Design a personalized e-learning system based on item response theory and artificial neural network approach. Ahmad Baylari, Gh.A. Montazer

Design a personalized e-learning system based on item response
theory and artificial neural network approach
Ahmad Baylari, Gh.A. Montazer *
IT Engineering Department, School of Engineering, Tarbiat Modares University, Tehran, Iran
a r t i c l e i n f o
Keywords:
e-Learning
Adaptive testing
Multi-agent system
Artificial neural network (ANN)
Item response theory (IRT)
a b s t r a c t
In web-based educational systems the structure of learning domain and content are usually presented in
the static way, without taking into account the learners’ goals, their experiences, their existing knowl-
edge, their ability (known as insufficient flexibility), and without interactivity (means there is less oppor-
tunity for receiving instant responses or feedbacks from the instructor when learners need support).
Therefore, considering personalization and interactivity will increase the quality of learning. In the other
side, among numerous components of e-learning, assessment is an important part. Generally, the process
of instruction completes with the assessment and it is used to evaluate learners’ learning efficiency, skill
and knowledge. But in web-based educational systems there is less attention on adaptive and personal-
ized assessment. Having considered the importance of tests, this paper proposes a personalized multi-
agent e-learning system based on item response theory (IRT) and artificial neural network (ANN) which
presents adaptive tests (based on IRT) and personalized recommendations (based on ANN). These agents
add adaptivity and interactivity to the learning environment and act as a human instructor which guides
the learners in a friendly and personalized teaching environment.
Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
The recent applications of information communication technol-
ogies (ICT) have a strong and social impact on the society and the
daily life. One of the aspects of society that has been transforming
is the way of learning and teaching. In the recent years, we have
seen exponential growth of Internet-based learning. The transition
to online technologies in education provides the opportunities to
use new learning methodology and more effective methods of
teaching (Georgieva, Todorov, & Smrikarov, 2003). In a simple def-
inition e-learning is defined as the use of network technology,
namely the Internet, to design, deliver, select, administer and ex-
tend learning (Hamdi, 2007). Important features of this form of
learning are the separation of learner and teacher and can take
place anywhere, at any time and at any pace. Thus e-learning can
take place at people’s work or at home, at the time available
(Kabassi & Virvou, 2004). The other perspectives of using e-learn-
ing can be generalized as follows: an opportunity for overcoming
the limitations of traditional learning, such as large distance, time,
budget or busy program; equal opportunities for getting education
no matter where you live, how old you are, what your health and
social status is; better quality and a variety of lecture materials;
new consortia of educational institutions, where a lot of specialists
work in collaboration, use shared resources and the students get
freedom to receive knowledge, skills and experience from other
universities (Georgieva et al., 2003). Due to the flexibilities that
mentioned above many universities, corporations and educational
organizations are developing e-learning programs to provide
course materials for web-based learning. Also e-learning can be
used for online employee training in business (Chen, Lee, & Chen,
2005).
From another point of view, numerous Web applications, such
as portal websites (such as Google and Yahoo!), news websites,
various commercial websites (such as Amazon and eBay) and
search engines (such as Google) have provided personalized mech-
anisms to enable users to filter out uninteresting or irrelevant
information. Restated, personalized services have received consid-
erable attention recently because of information needs are differ-
ent among users (Chen et al., 2005). But in web-based
educational systems the structure of the domain and the content
are usually presented in the static way, without taking into ac-
count the learners’ goals, their experiences, their existing knowl-
edge and their abilities (Huang, Huang, & Chen, 2007) also
known as insufficient flexibility (Xu & Wang, 2006), and without
interactivity means there is less opportunity for receiving instant
responses and feedback from the instructor when online learners
need support (Xu & Wang, 2006). Therefore, adding interactivity
and intelligence to Web educational applications is considered to
0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2008.10.080
* Corresponding author. Tel./fax: +98 2182883990.
E-mail addresses: Baylari@modares.ac.ir (A. Baylari), Montazer@modares.ac.ir
(Gh.A. Montazer).
Expert Systems with Applications 36 (2009) 8013–8021
Contents lists available at ScienceDirect
Expert Systems with Applications
journal homepage: www.elsevier.com/locate/eswa

be an important direction of research (Hamdi, 2007). Personaliza-
tion is an issue that needs further attention, especially when it
comes to web-based instruction, where the learners’ population
is usually characterized by considerable heterogeneity with re-
spect to background knowledge, age, experiences, cultural back-
grounds, professions, motivation, and goals, and where learners
take the main responsibility for their own learning (Huang et al.,
2007).
