Multi-Relational and Social-Influence Model for Predicting Student Performance in Intelligent Tutoring Systems(STI)

Abstract

Recent studies have shown that Matrix Factorization (MF) method, deriving from recommendation systems, can predict student performance as part of Intelligent Tutoring Systems (ITS). In order to improve the accuracy of this method, we hypothesize that taking into account the mutual influence effect in the relations of student groups would be a major asset. This criterion, coupled with those of the different relationships between the students, the tasks and the skills, would thus be essential elements for a better performance prediction in order to make personalized recommendations in the ITS. This paper proposes an approach for Predicting Student Performance (PSP) that integrates not only friendship relationships such as workgroup relationships, but also mutual influence values into the Weighted Multi-Relational Matrix Factorization method. By applying the Root Mean Squared Error (RMSE) metric to our model, experimental results from KDD Challenge 2010 database show that this approach allows to refine student performance prediction accuracy.

Full text

International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249 – 8958, Volume-9 Issue-3, February, 2020
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: 10.35940/ijeat.C5169.029320
 Abstract: Recent studies have shown that Matrix Factorization
(MF) method, deriving from recommendation systems, can predict
student performance as part of Intelligent Tutoring Systems (ITS).
In order to improve the accuracy of this method, we hypothesize
that taking into account the mutual influence effect in the
relations of student groups would be a major asset. This criterion,
coupled with those of the different relationships between the
students, the tasks and the skills, would thus be essential elements
for a better performance prediction in order to make personalized
recommendations in the ITS. This paper proposes an approach for
Predicting Student Performance (PSP) that integrates not only
friendship relationships such as workgroup relationships, but also
mutual influence values into the Weighted Multi-Relational
Matrix Factorization method. By applying the Root Mean Squared
Error (RMSE) metric to our model, experimental results from
KDD Challenge 2010 database show that this approach allows to
refine student performance prediction accuracy.
Keywords : Matrix Factorization, Student Performance
Prediction, Intelligent Tutoring System, Social-Influence,
Recommender Systems.
I. INTRODUCTION
Intelligent Tutoring Systems development began in the
1970s with the goal to improve Computer-Assisted Learning
(CAL). STI-driven progress needed to be operationalized
through the use of Artificial Intelligence (AI) methods to
provide highly personalized feedback-based education
tailored to the needs of the students. Their aim is to support
learning by simulating the teaching skills and field expertise
Revised Manuscript Received on January 22, 2020.
Kouamé Abel ASSIELOU, Laboratoire de Recherche en Informatique
et Télécommunication (LARIT), Institut National Polytechnique Felix
HOUPHOUET Boigny (INP-HB), Yamoussoukro, Côte d'Ivoire.
kouame.assielou@inphb.ci
Cissé Théodore HABA, Department of Training and Research of
Electrical & Electronics Engineering, Institut National Polytechnique Felix
HOUPHOUET Boigny (INP-HB), Yamoussoukro, Côte d'Ivoire.
cissetheodore@yahoo.fr
Tanon Lambert KADJO, Laboratoire de Recherche en Informatique et
Télécommunication (LARIT), Institut National Polytechnique Felix
HOUPHOUET Boigny (INP-HB), Yamoussoukro, Côte d'Ivoire.
nonatipv6@yahoo.fr
Kouakou Daniel YAO, Laboratory of studies and prevention in
Psychoeducation (LEPPE-ENS), University Jean Lorougnon Guédé, Daloa,
Côte d'Ivoire, yahaudan@gmail.com
Bi Tra GOORE, Laboratoire de Recherche en Informatique et
Télécommunication (LARIT), Institut National Polytechnique Felix
HOUPHOUET Boigny (INP-HB), Yamoussoukro, Côte d'Ivoire.
bitra.goore@gmail.com
of hu-man tutors and to produce the same kind of learning
and flexibility between teachers and students [1]. An ITS is
made up of three domains: Computer Science, Psychology
and Education. Specifically, (i) artificial intelligence explains
how to reason about intelligence and therefore about
learning, (ii) psychology (cognitive science) explains how
people think and learn, and (iii) education is about center on
the best way to support teaching / learning [2]. Although,
there are different Intelligent Tutorial Systems with different
architectures, their basic architecture has four components
(modules / models) that are (see Figure 1):
 a Domain-Model that defines the content to be taught;
 a Tutoring Model that defines how to teach;
 a Student-Model that can personalize the learning taking
into account this one;
 an Interface-Model that defines the visible means
allowing the interrelation be-tween student and the
system.
Fig. 1. Classic Intelligent Tutoring System architecture
The Student Model is an important component for more
than one reason in any ITS. It can guide the interactions
between the student and the system. Student modeling is used
to represent student's knowledge evolution, to predict his /
her performance for different skills over time [3] and to
determine the next content to present to the student to give
continuity to his learning [4]. This modeling is also important
for re-searchers as it provides
them with practical information
to make decisions about how to
adapt the learning experience to
Multi-Relational and Social-Influence Model for
Predicting Student Performance in Intelligent
Tutorin
g
S
y
stems (ITS)
Kouamé Abel ASSIELOU, Cissé Théodore HABA, Tanon Lambert KADJO,
Kouakou Daniel YAO, Bi Tra GOORE
Tutoring Model Student
Model
Domain
Model
Interface
Student

