A Machine Learning Approach to Identify Dependencies Among
Learning Objects
Carlo De Medio
1
, Fabio Gasparetti
2
, Carla Limongelli
2
, Filippo Sciarrone
2
and Marco Temperini
1
1
Sapienza University of Rome, Dept. of Computer, Control and Management Engineering,
Via Ariosto, 25 - 00189 Rome, Italy
2
Engineering Department, Artificial Intelligence Laboratory, Roma Tre University,
Via della Vasca Navale, 79, 00146 Rome, Italy
Keywords:
E-learning, Data Mining, Wikipedia.
Abstract:
Selecting and sequencing a set of Learning Objects (LOs) to build a course may turn out to be quite a challeng-
ing task. In this paper we focus on such an aspect, related to the verification and respect of the relationships of
pedagogical dependence existing between two LOs added to a course (meaning that if a given LO has another
one as “pre-requisite”, then any sequencing of the LOs in the course will need to have the latter LO taken by
the learners before of the former). In our approach the sequencing of LOs in the course can still be managed
by the instructor, basing on her/his taste and preferences, yet s/he can also be helped by a set of suggestions,
related to the pre-requisite relationships existing among the LOs selected for the course. Such suggestions
(such relationships, in effect) can be computed automatically and provide the instructor with significant help
and guidance. We show a light-weight formalization of the LO, and how it can be “represented” by a set of
WikiPedia Pages (“topics”); then we show how such set of topics, together with a set of relevant hypotheses we
previously defined, can help establish the dependence relationship existing between two LOs. In this endeavor
we exploit the classification in categories available for the WikiPedia topics, and obtain interesting results for
our framework, in terms of precision and recall of the dependence relationships.
1 INTRODUCTION
When an instructor is faced with the task of building
or maintaining a web-based course, her/his work can
be complex, in several respects. On the one hand,
the availability of an ever increasing amount of edu-
cational material on the web offers a problem of sheer
quantity of possible choices. An idea of how vast and,
possibly, confusing the selection task for an instruc-
tor can be, is given by simply limiting the consider-
ation to learning material available under the formal-
ized shape of standardized Learning Objects (LOs),
from Learning Object Repositories (LORs) such as
Connexion
1
, Ariadne
2
, or Merlot
3
. In this kind of
task, recommender and filtering tools might be of
help (Revilla Mu˜noz et al., 2015; Limongelli et al.,
2010; Limongelli et al., 2012; Limongelli et al., 2015;
1
Connexions is a Learning Object Repository, available
at http://www.cnx.org (Accessed July 24 2015).
2
Ariadne Foundation, available at http://ariadne-eu.org
(Accessed July 24 2015).
3
Merlot is a Learning Object Repository, available at
http://www.merlot.org (Accessed July 24 2015)
Limongelli et al., 2016).
On the other hand, one of the main responsibilities
of the instructor, while assembling a course through
LOs, is to ensure the fundamentalpedagogicalaspects
of the course, such as the preservation of the exist-
ing relationships of dependence between two LOs in
the course: in other words, to ensure that a LO
j
in
the course is depending on another object LO
i
in the
course (i.e. “LO
j
has LO
i
as a prerequisite”), then
LO
i
will precede LO
j
in every admissible sequencing
of the course’s LOs.
How the instructor sequences the learning mate-
rial strongly depends on the actual learning content
of the LOs, as well as on a teacher’s taste/preference.
Nevertheless, having automated suggestions on how
certain LOs should be necessarily sequenced, in or-
der to preserve dependency relationships, can be of
great help for the instructor, since it can ease a part
of the selection and sequencing task, and allow the
instructor to focus on less automatable aspects.
During course construction the instructor usually
labels each selected LO with a set of pre-requisite
concepts (knowledge and/or skills that will definitely
Medio, C., Gasparetti, F., Limongelli, C., Sciarrone, F. and Temperini, M.
A Machine Learning Approach to Identify Dependencies Among Learning Objects.
In Proceedings of the 8th International Conference on Computer Supported Education (CSEDU 2016) - Volume 1, pages 345-352
ISBN: 978-989-758-179-3
Copyright
c
 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
345

need be covered prior to the learner engaging the LO).