The personalization can ensure that the system will take into
account the particular strengths and weaknesses of each individual
who is using the program. It is simple logic that response person-
alized to a particular student must be based on some information
about that student; in the area of artificial intelligence (AI) in edu-
cation, this realization led to student modeling, which became a
core or even defining issue for the field. As a result, student mod-
eling is used in intelligent tutoring systems (ITSs), intelligent learn-
ing environments (ILEs) and adaptive hypermedia systems (AHS)
to achieve personalization and dynamic adaptation to the needs
of each individual student(Kabassi & Virvou, 2004). In the last 10
years, the field of ITS research has been developing rapidly. Along
with the growth of computing capabilities, more and more ITS
researchers have focused on personalized virtual learning environ-
ments (PVLEs) to provide tailored learning materials, instructions
and instant interaction to suit individual learners or a group of
learners by using intelligent agent technology. Intelligent agent
technologies facilitate the interaction between the students and
the systems, and also generate the artificial intelligence model of
learning, pattern recognition, and simulation, such as the student
model, task model, pedagogical model, and repository technology.
These models work together in a productive way to support stu-
dents’ learning activities adaptively. Therefore, the properties of
intelligent agents, i.e. autonomy, pre-activity, pro-activity and co-
operativity, support PVLEs in recognizing online learners’ learning
stage and in reacting with tailored instruction including personal-
ized learning materials, tests, instant interactions, etc. (Xu & Wang,
2006).
In this study, we will propose a framework for constructing
adaptive tests that will be used as a post-test in our system. Thus
a multi-agent system is proposed which has the capability of esti-
mating the learners’ ability based on explicit responses on these
tests and presents him/her a personalized and adaptive test based
on that ability. Also the system can discover learner’s learning
problems via learner responses on review tests by using an artifi-
cial neural network (ANN) approach and then recommends appro-
priate learning materials to the student. So, the organization of this
paper is as follows. The following section briefly reviews the rele-
vant literature on personalization for e-learning. After describing
item response theory (IRT) in Section 3, the test construction pro-
cess will be presented in Section 4. Section 5 describes the system
architecture. Agent design and system evaluation are addressed in
Sections 6 and 7, respectively. The final section provides a conclu-
sion for our work.
2. Personalization concept in e-learning systems
Many researchers have recently endeavored to provide person-
alization mechanisms for web-based learning (Chen et al., 2005).
Therefore, personalized learning strategy is needed for most e-
learning systems currently. Learners enjoyed greater success in
learning environments that adapted to and supported their indi-
vidual learning orientation (Xu & Wang, 2006). Nowadays, most
recommendation systems consider learner/user preferences, inter-
ests, and browsing behaviors when analyzing learner/user behav-
iors for personalized services. These systems neglect the
importance of learner/user ability for implementing personalized
mechanisms. On the other hand, some researchers emphasized
that personalization should consider different levels of learner/
user knowledge, especially in relation to learning. Therefore, con-
sidering learner ability can promote personalized learning perfor-
mance (Chen et al., 2005). Also most e-learning systems lack the
presence and control of an instructor to the learning process to as-
sist and help learners in these environments (also known as human
touch). Thus modeling the behavior of the instructor and provide
instant feedbacks is an important task in these environments. Shi
et al. have proposed a method to personalize the learning process
by a SOM agent which replaces the human instructor and controls
in an e-learning environment (Shi, Revithis, & Chen, 2002). Xu and
Wang developed a multi-agent architecture for their personalized
model (Xu & Wang, 2006). Chen et al. proposed a personalized e-
learning system based on IRT (PEL-IRT) which considers both
course material’s difficulty and learner’s ability to provide individ-
ual learning paths for learners (Chen et al., 2005). So far he and his
colleagues have presented a prototype of personalized web-based
instruction system (PWIS) based on the modified IRT to perform
personalized curriculum sequencing through simultaneously con-
sidering courseware difficulty level, learner’s ability and the con-
cept continuity of learning pathways during learning (Chen, Liu,
& Chang, 2006).