Multi-Relational and Social-Influence Model for Predicting Student Performance in Intelligent Tutoring Systems (STI)
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student’s needs. Thus, in order to determine the next content
to be displayed and specially to adapt the learning, it is
important for the current systems, to have a precision of the
students’ performances prediction. The prediction of student
performance is therefore a relevant issue and a major asset for
improving learning in all ITS.
In this contribution, we want to solve the PSP problem by
proposing a weighted multi-relational matrix factorization
model that takes advantage of student-workgroup
relationships with the consideration of Student Individual
Influence Effect. We seek to provide our model with
significant data to improve the accuracy of student
performance predicting.
The organization of our paper is as follows: Section 2
provides the state-of-the-art techniques used for predicting
student performance. Section 3 presents, in turn, the classical
matrix factorization techniques while section 4 describes our
multi-relational approach to predict student performance.
Section 5 presents an evaluation of this approach and
discusses our results with those of the state-of-the-art.
Section 6 concludes the paper.
II. STATE-OF-THE-ART AND RELATED WORK
Personalized learning has the potential to improve learning
process and overall learning outcomes [5][6]. This
customization can be achieved through learning content
adaptation and the application of an individualized learning
strategy. Therefore, it is important for current ITS to have not
only relevant information about students but also to predict
their performance at each stage of their learning.
In the associated scientific literature, there is a wide variety
of work related to Student Performance Predicting. Most of
them are based on traditional methods such as Knowledge
Tracing (KT) [7], linear regression [8], logistic regression
[9], k-NN algorithms [10], support vector machines [11][12]
[13][14], decision trees [15][16], neural networks [17][18].
Recently, some authors such as Thai-Nghe and al., [19]
[20] proposed to use techniques from the recommendation
systems, in this case the Matrix Factorization (MF), for
student performance prediction. The PSP problem could be
considered as that of the prediction of an evaluation. From
this perspective, the student, the task and the performance
would become the user, the article and the evaluation
respectively as presented in the classical recommendation
systems. These researchers showed that the use of this
technique could improve prediction results over regression
methods by relying on past stu dent per formanc e. Othe r works
like those done in [21] have shown that the MF method can
be applied to students' raw scores by taking into account the
notes in an interval of 0 and 100 instead of 0 and 1 as the
work done in the literature. In [22][23], the authors proposed
to improve this method by integrating the temporal effect as
the students' knowledge improves over time. Experimental
results show that the proposed approaches are promising.
However, these works considered only one relation: that
existing between the student and the task to be realized. To
extend the predictive efficiency of this method, the authors
Thai-Nghe and al., [24] proposed to explore multiple
relationships that may exist between students, tasks and their
metadata using Multi-Relational Matrix Factorization model
(MRMF). They also propose a Weighted Multi-Relational
Matrix Factorization (WMRMF) model to take into account
the main relationship that contains the target variable. The
authors Nedungadi et al., [25] propose, in addition to the
Multi-Relational factor, to integrate the student's bias, which
is defined by the probability that a student performs task and
task's bias that can reflect the degree of difficulty of the task.
However, these methods have not benefited from social
relationships that can be integrated. They ignored significant
connections between students (registered in workgroups, for
example), which is not in line with real-world observations. It
has been shown, in fact, that group work promotes
collaboration among students to achieve common learning
goals and increases their performance, perseverance, and
attitudes [26][27].
With the advent of social networks, social networking
approaches to online referral are growing. These approaches,
such as those proposed in [28][29][30], assume the existence
of a social network among the users to make
recommendations to a user on the basis of the evaluations of
users having direct or indirect social relations with the given
user. In [31], the authors Thanh-Nhan and al., Propose
precisely an approach to integrate the social relations of the
users / students (for example, a friend of class) in the classic
MF. The results show that this approach makes it possible to
take advantage of student-to-model relationships and thereby
improve forecasting results. However, this approach does not
exploit the individual influence factor of group members. It
does not exploit the different relationships between students,
tasks and their metadata either.
In order to extend the functions of existing systems,
Lukasenko [6] aims to define a complete content of a student
model that can be taken into account by the intelligent and
adaptive functions of knowledge assessment systems and
learning. This empirical model contains categories of
information such as: contact information, learning style,
student current state (mood, mental state, physiological state)
current level of knowledge and skills, objectives, learning
progress, learning material used, user interface
configuration... This point of view is shared by the authors
Bicans and al., [32] who propose the automatic addition of
students learning style in the computer learning systems in
general.
In this paper, we propose MRMF and WMRMF
approaches that aggregate not only friendships with
integration of the influence effect, but also relationships
be-tween students, tasks, and their metadata, so improve the
accuracy of PSP in ITS.
III. MATRIX FACTORIZATION APPROACHES
A. Classical Matrix Factorization (MF) method
Let Sdenote a set of students, I a set of tasks and
P
a
range of possible performance scores. According to the
literature of recommendation systems models [33][25], the
"student-performs-task" matrix R, considering a single
attribute, can be approximated
by a product of two small
matrices 1
W (student) and 2
W