These pre-requisites statements provide a set of con-
straints that have to be verified during the course se-
quencing definition. Because of the intrinsic depen-
dence of such constraints on the LOs’ contents, nei-
ther their definition, nor their evaluation is a trivial
task, the former possibly being quite time-consuming
and error-prone.
In a previous work (Gasparetti et al., 2015b) we
have proposed six hypotheses that help to decide,
given two LOs, their prerequisite relationship. We
proposed and validated the hypotheses (described in
Section 3) and showed that, although these are statis-
tically significant, we get a low precision, at most 0.4.
In this paper, starting from the results of the pre-
vious work, we propose a different study based on
a traditional machine learning approach (Mitchell,
1997). We expand the set of data on which the anal-
ysis is done, and identify some features derived from
the above assumptions and feed the training system
(Weka).
The protocol of application of the criteria/features,
proceeds by passing the learning objects of a course
through Wikipedia Miner (Milne and Witten, 2013),
collect data and then feed Weka (Hall et al., 2009) in
such a way to obtain a set of suggestions about the
possible dependence relationships among LOs and
wiki pages. The results show good precision and re-
call values, increasing with the number of LOs em-
ployed in the course. This led us to think that our pro-
tocol can provide the teacher with valuable sugges-
tions about the possible sequencing of their learning
material.
In the following section we present some related
work. Then, in Section 3 we illustrate the six revised
hypotheses on which we base the inference of depen-
dence relationships; in this section we also provide
a lightweight formal background to discuss the char-
acteristics of a LO, based on its representation as set
of Wikipedia Pages (topics). Here we also discuss
the quantitative features computed for a LO during
the relationships inference. Section 4 presents the re-
sults obtained through the use of Weka (Hall et al.,
2009), that we trained with five different sets of LOs.
Section 5 comments on the experimental results and
proposes how to reinforce and generalize the present
results.
2 RELATED WORK
Associating learning material, of diverse origin, in
one’s own course material is a delicate task, since
the learning material is often not to be treated as a
mere additive on the activities proposed to students,
yet the new resources have to undergo some pedagog-
ical adaptation.
Curriculum Sequencing is an interesting challenge
in the educational research area: research in this
field aims to automatically produce a personalized se-
quence of didactic materials or activities (Brusilovsky
and Vassileva, 2003), or to allow a sequence of in-
structional material ”on demand”, by means of sys-
tems that deliver training to workers when and where
they need it (Capuano et al., 2009). Our proposed ap-
proach focuses on the possibility that the learning ob-
jects through which the teacher makes her selection
have already been labeled as to their possible depen-
dency relationships. The teacher has full control of
such dependency determinations: s/he can still accept
or discard such suggestions. On the other hand, such
hints can also simply add information that the teacher
had not noticed, resulting even more fruitful. Such as-
sistance is admittedly specific, even narrow, yet it can
still be of good use and let the teacher save time to be
dedicated to other pedagogical aspects.
Resources from the Web, and in particular from
Wikipedia, have been investigated as a source for
enrichment of the learning contents of a LMS or
LOR (Parker and Chao, 2007; Cole, 2009; Stuurman
et al., 2012; Gentili et al., 2001; Sciarrone, 2013).
Other kinds of resources have also been considered
for automated treatment and inclusion in the learning
resources of a course, such as the podcasts (Cebeci
and Tekdal, 2006), and the use of wikis also as means
for contribution from students into the course’s mate-
rial (Allen and Tay, 2012; Sun and Qiu, 2014).
The task of including such external material in a
course remains, however, a hard one, both on a tech-
nical and pedagogical level.
Wikipedia provides a wealth of information and
possibly learning resource documents, so the idea of
using such resources to enrich a course’s learning ma-
terial is compelling. In addition Wikipedia is instru-
mented on the web, so that the analysis and evalua-
tion of semantic relationships between documentsand
concepts is supported, down to the comparison with
words or text excerpts (Strube and Ponzetto, 2006;
Gabrilovich and Markovitch, 2009; Milne and Wit-
ten, 2008; Biancalana et al., 2013). This can allow
for an effective treatment of the wikipedia contents in
advance of their uses to support learning in a formal
environment.