In all systems described above, the importance of tests, con-
structing and adapting them to learner’s ability have been ne-
glected. They have only adapted the content and personalized
part of their systems is sequence and organization of the content.
So in this paper, designing the tests and adapting these tests to
learners and simulating an instructor that control the learning pro-
cess is desired. To achieve these goals, a multi-agent system will be
proposed. Theses agents play an important role to provide person-
alization for the system. Agents are a natural extension of current
component-based approaches and should at least be able to model
the preferences, goals, or desires of their owners and to learn as
they perform their assigned tasks (Xu & Wang, 2006). In our sys-
tem, we have three tests: pre-test, adaptive post-tests and review
tests. Post-tests are adaptive and will be adapted to the learner’s
ability. By review tests the instructor can diagnose learner’s learn-
ing problems and will recommend personalized learning materials
to the learner. Nice features of our system are dynamic and person-
alized tests and personalized recommendations of a simulated hu-
man instructor.
3. Item response theory (IRT)
Item response theory (IRT) was first introduced to provide a for-
mal approach to adaptive testing (Fernandez, 2003). The main pur-
pose of IRT is to estimate an examinee’s ability (h) or proficiency
(Wainer, 1990) according to his/her dichotomous responses
(true/false) to test items. Based on the IRT model, the relationship
between examinee’s responses and test items can be explained by
so-called item characteristic curve (ICC) (Wang, 2006). In the case
of a typical test item, this curve is S-shaped (as shown in Fig. 1);
the horizontal axis is ability scale (in a limited range) and the ver-
tical axis is the probability that an examinee with certain ability
will give a correct answer to the item (this probability will be smal-
ler for examinees of low ability and larger for examinees of high
ability). The item characteristic curve is the basic building block
of item response theory; all the other constructs of the theory de-
pend upon this curve (Baker, 2001).
Several nice features of IRT include the examinee group invari-
ance of item parameters and item invariance of an examinee’s abil-
ity estimate (Wang, 2006).
Under item response theory, the standard mathematical model
for the item characteristic curve is the cumulative form of the lo-
8014 A. Baylari, Gh.A. Montazer / Expert Systems with Applications 36 (2009) 8013–8021

gistic function. It was first used as a model for the item character-
istic curve in the late 1950s and, because of its simplicity, has be-
come the preferred model (Baker, 2001).
Based on the number of parameters in logistic function there
are three common models for ICC; one parameter logistic model
(1PL) or Rasch model, two parameter logistic model (2PL) and
three parameter (3PL) (Baker, 2001; Wang, 2006). In the 1PL mod-
el, each item i is characterized by only one parameter, the item dif-
ficulty bi, in a logistic formation as shown
PiðhÞ ¼
1
1 þ expðÀDðh À biÞÞ
; ð1Þ
where D is a constant and equals to 1.7 and h is ability scale. In the
2PL model, another parameter, called discrimination degree ai, is
added into the item characteristic function, as shown
PiðhÞ ¼
1
1 þ expðÀaiDðh À biÞÞ
: ð2Þ
The last 3PL model adds a guess degree ci to the 2PL model, as
shown in Eq. (3), modeling the potential guess behavior of exami-
nees (Wang, 2006).
PiðhÞ ¼ ci þ frac1 À ci1 þ expðÀaiDðh À biÞÞ: ð3Þ
Several assumptions must be met before reasonable and precise
interpretations based on IRT can be made. The first is the assump-
tion of unidimensionality, which assumes there is only one factor
affecting the test performance. The second assumption is the local
independence of items, which assumes test items are independent
to each other. This assumption enables an estimation method called
maximum likelihood estimator (MLE) to effectively estimate item
parameters and examinee’s abilities (Wang, 2006).
Lðhju1; u2; . . . ; unÞ ¼
Yn
i¼1
PiðhÞui
QiðhÞ1Àui
; ð4Þ
where Qi(h) = 1 À Pi(h). Pi(h) denotes the probability that learner can
answer the ith item correctly, Qi(h) represents the probability that
learner cannot answer the ith item correctly, and ui is 1 for correct
answer to item i and 0 for incorrect answer to item i (Wainer, 1990).
Since Pi(h) and Qi(h) are functions of learner ability h and item
parameters, the likelihood function is also a function of these
parameters. Learner ability h can be estimated by computing the
maximum value of likelihood function. Restated, learner ability
equals the h value with maximum value of likelihood function
(Chen et al., 2005).
