1 Analysis of the Effects of Relation-Time

Context Features

To assess the effectiveness of relation-time features,

we varied the proportion of these features by adjusting

the hyperparameter γ. A value of γ = 1 corresponds

to using only the original relation embedding, while

γ = 0 indicates exclusive use of the relation-time fea-

ture embedding. The results, shown in Table 4, show

that relation-time features make the proposed model

better by an average of 0.76% across four datasets

compared to the model that does not use these fea-

tures. However, in the GDELT dataset, these features

do not signiﬁcantly impact performance. This out-

come highlights the challenges in optimally tuning

control variables for original relations and relation-

time features.

Improving Temporal Knowledge Graph Completion via Tensor Decomposition with Relation-Time Context and Multi-Time Perspective

331

Table 4: The inﬂuence of relation-time context features on the datasets.

Case study

MRR ↑ Hit@1 ↑ Hit@10 ↑ MRR ↑ Hit@1 ↑ Hit@10 ↑

ICEWS14 ICEWS05-15

Only relation-time 0.923 0.912 0.940 0.930 0.920 0.948

W/o relation-time 0.920 0.910 0.940 0.946 0.939 0.963

Fusion features 0.941 0.931 0.957 0.962 0.957 0.974

YAGO15k GDELT

Only relation-time 0.794 0.774 0.834 0.719 0.680 0.793

W/o relation-time 0.774 0.752 0.815 0.719 0.680 0.793

Fusion features 0.904 0.899 0.914 0.676 0.630 0.762

Figure 2: Visualization of the effect of α

,α

,β

,γ for

MPComplEx on the ICEWS14, ICEWS05-15, YAGO15k,

and GDELT datasets.

4.3.2 Analysis of the Effects of Weight

Combinations

The proposed model incorporates weights for com-

bining entity embeddings with additional temporal

embeddings, speciﬁcally α

,α

,β

, and relation

embeddings with relation-time embeddings, denoted

by γ. To evaluate the impact of these weights on

model performance, we conduct experiments with

different weight combinations across four datasets:

ICEWS14, ICEWS05-15, YAGO15k, and GDELT.

The results are presented in Fig. 2 which each hyper-

parameter combination has order α

,α

,β

,γ. For

the ICEWS14, ICEWS05-15, and GDELT datasets,

the MPComplEx model consistently improves across

all evaluation metrics as the weight values increase,

with optimal performance observed when the relation

embedding weight is set to γ = 0.5. In contrast, for the

YAGO15k dataset, smaller weight values yield sub-

optimal results. However, when the weights are set

to 2.5 or higher, coupled with a relation embedding

weight of γ = 0.75, the model exhibits signiﬁcant per-

formance gains, achieving its highest performance.

5 CONCLUSIONS

This paper introduces the Multi-Time Perspective

Relation-Time Context ComplEx Embedding model

(MPComplEx), which addresses several key chal-

lenges of interpolation models based on tensor de-

composition. By incorporating additional ﬂexible

temporal embeddings with adjustable weights, our

model enhances ﬂexibility and improves the ability

to capture various time perspective properties while

maintaining computational efﬁciency with a ﬁxed

number of parameters compared to baseline models.

Especially, the correlation between relation embed-

dings and their corresponding timestamps is modeled

and integrated with weighted contributions into the

scoring function, thereby enhancing the quality of re-

lation embeddings through temporal information and

improving prediction results. Looking ahead, fur-

ther exploration of the model’s potential in managing

cross-temporal patterns and addressing the challenge

of extrapolation presents promising directions for fu-

ture research.

ACKNOWLEDGEMENTS

This research is supported by research funding from

Faculty of Information Technology, University of Sci-

ence, Vietnam National University - Ho Chi Minh

City.

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

332

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