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(task). Let 12
T
RWW, as illustrated in Figure 2. In this
relation, 1
SF
W
 is a matrix where each line s is a vector
containing the F latent factors describing the student s and
2
I
F
W
 is a matrix where each line i is a vector containing
the F factors latent describing the task i. Let 1
s
w and 2i
w be
the respective vectors of the matrices 1
W and 2
W such that
their elements are designated by 1
s
f
w and 2if
w. A student s
performance for a task i in the framework of MF technique
can be predicted by:
12 12
1
ˆ
s
fif si
FT
si f
pwwww


 (1)
Fig. 2. Example of matrix factorization for the « student-perform-task » relation.
ˆ
s
i
p is the predicted performance value. 1
W and 2
W are
the model parameters (latent factor matrices) or factor
matrices. These matrices can be learned by optimizing the
objective function (2) from a criterion, such as Root Mean
Square Error (RMSE), using the stochastic gradient descent
method as suggested in [34].




222
12 1 2
(,)
si
MF T
si FF
si R
ORwwWW


 
 (2)
With 2
.
F
being the Frobenius standard;

01



is a regularization term used to avoid over-adjustments. In
other words,

is a parameter that make a compromise
between the approximation error and the Frobenius norm of
the model [33]. Let
s
i
e denote the difference between the
real performance value and the predicted performance value
for each couple (student, task):


12
si
T
si si
eRww (3)
s
i
R represents the real value of the student's
performance for task i.
B. Multi-Relational Matrix Factorization Method
(MRMF)
The MF model refers to a single type of unique
relationship linking two types of entities. Let us consider a set


1,..., N
EE
of N types of entities connected by M types of
relations


1,..., M
R
R which can be strongly correlated with
each other. Let 12
, ,..., n
WW W(n ∈N) be the latent factor
matrices (designating the model parameters) of each of the
entity types. These latent factors describe the entity and are
constructed by considering each relationship to which the
entity is associated. Taking into account the several relations
of the domain, the objective function is given by [35] [24]
[36]:

22
12
1( ,) 1
si s i
r
MN
MRMF T
rrr n
F
rsiR n
ORwwW

 




 
(4)
With






12
;1...
rrr
REErM
.
When learning model parameters, each factor matrix is
updated according to all the relationship types it implies until
a common convergence is reached [8] or the maximum
number of pre-defined iterations is achieved.
C. Weighted Multi-Relational Matrix Factorization
method (WMRMF)
Assuming some relationships have more weight
compared to others, a

weight factor is added to the MRMF
model. The objective function thus becomes [24] [36] [37]:

22
12
1(,) 1
si s i
r
MN
WMRMF T
rrrr n
F
rsiR n
Rww W

 

  


 
(5)
The weight function may be defined as follows:
1,
, (0 1)
r
if r is the main relationship
if




 (6)
For the learning process, the WMRMF model updates its
latent factors using equations (7) and (9):
11
1
WMRMF
sk sk
sk
rr r
O
ww w








(7)

Multi-Relational and Social-Influence Model for Predicting Student Performance in Intelligent Tutoring Systems (STI)