Item information function (IIF) in IRT plays an important role in
constructing tests for examinees and evaluation of items in a test.
Any item in a test provides some information about the ability of
the examinee, but the amount of this information depends on
how closely the difficulty of the item matches the ability of the
person. The amount of information, based upon a single item,
can be computed at any ability level and is denoted by Ii(h), where
i is the number of the items. Because only a single item is involved,
the amount of information at any point on the ability scale is going
to be rather small (Baker, 2001). If the amount of item information
is plotted against ability, the result is a graph of the item informa-
tion function such as shown in Fig. 2.
As shown in this figure it can be seen that an item measures
ability with greatest precision at the ability level corresponding
to the item’s difficulty parameter. The amount of item information
decreases as the ability level departs from the item difficulty and
approaches zero at the extremes of the ability scale (Baker, 2001).
Item information function is defined
IiðhÞ ¼
P02
i ðhÞ
PiðhÞQiðhÞ
; ð5Þ
where P
0
(h) is the first derivative of Pi(h) and Qi(h) = 1 À Pi(h). A test
is a set of items; therefore, the test information at a given ability le-
vel is simply the sum of the item information at that level. Conse-
quently, the test information function (TIF) is defined as:
IðhÞ ¼
XN
i¼1
IiðhÞ; ð6Þ
where Ii(h) is the amount of information for item i at ability level h
and N is the number of items in the test. The general level of the test
information function will be much higher than that for a single item
information function. Thus, a test measures ability more precisely
than does a single item. An important feature of the definition of
test information given in Eq. (6) is that the more items in the test,
the greater the amount of information. Thus, in general, longer tests
will measure an examinee’s ability with greater precision than will
shorter tests (Baker, 2001).
Item response theory usually is applied in the computerized
adaptive test (CAT) domain to select the most appropriate items
for examinees based on individual ability. The CAT not only can
efficiently shorten the testing time and the number of testing items
but also can allow finer diagnosis at a higher level of resolution.
Presently, the concept of CAT has been successfully applied to re-
place traditional measurement instruments (which are typically
fixed-length, fixed-content and paper–pencil tests) in several
real-world applications, such as GMAT, GRE, and TOEFL (Chen
et al., 2006).
Fig. 1. Sample item characteristic curve.
Fig. 2. Item information function for an item demonstrated in Fig. 1.
A. Baylari, Gh.A. Montazer / Expert Systems with Applications 36 (2009) 8013–8021 8015

In this paper, we will use IRT-3PL model to test construction,
ability estimation and appropriate post-test selection for learners.
In the following section we will describe test construction process.
4. Test construction process
We have three types of tests in our system; pre-test, post-test
and review tests. In this section construction process of these three
types will be described. All of these tests have 10 items. For post-
test construction, as shown in Fig. 3, at the ﬁrst step the teacher
analyzes the learning contents based on learning objectives and
designs suitable multiple choice items from each learning object
(LO). Every item has its unique code and is stored in testing items
database. Then these items were presented to students to answer
them. Having collected their responses, according to IRT their test-
ing data were analyzed by the BILOG program to obtain the appro-
priate item parameters under 3PL model. Therefore, each item has
its own a, b and c parameters and we will have a calibrated item
bank, which can be used for item selection in CAT and test con-
struction. Afterwards we designed a set of adaptive tests for our
system. At this step, the teacher constructs a few appropriate tests
at each ability level. For example let h = 0.5 and the items of 3rd
session have been ranked based on their item information func-
tion. Then the teacher selects 10 items from top to down and con-
structs the desired test. The selection of items is based on their
information and their content. These tests are constructed for each
ability scale. Then they were stored with their item codes, item
parameters and the session number in the test database. This pro-
cess was repeated for each session. These tests are adaptive and
will be used as post-test in the system.
Fig. 3. The applicable process for constructing adaptive post-tests.
Learner interface
Activity
agent
Remediation agent
LOs
database
Learner
profile
database
Test
database
Planning agent Test agent
Learner layer
Agent layer
Repository layer
Fig. 4. System architecture.

To construct review tests, the learning contents were analyzed
and the learning concepts were extracted. Then appropriate tests
were designed. They are fixed and static in the learning process
and can be considered as the teacher’s expectation from learners.