In this paper we propose a method to exploit the
informative resources of weak-semantic taxonomies,
in particular Wikipedia, to allow sequencing LOs with
external resources, and to make the LOs enrichment
possible, by annotating them through the external re-
CSEDU 2016 - 8th International Conference on Computer Supported Education
346

sources.
To our knowledge our approach is novel, yet we
have found correspondences in literature.
An approach to the identification of prerequisite
relationships among “knowledge components” is in
(Scheines et al., 2014), where causal discovery is used
on components represented as latent (unmeasured)
variables. To validate the approach, simulated data
are used, representing a dataset of student-skills mea-
sures.
Voung et al. (Vuong et al., 2011) propose to an-
alyze large-scale assessment to determine the depen-
dency relationships between knowledge units. Given
sufficient user data, the authors prove that prerequi-
sites for each instructional unit can be identified. On
the contrary, the methodology cannot be applied to
new curriculums, that is, units to which student per-
formances have not been extensively evaluated.
Recently (Gasparetti et al., 2015c) proposed an
early attempt to exploit Wikipedia as a source of
learning materials. Analyzing the links present in
the Wikipedia pages, they build courses based on the
Grasha teaching styles and on a social didactic ap-
proach. A further early attempt to exploit Wikipedia
for the sequencing task has been proposed in (Gas-
paretti et al., 2015a).
3 HYPOTESES AND FEATURES
FOR COMPARING LOS
In the previous work (Gasparetti et al., 2015b) we
have proposed an approach for extracting prerequi-
site relations from textual LOs by means of wikipedia
miner (Milne and Witten, 2013) that is a tool to access
to Wikipedia’s structure and content.
The process goes from information extraction out
of the involved LOs, through determination of the
WikiPedia pages (topics henceforth) that are associ-
ated to each one of the LOs, up to the analysis of a set
of features of such topics, allowing to establish the
possible dependency relationships between the LOs.
It can be summarized as follows:
• given the learning objects LO
i
and LO
j
, the
Wikipedia Miner Toolkit is activated on them;
• for each LO the textual content is extracted
and analyzed, so as to pair portions of it
with annotations, relating to categories in the
Wikipedia taxonomy (made by metatags inside
the Wikipedia’s pages and perfected by the com-
munity of Wikipedia, it is the division into cat-
egories of the information; the system generates
a graph of the categories that can be questioned
without fetch the whole page);
• for each LO, the set of annotations is used to relate
the LO to a set of topics;
• then we apply certain criteria of evaluation to the
two sets of topics associated to LO
i
and LO
j
;
• we infer the existence of dependencyrelationships
on the basis of a set of hypotheses.
The dependency relation of prerequisites is expressed
as LO
i
→ LO
j
meaning that LO
i
is a prerequisite for
LO
j
.
In the following we provide a revised set of hy-
potheses and explain the features of the topics asso-
ciated with the LOs, which we use to test such Hy-
potheses.
H1
if the distance that connects the Wikipedia two
categories to which LO
i
and LO
j
belong respec-
tively (even through a common ancestor category)
is less than a given threshold, the prerequisite re-
lation exists. The threshold is set to 2, with val-
ues higher than 2 the execution of the program
slows down dramatically and the performance is
not improved. The hypothesis is inspired by the
semantic similarity defined over a IS-A taxonomy
proposed by Resnik (Resnik, 2011).
H2
more general topics need longer discussions to be
described, compared to very specific ones.
H3
if a Wikipedia author has found the necessity
to define a concept by means of other concepts,
probably the former one is more specific than the
latter.
H4 more general concepts create several connections
to specific ones, especially if the author wants to
give an overview of the domain leaving it up to the
reader to deepen discussions on specialized pages.
H5 In this hypothesis we extract the nouns from the
two articles and assume that nouns in a Wikipedia
article correspond to concepts. Therefore, articles
dealing with multiple concepts should be consid-
ered more general.
H6 The last hypothesis analyzes the length of LOs in
terms of number of words included in the descrip-
tion (i.e., first paragraph) of the articles. If the
number of words of the article associated with LO
i
is much greater than the ones of LO
j
, LO
i
→ LO
j
exists. Again, we follow a similar rationale of
the hypotheses H4 and H5, but the computational
complexity is limited in this case.