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22
2
WMRMF
ik ik
ik
rr r
O
ww w








(8)
With

that is the learning rate. By determining the
gradients
1
WMRMF
sk
r
O
w

 and
2
WMRMF
ik
r
O
w

 , we finally obtain:

11 2 1
2
sk sk si ik sk
rr rrr r
ww ew w

  (9)

22 1 2
2
ik ik si sk ik
rr rrr r
ww ew w

  (10)
IV. PROPOSED APPROACH
We propose a multi-relational factorization approach that
can integrate not only friendship relationships such as
workgroup relationships, but also mutual influence values.
The proposed methods are named So-MRMF
(Multi-Relational Matrix Factorization and Social) and
So-WMRMF (Weighted Multi-Relational Matrix
Factorization and Social)
A. Problem formulation
Our approach is essentially based on the work done in [31].
We propose a multi-relational approach integrating
workgroup relationships. In this approach, we consider the
relationship « student-performs-task » as the main
relationship. Figure 3 presents in the form of
entity-association diagram, the information that we take into
account in our model. At the completion of a task by the
student, we associate a performance score and the number of
indices requested by the student. To properly solve task, the
student must know specific skills, and the task itself is also
associated with the skills to be learned by the student.
"Occurrence" attribute gives the number of times the student
has learned the skill.
Fig. 3. Entity-association diagram for student performance prediction
B. Relationship matrix with social influence effect
In addition to the different relationships previously
explored, our approach combines student friendly
relationships such as workgroup relationships. The friendship
network can essentially be modeled using a confidence graph
of Figure 4 (a) or using a confidence matrix as shown in
Figure 4 (b). In the confidence graph shown in Figure 4(a), 5
students (nodes, from S1 to S5) are connected to each other at
8 relationships (edges), and each relation is associated with a
weight Ts,u (influence value) in interval ] 0;1]. Ts,u is the
influence value of student
s
uN (
s
N being all student s
friends) on student s. Thus, the influence value of the student
S4 on student S1 is equal to 0.2 while that of the student S5 on
the student S1 is equal to 0.5. For S2, S1 has more influence on
his learning than S4.
Fig. 4. Example of trust relationships
Unlike the work done in [31], our matrix T is not binary;
the value Ts,n has rather a social influence effect belonging to
the interval ]0 ;1]. The value 1 corresponds to the influence
Ts,s that a student s has on himself. We hypothesize that the
student has more impact on their own learning process than
others have on him. This value taken is equal to 1. An
influence value Ts,n = 0 means that there is no relationship of
friendship between the student s and the student n.
By integrating the fact that the behavior of a student s is
affected by his direct neighbors [31][38], likewise, s
characteristic vector depends on the characteristic vectors of
its direct neighbors. This formulation is given by:
,1
1
,
ˆ
u
s
s
s
su
uN
su
uN
Tw
wT