They are used to diagnose the learner’s learning problems. And at
last we need pre-test at the entrance of each session. Theses tests
are static too, and are stored in our test database. Finally, we have a
test database which may be used for assessment of the learners in
our system.
5. System architecture
Integrating multiple intelligent agents into distance learning
environments may help bring the benefits of the supportive class-
room closer to distance learners, therefore, intelligent agents are
becoming more and more hot in ITS study (Zhou, Wu, & Zhang,
2005). Also The agent metaphor provides a way to operate and
simulate the ‘human’ aspect of instruction in a more natural and
valid way than other controlled computer-based methods (Xu &
Wang, 2006). Therefore, the proposed architecture is a multi-agent
system which will be used for personalization of the learning envi-
ronment. As shown in Fig. 4, the proposed architecture is a three-
layer architecture. The middle layer contains four agents: activity
agent, test agent, planning agent and remediation agent.
Activity agent: This agent records e-learning activities, online
learners’ learning activities (such as mouse action) learning
duration on a particular task, documents load/unload, etc. and
stores them in the learner’s profile.
Planning agent: This agent plans the learning process. At start
of each session, this agent asks the learner whether he/she is
familiar with the session. If the answer is ‘no’ the agent permits
the learner to enter the session, but if the answer is ‘yes’ then
this agent requests the test agent to present him/her a pre-test.
Based on the learner responses on this test, the agent can decide
which part of the next session does not need to be presented to
the learner. At the end of the session this agent requests the test
agent to present him/her the appropriate post-test. After some
sessions e.g. three sessions this agent asks from test agent to
present the review test to the learner and then presents their
responses to the remediation agent.
Test agent: This agent based on the requests of planning agent,
presents appropriate test type to the learner. So this agent
selects the suitable test from test database and presents it to
the learner. Also in the case of post-test, this agent extracts lear-
ner’s ability from his/her profile and presents the most appropri-
ate post-test to the learner based on his/her ability, then
estimates learner’s ability in this post-test and updates it in
the profile.
Remediation agent: This agent analyzes the results of review
tests, and diagnoses learner’s learning problems, like a human
instructor, and then recommends the appropriate learning
materials to the learner.
Therefore, these agents cooperate with each other to help and
assist learners in the learning process, like a human instructor,
and increase the quality and effectiveness of learning.
The lower layer is the repository layer and contains learner pro-
file database which stores user profile, learning objects database
which store learning materials as learning objects and test data-
base which has been designed in the previous section. The system
operates as follows:
At first, the planning agent asks the learner whether he/she is
familiar with the first session. If the answer is positive this agent
asks test agent to present him/her a pre-test. Having analyzed
the learner’s responses, this agent presents the appropriate first
session LOs. Otherwise this agent presents all first session LOs. At
the end of this session test agent presents the appropriate post-test
with medium difficulty based on IRT. This is because there is no
information about the learner ability at the first session. At the
end of each session test agent presents the appropriate post-test
from the test database that matches learner’s ability. At the end
of the third session (for example), test agent presents the review
test to the learner to diagnose his/her learning problems. When
the learner finishes, the remediation agent analyzes the responses
and after diagnosing learner’s learning problems, recommends the
appropriate LOs. So, the learner will be guided to a remediation
session to improve his/her learning problems. Then test agent pre-
sents a post-test and estimates learner’s ability and updates it in
his/her profile. The test agent receives learner’s responses in each
post-test and estimates his/her ability in each test by applying
maximum likelihood estimator and stores it in his/her profile. In
the next session’s post-test this agent selects and presents most
appropriate post-tests with respect to learner’s ability in his/her
profile. A post-test with a maximum information function value
under learner with ability h is presented to the learner. Restated
information of all test items in the learner’s ability are calculated
and summed. It must be noted that a test with a maximum infor-
mation function value under learner’s ability h has the highest rec-
ommendation priority.
6. System design and development
After designing the review tests, they were presented to some
students to collect their responses. Then their tests and responses
were presented to the instructor so he could diagnose their learn-
ing problems and recommend them appropriate learning materi-
als. Learning materials are in the form of LOs. The maximum
number of recommended LOs were five. Due to the large number
of responding states to a test (210
states for each test), an artificial
neural network was used for recommending remaining states. The
items of the test and the students’ responses have been considered
as the inputs of the network and the recommendations as the out-
put of the one. The network may be trained with these data; then
the trained network will recommend appropriate learning materi-
als instead of human instructor in the learning environment.
