Centroid-based Clustering for Student Models in Computer-based
Multiple Language Tutoring
Maria Virvou, Efthymios Alepis and Christos Troussas
Department of Informatics, University of Piraeus, 80, Karaoli and Dimitriou str., Piraeus, Greece
Keywords: User Modelling, User Clustering, Multiple Language Learning, Intelligent Tutoring Systems, K-means
Algorithm.
Abstract: This paper proposes an approach for the initialization and the construction of student models in an
intelligent tutoring system that teaches multiple foreign languages. The basic concept for the construction of
the initial user models is to assign each new student to a model with similar characteristics. As it is quite
easy to understand that a tutoring system has rather little information about its new users, our effort is to
provide as much information as possible for each specific user relying on the user’s initial data. To this end,
a machine learning algorithm, namely k-means, is responsible for creating clusters relying on the system’s
pre-entered past data and as a next step, each new entry is assigned to the nearest centroid.
1 INTRODUCTION
In the past few years, there has been an increasing
focus on the use of Internet, which allows greater
flexibility in all aspects of modern life, especially
with the spread of unmetered high-speed
connections. Educational material at all levels is
available from Internet. Regarding e-learning, it has
never been easier for people to access educational
information at any level from any place. The low
cost and nearly instantaneous sharing of ideas,
knowledge and skills has rendered the distant
learning process feasible for people with less spare
time. By these means, not only can a group cheaply
communicate and share ideas but the wide reach of
the Internet allows such groups to form in an easy
and efficient way. Hence, the development of web-
based applications has become common place.
Moreover, all the emerging needs of modern life
accentuate the importance of learning foreign
languages (Virvou and Troussas, 2011). Taking into
account the scientific area of Intelligent Tutoring
Systems (ITSs), there is an increasing interest in the
use of computer-assisted foreign language
instruction. Especially, when these systems offer the
possibility of multiple language learning at the same
time, the students may further benefit from this
educational process (Virvou et al., 2000).
An issue of great importance in e-learning is the
personalization of users, since it is quite difficult to
monitor users’ learning patterns (Licchelli et al.,
2004). Specifically, it is performed through student
modeling, which consists of the analysis of students’
behavior and prediction of their future behavior and
learning performance. A solution to this problem is
the exploitation of automatic tools for the generation
and discovery of user profiles in order to obtain an
effective student model based on his/her learning
performance and preferences, that in turn allows to
create a personalized education environment.
Adaptive personalized e-learning systems could
accelerate the educational process by revealing the
strengths and weaknesses of each student. Most
student models are concerned with representing the
student’s ability on portions of the domain (Beck
and Woolf, 2000). However, the way of mapping the
low-level knowledge to higher level teaching actions
is not always obvious.
In view of the above, in this paper we propose a
machine learning architecture which permits the
initialization of students’ models. Our framework
uses an innovative combination of stereotypes and
the k-means clustering algorithm in order to partition
multiple observations into a number of k clusters in
which each observation belongs to the cluster with
the nearest mean. Each cluster is represented by a
single mean vector. In particular, a student is first
assigned to a stereotype category on the basis of
his/her background knowledge level in the
instruction of multiple foreign languages. This is
198
Virvou M., Alepis E. and Troussas C..
Centroid-based Clustering for Student Models in Computer-based Multiple Language Tutoring.
DOI: 10.5220/0004128201980203
In Proceedings of the International Conference on Signal Processing and Multimedia Applications and Wireless Information Networks and Systems
(SIGMAP-2012), pages 198-203
ISBN: 978-989-8565-25-9
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
conducted based on the students’ performance on a
preliminary test posed to the student at the first time
of his/her interaction with the system. Then, the k-
means algorithm takes as input multiple students’
characteristics, which are described below and
serves as means for the initialization of the new-
student-model based on recognized similarities
between the new student and past students who
belong to the same stereotype category.