A Machine Learning Approach to Identify Dependencies Among Learning Objects
347

In the proposed approach, the features the hypotheses
are based upon are considered as an input of a ma-
chine learning algorithms. Eleven features represent-
ing relevant aspects of each LO’s are defined. Before
describing the features we introduce some definitions.
3.1 Formal Background
Following a trend used in several sources, a
WikiPedia Page associated to a LO will be named
”topic”.
In a topic anchors are spread, to connect such re-
source to other topics. Such references will be named
“links”.
For our purposes a link is then a URI (Uniform
Resource Identifier, i.e. a usual web address). Notice
that another significant link is the topic address.
As a web resource, the topic comprises multime-
dia, yet in our approach we will consider only its tex-
tual contents; such textual contents are basically com-
posed by all the topic’s text and links to other topics.
We differentiate between simple word and a nouns ,
they will be analyzed separately as suggested in H5.
Moreover, a Wikipedia page usually comprises a
first section, containing a summary of relevant aspects
of the page.
Here are some definitions for understanding the
formal background:
T the set of all the topics t associated to a LO
L the set of all the links to other topics in t: t.L
W the set of all the words used in t: t.W
N the number of the links to other topics in t: t.N
addr the topic address (another link): t.addr
FS the first section of the topic in its usual web-
publication: t.FS. It comprises sets of links,
nouns and words, that we consider subsets of,
resp., the links, words and nouns of the topic:
- set of links in the first section: t.FS.L ⊆ t.L
- set of words in the first section: t.FS.W ⊆ t.W
- set of nouns in the first section: t.FS.N ⊆ t.N
3.2 Features of a LO
Given two learning objects LO
i
and LO
j
, the features
can be formalized as follows:
1. avgLen(LO
i
): The average length of the text of the
Wikipedia topics associated to LO
i
defined in terms of
words obtained by a text tokenization process.
avgLen(LO
i
) =
∑
t∈T
LO
i
|t.W|
|T
LO
i
|
2. avgLen(LO
j
): Similar to avgLen(LO
i
) but evaluated on
LO
j
.
avgLen(LO
j
) =
∑
t∈T
LO
j
|t.W|
|T
LO
j
|
3. f sl(LO
i
): number of links in the first section of the
Wikipedia topics associated with LO
i
fsl(LO
i
) = t. FS.L
4. f sl(LO
j
): number of links in the first section of the
Wikipedia topics associated with LO
j
fsl(LO
j
) = t. FS.L
5. avgNL(LO
i
): The average number of links in the topics
associated to LO
i
avgNL(LO
i
) =
∑
∀t∈T
t.L
|T|
6. avgNL(LO
j
): Similar to avgNL(LO
i
) but evaluated on
LO
j
.
7. nouns(LO
i
): Number of distinct nouns in LO
i
extracted
by the part-of-speech tagger.
8. nouns(LO
j
): Similar to nouns(LO
i
) but on LO
j
.
9. nounsIntersect(LO
i
, LO
j
): Given the two sets of nouns
N
i
and N
j
extracted from LO
i
and LO
j
nounsIntersect(LO
i
, LO
j
) = |N
i
∪ N
j
|
10. avgFsLen(LO
i
): The average length of the text of the
Wikipedia topics associated to LO
i
defined in terms of
words obtained by the tokenization process limited to
the first section of the topics
avgFsLen(LO
i
) =
∑
∀t∈T
t.FS.W
|T|
11. avgFsLen(LO
j
): Similar to avgFsLen(LO
i
) but evalu-
ated on LO
j
.
All the features are represented by real or integer
numbers.
4 EXPERIMENTAL RESULTS
The system, programmed to operate on the features
described above, was tested through WEKA (Waikato
Environment for Knowledge Analysis), a free soft-
ware developed by the University of Waikata in new
Zealand which allows to apply Machine Learning al-
gorithms on large data-sets. In our case the training
set consists of 5 courses structured as shown in Ta-
ble 1.