In order to experiment the remediation agent, ‘‘Essentials of
information technology management” course was chosen. This
course was divided into several LOs and a few codes were allocated
for all LOs. The teacher designed the items from each LO and these
items had their unique code, too. Then five new tests were de-
signed from these items. They were presented to the students
and their responses were collected. The number of responses was
200 per each test. So there were 1000 responses totally. These
items and their responses were presented to the instructor. Table
1 shows a sample items and responses.
As shown, this table has 20 columns, first 10 columns from left
(I1 to I10) are item codes and latter 10 columns (R1 to R10) are cor-
responding responses which coded 1 for correct response and 0 for
incorrect response. These data were presented to the instructor,
and then he analyzed each item response pair and having diag-
nosed learner’s learning problems, recommended the suitable
LOs to the students. The recommended LOs for the item response
pairs in Table 1 have been shown in Table 2.
Thus Table 1 considers the input data to the neural network and
Table 2 the output ones. But in order to use these data to train the
network, a preprocessing part should be used. The details of the
neural network development process will be described in the sub-
sequent sub-sections.

6.1. The artificial neural network
A back-propagation network was used to learn from the data.
These networks are the most widely used type of networks and
are considered the workhorse of ANNs (Basheer Hajmeer,
2000). A back-propagation network (see Fig. 5) is a fully connected,
layered, feed-forward neural network. Activation of the network
flows in one direction only: from the input layer through the hid-
den layer, then on to the output layer. Each unit in a layer is con-
nected in the forward direction to every unit in the next layer. A
back-propagation network may contain multiple hidden layers.
Knowledge of the network is encoded in the (synaptic) weights be-
tween units. The activation levels of the units in the output layer
determine the output of the whole network (Hamdi, 2007). This
network can learn the mapping from one data space to another
using examples, and also has a high generalization capability.
The used network has twenty input nodes and five output neurons.
Ten of these inputs are item codes and the others are responses,
and the output neurons are recommended LOs.
6.2. Data normalization and partitioning
Normalization of data within a uniform range (e.g., 0–1) is
essential to prevent larger numbers from overriding smaller ones,
and to prevent premature saturation of hidden nodes, which im-
pedes the learning process. There is no one standard procedure
Table 1
Items responses data.
I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 R1 R2 R3 R4 R5 R6 R7 R8 R9 R10
121 122 123 166 167 193 194 195 244 245 1 1 1 0 0 0 0 0 0 1
61 62 111 112 166 167 201 202 224 225 0 1 0 0 0 0 1 0 0 0
166 167 171 172 196 197 204 205 234 235 1 0 0 0 0 1 1 1 0 0
76 77 78 136 137 183 184 185 246 247 0 1 1 1 1 0 1 1 1 0
121 122 123 166 167 193 194 195 244 245 0 1 1 1 0 1 1 0 1 0
103 104 129 130 132 133 201 202 203 204 0 1 1 0 0 0 1 1 1 0
76 77 78 136 137 183 184 185 246 247 0 1 1 1 0 0 1 0 0 0
166 167 171 172 196 197 204 205 234 235 0 1 0 1 1 0 0 1 1 1
121 122 123 166 167 193 194 195 244 245 1 1 0 0 0 0 1 0 0 0
61 62 111 112 166 167 201 202 224 225 1 1 1 0 1 1 0 0 1 1
Table 2
Recommended LOs.
LO1 LO2 LO3 LO4 LO5
0 7 29 1 0
2 6 7 30 31
14 7 11 0 39
5 0 0 7 0
0 14 0 6 0
6 0 8 0 15
5 19 10 9 0
8 15 12 16 0
0 7 16 3 0
0 13 0 8 0
Fig. 5. A multi-layer back-propagation network.
Fig. 6. Learning curve for a network with 15 neurons in the hidden layer.
Fig. 7. Learning curve for a network with 15 neurons in the first hidden layer and
10 neurons in the second hidden layer.

for normalizing inputs and outputs. One way is to scale input and
output variables (xi) in interval ½k1; k2Š corresponding to the range
of the transfer function:
Xn ¼ k1 þ ðk2 À k1Þ
xi À xmin
i
xmax
i À xmin
i
!