This paper is organized as follows. First, we
present the related scientific work. In sections 3 and
4, we discuss our system’s architecture, namely the
machine learning in student modelling and the k-
means clustering algorithm. Finally, in section 5, we
come up with a discussion about the usability of
centroid-based clustering for user models and we
present our next plans.
2 RELATED WORK
Teaching languages through computer-assisted
approaches is a quite significant field in language
learning. User modeling has already been applied in
a wide variety of scientific areas, including
educational software for language instruction.
Machine learning techniques have been applied to
user modeling problems for acquiring models of
users. In this section, we try to imprint the speckle of
the scientific progress of student modeling
concerning Machine Learning and CALL (Computer
Assisted Language Learning).
Basile et al (2011) proposed the exploitation of
machine learning techniques to improve and adapt
the set of user model stereotypes by making use of
user log interactions with the system. To do this, a
clustering technique is exploited to create a set of
user models prototypes; then, an induction module is
run on these aggregated classes in order to improve a
set of rules aimed as classifying new and unseen
users. Their approach exploited the knowledge
extracted by the analysis of log interaction data
without requiring an explicit feedback from the user.
Nino (2009) presented a snapshot of what has been
investigated in terms of the relationship between
machine translation (MT) and foreign language (FL)
teaching and learning. Moreover, the author outlined
some of the implications of the use of MT and of
free online MT for FL learning. Friaz-Martinez et al
(2007) investigated which human factors are
responsible for the behavior and the stereotypes of
digital libraries users so that these human factors can
be justified to be considered for personalization. To
achieve this aim, the authors have studied if there is
a statistical significance between the stereotypes
created by robust clustering and each human factor,
including cognitive styles, levels of expertise and
gender differences. Virvou and Chrysafiadi (2006)
described a web-based educational application for
individualized instruction on the domain of
programming and algorithms. Their system
incorporates a user model, which relies on
stereotypes, the determination of which is based on
the knowledge level of the learner. Liccheli et al
(2004) focused on machine learning approaches for
inducing student profiles, based on Inductive Logic
Programming and on methods using numeric
algorithms, to be exploited in this environment.
Moreover, an experimental session has been carried
out from the authors, comparing the effectiveness of
these methods along with an evaluation of their
efficiency in order to decide how to best exploit
them in the induction of student profiles. Tsiriga and
Virvou (2004) introduced the ISM framework for
the initialization of the student model in Web-based
ITSs, which is a methodology that uses an
innovative combination of stereotypes and the
distance weighted k-nearest neighbor algorithm to
set initial values for all aspects of the student model.
SignMT was implemented by Ditcharoen et al
(2010) to translate sentences/phrases from different
sources in four steps, which are word
transformation, word constraint, word addiction and
word ordering. Finally, Virvou and Troussas (2011)
described a ubiquitous e-learning tutoring system for
multiple language learning, called CAMELL
(Computer-Assisted Multilingual E-Language
Learning). It is a post-desktop model of human-
computer interaction in which students “naturally”
interact with the system in order to get used to
electronically supported learning. Their system
presents advances in user modeling, error proneness
and user interface design.
However, after a thorough investigation in the
related scientific literature, we came up with the
result that there was no implementation of
multilingual educational systems that combine
student modeling and machine learning. Hence, we
implemented a prototype system, which incorporates
intelligence in its diagnostic component, offers
proneness to students’ errors provides error
diagnosis and advice based on students’ needs.
3 MACHINE LEARNING IN
USER MODELING
Student modeling can undoubtedly benefit from
Centroid-basedClusteringforStudentModelsinComputer-basedMultipleLanguageTutoring
199
machine learning, given that machine learning
consists of the induction of knowledge, normally
leading to improvements in classifying objects in a
specific domain. Thus, our system’s student model
can extend or compile its background knowledge,
namely its bug library, so that the resulting student
model could be more accurate and efficient. User
modelers that deal with simple students’ behaviors
have the ability to collect a set of behaviors from
which to induce a student model. The task of
constructing the student model from a multiple
behaviors set can be regarded as an inductive
learning task and therefore machine learning
techniques can be used to address this task.