The courses were chosen in order to have sam-
ples differing both in terms of number of LOs and in
terms of content and materials. Some of the LOs con-
tent presents a very formal language (e.g.: Program-
ming Language (Java) and Advanced Computer Sci-
ence) and other LOs show historical references and
CSEDU 2016 - 8th International Conference on Computer Supported Education
348

Table 1: Description of test courses.
Course N. of LOs N. of expected
Name dependences
Advanced 85 2256
Computer Science
Programming 18 41
Language (Java)
Economy 5 10
Futurism 4 5
Basic 4 5
Mathematics
descriptive content (e.g.: Futurism). The expected de-
pendencies are the relationships between prerequisite
and successor concepts represented by LOs. The LOs
are represented by text files containing the entire text
of the lessons; the system is implemented so as to ac-
cept
html pages, automatically retrieved (or not) by
the network. They are parsed and return the textual
file automatically. The entire data-set was classified
by the algorithm J48, an open source implementation
of the algorithm C4.5, which in the first tests was the
most encouraging one. Other algorithms are appli-
cable to data-sets but require larger data sets to see
significant results. The measures taken from the per-
formance analysis of the implemented system are the
following:
• π Precision in [0..1]: high precision means that
an algorithm returned more relevant results than
irrelevant results;
• ρ Recall in [0..1]: high recall means that an algo-
rithm returned most of the relevant results;
• F1 F-measure is a combination of precision and
recall, namely the harmonic mean;
• ROC Is the area under the ROC curve normalized
between [0..1] and it is equal to the probability
that a classifier will rank a randomly chosen posi-
tive instance higher than a randomly chosen neg-
ative one.
In addition, given a pair of LOs: LO
1
and LO
2
we
distinguish two classes results for the classifier:
• Class 1 (Cl1) Set of all pairs: LO
i
, LO
j
for which
there is the prerequisite relation LO
i
→ LO
j
;
• Class 2 (Cl2) Set of all pairs: LO
i
, LO
j
for which
there isn’t any prerequisite relation.
We carried out tests divided into courses; for each
test we show the measures described above and the
confusion matrix. This matrix is a specific table lay-
out that allows to visualize the performance of an al-
gorithm: each column of the matrix represents the
instances classified by the system for a given class,
while each row represents the instances in the ex-
pected class. The classifier works on the two classes
described above, so the corresponding confusion ma-
trix will be 2 X 2; on the primary diagonal we will
find the number of instances correctly classified: True
Positives (a prerequisite relation does exist and it is
found) and True Negatives (a prerequisite relation
does not exist and it is not found). On the secondary
diagonal the classifier errors are reported: False Pos-
itives (a prerequisite relation does not exist while it
is found) and False Negatives (a prerequisite relation
does exist and it is not found). The general confusion
matrix is shown in table 2.
Table 2: Confusion Matrix.
1 2 class
True Positives False Positives 1
False Negatives True Negatives 2
With the course of Advanced Computer Science,
composed of 85 LO , The System has responded with
good values of precision and recall as is shown in Ta-
ble 3.
Table 3: Results for the course Advanced Computer Sci-
ence.
instances n. Correct Wrong
1037 877 160
Cl 1 Cl 2
Precision 0,839 0,853
Recall 0,858 0,833
F1 0,848 0,843
ROC 0,894 0,894
1 2 class
448 74 1
86 429 2
The results for the course Programming Language
(Java) reported in Tab. 4 are lower than the course
of Advanced Computer Science because the second
course has more LOs than the first one, even if both
belong to a branch of science that is well categorized
in Wikipedia.
Table 4: Results for the course Programming Language
(Java).
instances n. Correct Wrong
289 256 33
Cl 1 Cl 2
Precision 0,633 0,915
Recall 0,463 0,956
F1 0,535 0,935
ROC 0,743 0,743
1 2 class
19 22 1
11 237 2
A Machine Learning Approach to Identify Dependencies Among Learning Objects
349

The Futurism course’s results are illustrated in Ta-
ble 5. The low number of training instances does not
allow the system to reach acceptable levels of preci-
sion and recall on Class1.