; ð7Þ
where Xn is the normalized value of xi, xmin
i and xmax
i are the maxi-
mum and minimum values of xi in the database, respectively (Bash-
eer Hajmeer, 2000). We normalized the input and output data
between 0.1 and 0.9.
In the second step, we have to say that the development of an
ANN requires partitioning of the parent database into three sub-
sets: training, test, and validation. The training subset should in-
clude all the data belonging to the problem domain and is used
in the training phase to update the weights of the network. The
validation subset is used during the learning process to check the
network response for untrained data. The data used in the valida-
tion subset should be distinct from those used in the training;
however they should lie within the training data boundaries. Based
on the performance of the ANN on the validation subset, the archi-
tecture may be changed and/or more training cycles applied. The
third portion of the data is the test subset which should include
examples different from those in the other two subsets. This subset
is used after selecting the best network to further examine the net-
work or confirm its accuracy before being implemented in the neu-
ral system and/or delivered to the end user (Basheer Hajmeer,
2000). We used 60% of all data for training, 10% for validation
and remaining data for testing the network.
6.3. Network architecture and training
In most function approximation problems, one hidden layer is
sufficient to approximate continuous functions (Basheer Haj-
meer, 2000). Generally, two hidden layers may be necessary for
learning functions with discontinuities (Masters, 1994). Therefore,
we might use one or two hidden layer in the network and then
trained it with various neurons in each layer in MATLAB software
environment. The sigmoid function was used as activation function
in hidden layer but for the output neurons, first the linear activa-
tion function and then sigmoid activation function were used.
Training algorithm was Levenberg-Marquart (Hagan Menhaj,
1994).
Training process is done to learn from training data by adjusting
the weights of the network. Two different criteria used to stop
training; one is training error (mean square error or MSE) which
has been adjusted to 10À4
and the other is maximum epoch which
has been adjusted to 1000 epochs. But one problem that would oc-
cur in training process is overtraining or overfitting. In this case,
the network would memorize the training data and its perfor-
mance in these data would be superior but when the new data
were presented to the network its performance would be low. This
Table 3
The results of training different networks.
No. First hidden layer neurons Second hidden layer neurons Activation function in output neurons Number of training epochs Training error Testing error
1 10 – Linear 384 0.0058 7.13
2 15 – Linear 144 0.0007 1.147
3 20 – Linear 411 8.43EÀ05 0.127
4 25 – Linear 285 9.84EÀ06 0.0193
5 10 7 Linear 90 0.003 2.65
6 15 10 Linear 231 9.97EÀ06 0.0158
7 15 15 Linear 166 9.90EÀ06 0.0213
8 20 10 Linear 176 1.19EÀ05 0.0239
9 10 – Sigmoid 94 2.70EÀ03 1.76
10 15 – Sigmoid 92 1.35E+00 1.61
11 20 – Sigmoid 844 2.60EÀ05 0.04
12 25 – Sigmoid 450 2.48EÀ05 0.0431
13 10 7 Sigmoid 396 2.90EÀ03 3.63
14 15 10 Sigmoid 152 1.55EÀ05 0.0265
15 15 15 Sigmoid 501 3.24EÀ05 0.0708
16 20 10 Sigmoid 69 1.51EÀ04 0.452
0.01
0.1
1
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Network architecture
testingerror
net 1
net 5
net 9
net 13
net 4
net 6
net 11
net 14
Fig. 8. Performances of 16 networks of different sizes in Table 3.

causes from the excessively large number of training cycles used,
and/or due to the use of a large number of hidden nodes (Basheer
Hajmeer, 2000). To avoid from this phenomena, we used early
stopping and validation data to stop training when the error on
these data increase. Training back-propagation network typically
starts out with a random set of connection weights (weight initial-
ization), then the network trained with different architectures (dif-
ferent number of hidden layers and hidden neurons in each layer).
For example in training a network with 15 neurons in one hidden
layer with sigmoid activation function and linear activation func-
tion in output layer neurons, learning curve becomes as shown
in Fig. 6. As shown in this figure, training error has been plotted
versus training epochs and we could reach 0.007 after 144 epochs.