Constructing student models in multiple language
learning environments is quite complex, since
student behaviors are likely to be inconsistent and
incomplete, which can be due to any of the
following reasons (Virvou and Troussas, 2011):
I. Accidental sips.
II. Quick elimination of old knowledge errors.
III. Recurrence of old knowledge errors.
IV. Sudden appearance of new knowledge errors.
Except for accidental slips, all the above error
categories that our student model can predict may
change over time in unforeseen ways. This causes
problems in the generation of student models
because the predictions become less accurate. The
degree of precise prediction conducted by the user
models can be ameliorated by the use of
unsupervised inductive learning techniques.
For the incorporation of the algorithm into the
resulting multilingual system (Fig. 3) we may
observe the following basic steps:
i. For the initialization of the system, the k-means
algorithm receives as input, pre-stored data or data
from empirical studies. It uses several fundamental
characteristics which tend to influence the
educational procedure:
a. the age of students,
b. their level of knowledge in one of the
foreign language taught,
c. the degree of carefulness when answering
questions and
d. the error proneness of the student in each
concept of the domain knowledge.
These characteristics have been found quite
significant in past language learning applications
(Tsiriga and Virvou, 2004).
ii. Machine learning techniques are used as a next
step in order to describe efficiently the cognitive
processes that underlie the student’s actions along
with the student’s behavioral patterns and
preferences.
iii. Based on the aforementioned characteristics, the
system creates clusters of the already existing
students. These clusters contain valuable
information about their members, considering their
behavior, their preferences and generally their
interaction with the system.
Our system uses this model to support students
while studying the theory and solving exercises. In
particular, based on the information that emanates
from the knowledge level of the student in each
concept of the domain knowledge, the system
provides personalized help and support when s/he
navigates through the curricula. The error proneness
of the student supported by the student modeler is
used for error diagnosis. In particular, this
information is used in cases where the system has to
disambiguate between competing hypotheses that
concern the cause of students’ mistakes (Tsiriga and
Virvou, 2004).
4 K-MEANS CLUSTERING
ALGORITHM
K-means clustering is a well known machine
algorithm that is widely used to classify or to group
objects based on attributes/features into a number of
k groups/sets. “K” is positive integer number. The
grouping is done by minimizing the sum of squares
of distances between data and the corresponding
cluster centroid. Thus the purpose of K-mean
clustering is to classify the data. Each object
represented by one attribute point is an example to
the algorithm and it is assigned automatically to one
of the cluster. This consists of unsupervised learning
as the algorithm classifies the object automatically
only based on the criteria of minimum distance to
the centroid. The learning process depends on the
training examples with witch the algorithm is fed.
There are two choices in this learning process:
i. Infinite training. Each data that feed to the
algorithm will automatically consider as the training
examples.
ii. Finite training. After the training is considered as
finished, the algorithm is started to work by
classifying the cluster of new points. This is
conducted simply by assigning the point to the
nearest centroid without recalculate the new
centroid. Thus after the training finished, the
centroid are fixed points.
The basic steps of k-means clustering are simple. In
SIGMAP2012-InternationalConferenceonSignalProcessingandMultimediaApplications
200
the beginning we determine number of cluster K and
we assume the centroid or center of these clusters.
We can take any random objects as the initial
centroids or the first K objects in sequence can also
serve as the initial centroids.
Then the K means algorithm will do the three
steps below until convergence is reached, namely
there is no object move in groups, as illustrated in
Figure 1:
i. Determine the centroid coordinate randomly
from the data set.
ii. Determine the distance of each object to the
centroids and creation of k clusters.
iii. Group the object based on minimum distance
and determine the new means as the centroid of each
one of the k clusters.