Table 5: Results for the course Futurism.
instances n. Correct Wrong
25 19 6
Cl 1 Cl 2
Precision 0,333 0,818
Recall 0,2 0,9
F1 0,25 0,857
ROC 0,53 0,53
1 2 class
1 4 1
2 18 2
The Economy course was created by taking the
LOs text directly from the Wikipedia pages in order
to see how the system works in an ideal situation. The
performance reported in the Table 6 shows good re-
sults despite the few LOs in the course.
Table 6: Results for the course Economy.
instances n. Correct Wrong
25 21 4
Cl 1 Cl 2
Precision 0,75 0,923
Recall 0,9 0,8
F1 0,818 0,857
ROC 0,87 0,87
1 2 class
9 1 1
3 18 2
In the Basic Mathematics course, results are re-
ported in Table 7. All the zero values are explained
by the fact that the system is unable to find a suffi-
cient number of relationships between pairs of LOs.
This is due to the mathematical formalism expressed
with the use of formulas in the text: Wikipedia Miner
service fails to find Wikipedia pages associated to the
mathematical formulas and doesn’t associate topics to
concepts.
To see how the system works in a real situation,
with LO taken from courses of different types, a
dataset consisting of all instances of Advanced Com-
puter Science, Programming Language (Java) and Fu-
turism was created. We left out the mathematics
course owing to the low results obtained, as shown
above. The tests are shown with and without the ideal
course of Economy so we can see the peak present
at low numbers of LO’s components in the course.
Table 7: Results for the course Basic Mathematics.
instances n. Correct Wrong
5 4 1
Cl 1 Cl 2
Precision 0 0,8
Recall 0 1
F1 0 0,889
ROC 0,5 0,5
1 2 class
0 1 1
0 4 2
The test performed on the data set composed of 1-
2-3 courses highlights how the training stabilizes the
system levels of precision and recall around the 0.848
using a big training set.
Table 8: Results for the course course 1-2-3.
instances n. Correct Wrong
5498 4660 838
Cl 1 Cl 2
Precision 0,835 0,859
Recall 0,845 0,85
F1 0,84 0,855
ROC 0,895 0,895
1 2 class
2199 403 1
435 2461 2
Here is the trend of results sorted by number of
instances in the dataset of the course.
Figure 1: On the x-axis the courses are ordered by LO nu-
merousness, on the y-axis the value of the precision and
recall.
As expected, the results show an improvement in
system performance with the growth of the size of
the data set used as a training set. Plus, an analysis
of decision trees generated by the algorithm J48 for
each iteration shows that initially the features with a
higher content of information are the two measures
associated with the amount of nouns in the wikipedia
CSEDU 2016 - 8th International Conference on Computer Supported Education
350

page associated to the LO. Just below these measures,
in the decision tree, two other measures are close to
the root: the average length of the initial parts of
wikipedia pages related to the LO, and the number
of the internal links. Including in the graph the results
of the Economy course we have a peak in the graph at
a low level of instances as shown in Fig. 2.
Figure 2: On the x-axis the courses are ordered by LO nu-
merousness, on the y-axis the value of the precision and
recall.
5 CONCLUSIONS
The composition of web based instructional courses,
especially if personalization and adaptivity are sup-
ported (Sterbini and Temperini, 2009; De Marsico
et al., 2013) can result in a burdensome task for the
teacher, encompassing both the selection of suitable
learning objects, and the control on their sequencing.
In this paper we have presented an approach for sup-
porting the teacher in the management of the relation-
ships of dependencies between learning objects: such
relationships can be suggested/discovered automati-
cally, so as to allow the teacher to adopt or change
them. An effective automated determination of such
relationships can also be very useful in contexts of
personalized e-learning, where the learner is proposed
learning objects that are automatically sequenced.
Experimental results presented in this article have
confirmed the suitability of an approach based on the
data, namely a machine learning approach that pro-
vides precious indications that strengthen our work-
ing hypothesis. Obviously, since this approach is data
driven, the provided information may be domain-
dependent.
In order to produce results as independent domain
as possible, in future we will consider resorting to dif-
ferent machine learning approaches (neural networks,
Bayesian networks, etc.) and to substantiate the va-
lidity of our work hypotheses, on a theoretical level
too.
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