 (11)
Where 1
ˆ
s
w is the estimated characteristic vector (latent
factor vectors) of student s, given the characteristic vectors of
his direct neighbors. The graphical model of Figure 5 is an
example representing the integration of the confidence matrix
through latent factor matrix W.
Performs
Student Task
Skill
Re
q
uires
Descriptions
Descriptions
Has Has
Performance
Has learnt
Occurrence
H
as
friends
Influence
S4 S5
S2 S3
S1
0.2
0.5
0.3
0.7
0.1
0.7
0.2
0.4
T S1 S2 S3 S4S5
S1 1 0.2 0.5
S2 0.7 1 0.3
S3 0.1 1
S4 0.4 1 0.2
S5 0.4 1
a) Trusted graph b) Trusted Matrix

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Fig. 5. Graphic model of performance prediction technique with
social influence
T

is a regularization term (regularization weight) that
will be added to normalize objective function terms. By
replacing 1
s
w by 1
ˆ
s
w in equation (1), for predicting
student s performance, we obtain:
12 12
1
ˆˆ ˆ
s
fif si
FT
si f
pwwww


 (12)
C. Multi-Relational Matrix Factorization and
Social-influence approach (So-MRMF)
Taking into account the estimated characteristic vector of
student s, the objective function expressed in equation (2)
becomes:




222
12 1 2
(,)
2
,1
1
1,
si
u
s
s
s
So MF T
si FF
si R
su
SuN
Tssu
uN
ORwwWW
Tw
wT







 









(13)
In this case, our multi-relational and social objective function
is given by expression:
11
So MRMF rr
OOO


 (14)
So that functions 1r
O and 1r
O are given by the equations
(15) and (16)




222
11212
(,)
2
,1
1
1,
ˆ
u
s
s
s
T
rsisi FF
si R
su
SuN
Tssu
uN
ORwwWW
Tw
wT







 









(15)

22
112
2( ,) 1
si s i
r
MN
T
rrrrn
F
rsiR n
ORwwW


 




  (16)
It is assumed that 1r denotes the main
relationship taking into account the entities "student" and
"task". The objective function 1r
O is thus defined for the
value 1r

. The objective function 1r
O, for its part, is
defined for any other value of (1)rr. The objective
function (14) is optimized by using stochastic gradient
descent. Thus, our So-MRMF model updates its parameters
by equations (17) and (18) :




121
1
121
2 , 1
2 , 1
sk ik sk
sk
sk si ik sk
rsirrT
r
rrrr
weww XYifr
wwewwifr




 

 


(17)


22 1 2
2
ik ik si sk ik
rr rr r
ww ew w

  (18)
X and Y expressions are given through equations (19) et (20)
,1
,
1
,,
1
uk
s
sk
ss
su
uN
ss
su su
uN uN
Tw
T
Xw
TT


 
 

 
 
 


(19)
,1
,
1
\,,
wk
t
tk
S
tt
tw
wN
ts
tN s tw tw
wN wN
Tw
T
Yw
TT











(20)
Equations (19) and (20) have been proposed to give a reduced
form of equation (17).
D. Weighted Multi-Relational Matrix Factorization and
Social-influence approach (So-WMRMF)
Considering the fact that some relations have more impact on
the prediction than others, in weight term, the objective
function of So-WMRMF model is given by:
11
So WMRMF W W
rr
OOO