Figure 1: Steps of K-means algorithm.
More specifically, the above steps can be
summarized as follows (Teknomo, 2006):
i. Step 1. Begin with a decision on the value of k as
the number of clusters.
ii. Step 2. Put any initial partition that classifies the
data into k clusters. Assign of the training samples
randomly, or systematically as the following:
a. Take the first k training sample as single-
element clusters.
b. Assign each of the remaining (N-k) training
sample to the cluster with the nearest centroid.
After each assignment, recomputed the centroid
of the gaining cluster.
iii. Step 3. Take each sample in sequence and
compute its distance from the centroid of each of the
clusters. If a sample is not currently in the cluster
with the closest centroid, switch this sample to that
cluster and update the centroid of the cluster gaining
the new sample and the cluster losing the sample.
iv. Step 4. Repeat step 3 until convergence is
achieved, namely until a pass through the training
sample causes no new assignments.
The key idea of k means is simple and is described
as follows: In the initialization phase, the number of
clusters k is determined. Then the algorithm assumes
the centroids or centers of these k clusters. These
centroids can be randomly selected or designed
deliberately. If the number of data is less than the
number of clusters, then each data is assigned as the
centroid of the cluster. Each centroid will have a
cluster number. If the number of data is greater than
the number of clusters, the algorithm computes the
Euclidean distance between each object and all
centroids to get the minimum distance. This data is
belongs to the cluster that has minimum distance
from itself. Given that the location of the real
centroid is unknown during the process, the
algorithm needs to revise the centroid location with
regard to the updated information (i.e., minimum
distance between new objects and the centroids).
After updating the values of the centroids, all the
objects are reallocated to the k clusters. The process
is repeated until the assignment of objects to clusters
ceases to change much, or when the centroids move
by negligible distances in successive iterations.
Mathematically the iteration can be proved to be
convergent.
Since the location of the centroid cannot be fixed
or prearranged, the centroid location is adjusted,
based on the current updated data. Then all the data
is assigned to this new centroid. This process is
repeated until no data is moving to another cluster
anymore. Mathematically, this loop can be proved to
be convergent. The convergence will always occur if
the following condition satisfied:
i. Each switch in step 2 the sum of distances from
each training sample to that training sample's group
centroid is decreased.
ii. There are only finitely many partitions of the
training examples into k clusters.
In order to better clarify the clustering algorithmic
process, we are providing the pseudo-code of k-
means algorithm:
Input: A dataset D, a user specified
number k
Output: k clusters
Initialize cluster centroids (randomly);
While not convergent
For each object o in D do
Find the cluster c whose centroid is
most close to o;
Allocate o to c;
End
For each cluster c do
Recalculate the centroid of c based
on the objects allocated to c;
End
End
Centroid-basedClusteringforStudentModelsinComputer-basedMultipleLanguageTutoring
201
The two key features of k-means which make it
efficient are often regarded as its biggest drawbacks:
i. Euclidean distance is used as a metric and
variance is used as a measure of cluster scatter.
ii. The number of clusters k is an input parameter:
an inappropriate choice of k may yield poor results.
That is why, when performing k-means, it is
important to run diagnostic checks for determining
the number of clusters in the data set. The correct
choice of k is often ambiguous, with interpretations
depending on the shape and scale of the distribution
of points in a data set and the desired clustering
resolution of the user. In addition, increasing k
without penalty will always reduce the amount of
error in the resulting clustering, to the extreme case
of zero error if each data point is considered its own
cluster (i.e., when k equals the number of data
points, n). Intuitively then, the optimal choice of k
will strike a balance between maximum compression
of the data using a single cluster, and maximum
accuracy by assigning each data point to its own
cluster. If an appropriate value of k is not apparent
from prior knowledge of the properties of the data
set, it must be chosen somehow. There are several
categories of methods for making this decision. One
simple principle, that we incorporated in the
implementation of k-means algorithm, sets the
number to (Mardia et al., 1979):
(1)
with n as the number of objects (data points). In our
case, given that the data points, which are an
outcome from empirical studies, are 32 we come up
with the conclusion that k=4. Figure 2 illustrates a
snapshot of our system and specifically a report of k-
means, the initial user data, the resulting k-mean
vectors, the number and members of means.