Then the test data given to the network and this MSE error was
7.13. As another example, in training a network with 15 neurons
in first hidden layer and 10 neurons in second one with sigmoid
activation function in both hidden layer neurons and linear activa-
tion function in output layer neurons, learning curve becomes as
shown in Fig. 7. As the reader can see, training error reached
9.97eÀ6 after 231 epochs. Then the test data given to the network
and this MSE error was 0.0158. Table 3 summarizes the results of
trained networks with different architectures.
Fig. 8 shows the testing error as a function of network architec-
ture. As can be seen, four networks (network 4, 6, 11 and 14) have
fewer errors. Since a simple network architecture is always more
preferable to a complex one, we can also select a smaller network.
Therefore, the network configuration 20-20-5 (network No. 11)
was selected as the best network configuration instead of other
networks in terms of test error.
7. System evaluation
The final model was tested with the new test set data. For this
purpose 6 different responses were collected for each test and were
presented to the network. Then the recommended LOs from the
network compared with recommended LOs from a human instruc-
tor. For 25 of 30 tests (83.3%), the network’s actual output was ex-
actly the same as the target output, i.e., the network suggested the
same LOs as the human instructor does (Tables 4 and 5).
8. Conclusion
This paper proposed a personalized multi-agent e-learning sys-
tem which can estimate learner’s ability using item response the-
ory and then it can present personalized and adaptive post-test
based on that ability. Also, one of the agents of the system can
diagnose learner’s learning problems like a human instructor and
then it can recommend appropriate learning materials to the lear-
ner. This agent was designed using artificial neural network. So the
learner would receive adaptive tests and personalized recommen-
dations. Experimental results showed that the proposed system
can provide personalized and appropriate course material recom-
mendations with the precision of 83.3%, adaptive tests based on
learner’s ability, and therefore, can accelerate learning efficiency
and effectiveness. Also this research reported the capability of
the neural network approach to learning material
recommendation.
Acknowledgments
This paper is provided as a part of research which is financially
supported by Iran Telecommunication Research Center (ITRC) un-
der Contract No. T-500-10117. So, the authors would like to thank
this institute for its significant help.
References
Baker, F. (2001). The basics of item response theory. ERIC clearing house on
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Basheer, I. A., Hajmeer, M. (2000). Artificial neural networks: Fundamentals,
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Table 4
The network’s recommendations.
LO1 LO2 LO3 LO4 LO5
7.400695 0.003249 8.092381 11.79518 19.08823
6.998931 0.00946 0.043546 19.16121 22.98846
6.000922 0.001234 7.932761 11.77159 19.02395
–0.00082 12.98149 7.83923 18.07264 4.095693
3.000022 –0.00024 16.10811 6.058124 À0.05552
9.000435 6.997884 0.188911 0.016807 À0.0648
0.000737 1.995976 7.823159 12.1196 30.98434
0.001033 7.002031 8.139213 3.016954 À0.00066
6.996032 15.00508 10.99664 15.9784 37.00498
9.998321 9.002728 10.77043 11.75052 19.01869
0.000895 0.003996 11.97433 19.08917 0.005405
0.000273 0.001527 8.001427 30.02636 19.03718
À0.00135 8.997218 8.06572 0.103334 14.97708
13.99193 0.000875 À0.04542 0.009478 38.9834
3.000175 5.998167 7.144523 7.855729 34.97909
À0.00023 13.99366 19.40886 5.888998 0.115133
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3.110294 À0.2036 7.307486 30.22614 À0.42046
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The instructor’s recommendations.
LO1 LO2 LO3 LO4 LO5
7 0 8 12 19
7 0 0 19 23
6 0 8 12 19
0 13 8 18 4
3 0 16 6 0
9 7 0 0 15
0 2 8 12 31
0 7 8 3 0
7 15 11 16 37
10 9 10 11 23
0 0 12 19 0
0 0 8 30 19
0 8 10 3 19
14 0 0 0 39
3 6 7 8 35
0 14 19 6 0
5 8 10 9 30
0 0 29 1 4
6 19 10 9 0
3 8 9 7 31
6 8 0 6 4
2 13 14 30 31
6 9 0 0 19
1 19 17 0 0
8 7 15 19 23
0 0 6 30 0
0 2 14 12 35
7 0 0 19 23
6 9 11 30 15
3 0 7 30 0

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