 (21)
Such that the functions 1
W
r
O

and 1
W
r
O are given by the
equations (22) and (23)




222
11212
(,)
2
,1
1
1,
ˆ
si
u
s
s
s
WT
rr si FF
si R
su
SuN
Tssu
uN
ORwwWW
Tw
wT








 









(22)

22
112
2(,) 1
si s i
r
MN
WT
rrrrr n
F
rsiR n
ORwwW


 

  


  (23)
Our So-WMRMF model updates these parameters for each
relationship via equations (24) and (25).




121
1
121
2 , 1
2 , 1
sk ik sk
sk
sk si ik sk
rrsirrT
r
rrrrr
wewwXYifr
wwewwifr




 

  


(24)


22 1 2
2
ik ik si sk ik
rr rrr r
ww ew w

  (25)
Ii Ss
Psi Snl
s
lN
Students
Tasks
Friend
s
nN
Sn2
Sn1
.
.
.
T

.
.

. .


2
iW
1
s
W
Performance
,1
s
n
T
,2
s
n
T
,
s
nl
T

Multi-Relational and Social-Influence Model for Predicting Student Performance in Intelligent Tutoring Systems (STI)
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O
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: 10.35940/ijeat.C5169.029320
E. Learning phase: proposal of an algorithm for
updating parameters.
The main issue of this technique is to find the optimal
parameters 12
, ,..., n
WW W, we proposed the algorithm 1
(using a stochastic gradient descent) iterative below to update
our model parameters. The algorithm 1 proposed for the
model So-WMRMF proceeds by initializing the parameters
from the normal distribution


2
,N


, taking for
expectation 0

 and for standard deviation 0.01

.
Al
g
orithm 1
Input
N : number of entities ;
M
: number of relations ; F : number of
latent factors ; r
R
: for each relations ;

: weight ;

:
regulation term ; T

: regulation term;

: learning rate ;
K
:
Latent factors ; T : Matrix factors.
Output


1...
jjN
W : latent factor matrices for each entity j
1. Initialize
j
W for each of the N entities using


2
,N


2. Initialize r
 for each of the
M
relations
3. While (Stopping criterion is not met) do
4. for each relation



12
;
rrr
REE in


1,..., M
EE
do
5. for s = 0 to number of rows-1 of r
R do
6. for i = 0 to number of rows-1 of r
R do
7. ˆ
s
isisi
eRp
8. for k = 0 to K-1 do
9. ,
s
s
is Tnf 
10. if r = 1 do
11. for n = 1 to
s
N
do
12. ,
s
n
infnx inf x Tn
13.




,1su
X
XT Wsk 
14. end for
15.






1//1infs infnx infnxXWskX
16. for t = 1 to \
S
N
s do
17. for w = 1 to
s
N
do
18. ,tw
infny inf y Tn
19.




11 , 1tw
YYT Wwk 
20. end for
21.


,11
//
tk
ts infny infnyYY T w Y 
22. end for
23.











11 21
2ik sk
rsi r r
T
Wsk Wsk ew w
XY




24. else
25.
 


11 21
2ik sk
rsi r r
Wsk Wsk ew w


26. end if
27. end for
28.
   