Figure 2: Snapshot of k-means algorithm.
5 CONCLUSIONS
In this paper we have presented our approach for
improving student models in the initialization phase
of an educational system. We have already our own
implementation of the k-means machine learning
algorithmic approach, as well as a tutoring system
for multiple language learning. After processing user
personal data we come up with more sophisticated
user models containing stereotypic information that
is based on similarities with other user groups seen
as clusters. We believe that this approach will
produce good results since it uses well known
techniques, already implemented in other similar
scientific areas with quite promising reports. As a
next step, it is in our near future plans to give our
resulting system to real students to use it
supplementarily for their language learning courses
in order to evaluate it and test its usefulness as an
educational tool.
REFERENCES
Niño, A., 2009. Machine translation in foreign language
learning: Language learners and tutors perceptions of
its advantages and disadvantages. In ReCALL. Vol. 21,
pp. 241-258.
Friaz-Martinez, E., Chen, S. Y., Macredie, R. D., Liu, X.,
2007. The role of human factors in stereotyping
behavior and perception of digital library users: a
robust clustering approach. In User Modelling and
User-Adapted Interaction. Vol. 13, pp. 305-337.
Webb, G. I., Pazzani, M. J., Billsus, D., 2001. Machine
Learning for User Modeling. In User Modelling and
User-Adapted Interaction. Vol. 11, pp. 19-29.
Virvou, M., Troussas, C., 2011. CAMELL: Towards a
ubiquitous multilingual e-learning system. In CSEDU
2011 - Proceedings of the 3rd International
Conference on Computer Supported Education. Vol.
2, pp. 509-513.
Virvou, M., Troussas, C., 2011. Web-based student
modeling for learning multiple languages. In
International Conference on Information Society, i-
Society 2011. Article number 5978484, pp. 423-428,
2011.
Virvou, M., D. Maras, D., Tsiriga, V., 2000. Student
modelling in an intelligent tutoring system for the
passive voice of english language. In Educational
Technology and Society.
Virvou, M., Chrysafiadi, K., 2006. A web-based
educational application for teaching of programming:
Student modeling via stereotypes. In Proceedings -
Sixth International Conference on Advanced Learning
Technologies, ICALT 2006. Vol. 2006, pp. 117-119.
Ditcharoen, N., Naruedomkul, K., Cercone, N., 2010.
SignMT: An alternative language learning tool. In
SIGMAP2012-InternationalConferenceonSignalProcessingandMultimediaApplications
202
Computers and Education, Vol. 55, pp. 118-130.
Licchelli, O., Basile, T. M. A., Di Mauro, N., Esposito, F.,
Semeraro, G., Ferilli. S., 2004. Machine Learning
Approaches for inducing Student Models. In Lecture
Notes in Artificial Intelligence (Subseries of Lecture
Notes in Computer Science). Vol. 3029, pp. 935-944.
Basile, T., Esposito, F., Ferilli, S. 2011. Improving User
Stereotypes through Machine Learning. In
Communications in Computer and Information
Science. Vol. 249, pp. 38-48.
Tsiriga, V., Virvou, M., 2004. A framework for the
initialization of student models in web-based
intelligent tutoring systems. In User Modelling and
User-Adapted Interaction. Vol. 14, pp. 289-315.
Mardia, K. et al.,1979. Multivariate Analysis, In Academic
Press.
Teknomo, K., 2006. K-Means Clustering Tutorials.
Centroid-basedClusteringforStudentModelsinComputer-basedMultipleLanguageTutoring
203