22 12
2si sk ik
rr r r
Wik Wik ew w


29. end for
30. end for
31. end for
32. end while
33. Return


1...
jjN
W
V. EVALUATION OF THE PROPOSED MODELS
A. Data Set
The data set for machine learning and testing comes from
KDD Challenge 2010 ( Knowledge Discovery Data)
database. This database is the result of interaction records
between students and computer-assisted tutoring systems. In
the KDD Challenge 2010 datasets ie "Algebra", the problem
is the central element of the interaction between students and
the Tutoring System. Students solve problems in the tutor and
each interaction between the student and the system is
recorded as a transaction line. The information about
students, tasks and skills in this database is shown in Table 1.
Table 1. Information of students, tasks and performances
Data set #Student #Task #Skill #Performance
Algebra
2008-2009 3,310 1,422,200 2,979 8,918,054
B. Evaluation
For our models’ evaluation, we used the dataset "Algebra".
Given the high data size of this database for our work
environment, we reduced the sample for the evaluation. This
sample is composed of:
 247 students;
 4000 tasks;
 1664 skills;
In this sample, we extracted three (3) matrices. The first
is related to the relationship "student-performs -tasks". This
matrix is of dimension 247 x 4000. This matrix comprises
180676 known performances. We used two datasets: one for
machine learning and one for testing. To perform cross
validation, we used 9/10 performance for the machine
learning phase and 1/10 for the prediction phase. The second
matrix relates to "student-as learnt-skill" relationship and the
third to "task-requires-skill" relationship. Since the learning
base does not have student group relationships, we simulated
two group formation scenarios in all of the 247 students used
for experiment. For each of the two scenarios, 40 groups of 4
students are formed. 160 students belong to a group while 87
belong to no group. In the scenario 1 noted So1., The
influence values between students are all set at 1. In the
scenario 2 noted So2., these values are a function of the
performances obtained by each student in the group. The
average yield of a member of the group is calculated, in the
interval ] 0;0.5], on the basis of the tasks performed. This
yield is taken by default as the influence value of this member
on the others. However, the influence value of a member of
the group on itself is equal to 1.

International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249 – 8958, Volume-9 Issue-3, February, 2020
2064
Published By:
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etrieval Number: C5169029320/2020©BEIESP
D
O
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: 10.35940/ijeat.C5169.029320
C. Results
We implement So-MF, So-MRMF and So-WMRMF models
taking into account three attributes (three relations) and the
group relation as described in our association entity diagram.
Our work environment is a 64-bit operating system computer,
4GB of ream, intel Core i3. Our model is designed in Python
language.
To compare our approach with classical matrix factorization
methods (MF, MRMF and WMRMF), we used the RMSE
(Root Mean Squared Error) metric. This metric is calculated
as follows :

2
(,,)
ˆ
test si si
rsi D
test
pp
RMSE D




(26)
For this, the parameters used to optimize the model are
contained in table 2.
Table 2. Optimizing parameters
Methods Parameter
MF 3K; #iter = 30 ; 3
2.10


 ;
5
55.10



So1-MF ;
So2-MF
3K ; #iter = 60 ; 3
2.10


 ;
5
15.10


; 5
15.10
T



MRMF ;
So1-MRMF ;
So2-
M
RMF ;
4
K
 ; #iter = 70 ; 3
2.10


 ;
5
55.10


; 5
55.10
T



WMRMF ;
So1-WMRMF ;
So2-WMRMF ;
4
K
 ; #iter = 80 ; 3
2.10


 ;
5
55.10


; 5
55.10
T


 ;


0.85;0.80;0.70


Figure 6 gives the results of the experiments carried out
by applying the two scenarios described above to each of the
MF, MRMF and WMRMF methods.
(a) RMSE with MF method (b) RMSE with MRMF method
(c) RMSE with WMRMF method
Fig. 6. RMSE results on Algebra data set using the two
scenarios So1 and So2
In Figure 6 (a), So1-MF and So2-MF models outperform the
MF model. Figure 6 (b) shows that So1-MRMF and
So2-MRMF models are significantly more accurate than the
MRMF model. In Figure 6 (c), the So1-WMRMF model is
significantly better compared to the WMRMF model while
the So2-WMRMF model greatly outperforms WMRMF and
So1-WMRMF models. Figure 7 gives a summary of RMSE
metric for So2-MF, So2-MRMF and So2-WMRMF methods.
Fig. 7. RMSE results on Algebra data set using the two
scenarios So1 and So2
These results show that the So2-WMRMF model
outperforms all other models. Taking into account the
influence factor on Weighted Multi-Relational Matrix
Factorization, in order to predict performance, gives not only
a better accuracy of prediction on the performances, but also,
that it presents better results compared to the methods of
standard Matrix Factorization.
VI. CONCLUSION
In this paper, we have proposed a student performance
prediction approach that integrates not only friendship
relationships such as workgroup relationships, but also
mutual influence values into Weighted Multi-Relational
Matrix Factorization method. By applying RMSE metric to
our models (So2-MF, So2-MRMF, So2-WMRMF),
experimental results from the KDD Challenge 2010 database
have shown that this approach can refine the accuracy of
student performance prediction. The So2-WMRMF model
outperforms all other models.
In future work, the addition of some information such as the
influence factor per student and per task and the definition of
an influence value that takes advantage of real-life situations,
would further improve the results of students’ performances
predictions in ITS.

Multi-Relational and Social-Influence Model for Predicting Student Performance in Intelligent Tutoring Systems (STI)
2065
Published By:
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etrieval Number: C5169029320/2020©BEIESP
D
O
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: 10.35940/ijeat.C5169.029320
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AUTHORS PROFILE
Kouamé Abel ASSIELOU received the master's
degree in Computer Engineering from the University
Nangui Abrogoua (Côte d’Ivoire) and also the diploma of
Engineering in network and telecommunication at the
training institute for high expertise of BNETD (Bureau
National d’étude technique et de Développement). He is
currently a PhD student at the INP-HB (Institut National Polytechnique Félix
Houphouët Boigny de Yamoussoukro). His current research interest is
related to designing, modeling of Intelligent Tutoring Systems (ITS).
Théodore Cissé HABA received the Ph.D. degree from
the University of Paul Sabatier de Toulouse III (France).
He is currently a Professor and researcher at Institut
National Polytechnique Houphouët Boigny (INP‐HB) of
Yamoussoukro (Côte d’Ivoire). He worked on the
frequency behavior of fractional impedance
microelectronic devices. Currently,
his is working on digital processing
and the implementation of electronic
devices for solar.

International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249 – 8958, Volume-9 Issue-3, February, 2020
2066
Published By:
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etrieval Number: C5169029320/2020©BEIESP
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O
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: 10.35940/ijeat.C5169.029320
Dr Lambert Tanon KADJO received his BS in
Computer Science from University of Cocody (Côte
d’Ivoire) in 2003, his M.S. in Numerical Analysis from
University of Abobo-Adjamé Abidjan in Côte d’Ivoire in
2005 and professional Master of engineering from CFTIC
(Centre de Formation en Technologies de l’Information et de la
Communication) at INPHB – Abidjan in Cote d’Ivoire in 2007. He received
PhD in Telecommunications at University of Cheikh Anta Diop of Dakar in
Senegal in 2009.
His research interests include IPv6 Mobility, IP Multicast, IP Network
security, 4G networks, Social network. He is authors/co-authors of 11 paper s
published in these arears. He is working as Assistant Professor at Institut
National Polytechnique Felix HOUPHOUET Boigny (INP-HB). profile
which contains their education details, their publications, research work,
membership, achievements, with photo that will be maximum 200-400
words.
YAO k. Daniel received the Ph.D. degree in
psychology from the University of Félix Houphouët
Boigny (Abidjan/Ivory Coast). He is an Assistant
Professor in the university jean Lorougnon Guédé de
Daloa. (Côte d’Ivoire). He conducted a series of works on
educational psychology, urban violence and juvenile marginality.
Bi Tra GOORE He is currently a Professor with the
INP-HB (Institut National Polytechnique Houphouët
Boigny de Yamoussoukro). Where he spent several years
in teaching the computer science and Network. He is a
member of the rearch laboratory LARIT ( Laboratoire de
recherche en Informatique et Télécommunication). His research field include
design, modeling, and performance evaluation of wireless sensor networks
design, His current research interests include design, modeling, and
performance evaluation of networks and telecommunication system