A BAYESIAN APPROACH FOR AUTOMATIC BUILDING

LIGHTWEIGHT ONTOLOGIES FOR E-LEARNING

ENVIRONMENT

Francesco Colace, Massimo De Santo, Mario Vento

DIIIE, Università degli Studi di Salerno, Via Ponte Don Melillo 1, 84084, Fisciano (Salerno), Italy

Pasquale Foggia

DIS, Università di Napoli “Federico II”, Via Claudio, 21, 80125 Napoli, Italy

Keywords: Bayesian Networks, Ontology, MultiExpert System

Abstract: In the last decade the term “Ontology” has beco

me a fashionable word inside the Knowledge Engineering

Community. Although there are several methodologies and methods for building ontologies they are not

fully mature if we compare them with software and knowledge engineering techniques. In this paper we

propose a novel approach for building university curricula ontology through analysis of real data: answers

of students to final course tests. In fact teachers design these tests keeping in mind the main topics of course

knowledge domain and their semantic relation. The ontology building is accomplished by means of

Bayesian Networks.

1 INTRODUCTION

One of the greatest challenges in scientific research

is the development of advanced educational systems

that are adaptable and intelligent. Methodologies for

the knowledge representation are the key elements

for building intelligent and advanced training

systems. In fact, a set of well-structured concepts can

improve interoperability and information sharing

between systems. In literature a set of concepts and

their relationships is called ontology (Gruber,1993).

Ontology is one of the most effective tools for

formalizing knowledge shared by groups of people

but their building process is neither trivial nor easy

but it is very important because it is the starting point

of content sequencing both in traditional and on-line

courses. Teachers, who have to describe the

relationships among the subjects belonging to a

course, often provide a very detailed representation

creating ontologies with a large number of states that

could not be easily interpreted and used. A further

problem is related to the evaluation of the links and

their semantic values between the different states. In

this paper we will propose a method for ontology

building that can be applied to knowledge domain

related to university curricula. In this case it is more

correct to say lightweight ontology because we are

finding an advanced taxonomy. In order to solve this

problem we have a powerful source of evidence: the

end course evaluation tests. Final tests could

represent the ontology course because they have

been designed by teachers keeping in mind the

sequencing and propaedeuticity courses subjects. It

may be useful to extract the ontology from answers

given by students on such tests. Bayesian networks

approach represents an useful technique for this

purpose. In recent years, such networks have been

more and more often used for encoding knowledge

domains provided by experts with a grade of

uncertainty and they have proved to be effective for

solving data-modelling problems. So the aim of this

paper is the introduction of a methodology, based on

structural learning Bayesian network algorithms,

allowing an unattended lightweight ontology

building. So firstly we define ontologies and

advantages coming from their use in knowledge-

based systems. Secondly, we discuss Bayesian

networks and how they can easily map an ontology.

In particular we will give some information about

structural learning algorithms and their properties.

Finally, we will describe the proposed algorithm and

we will present some obtained results.

386

Colace F., De Santo M., Vento M. and Foggia P. (2005).

A BAYESIAN APPROACH FOR AUTOMATIC BUILDING LIGHTWEIGHT ONTOLOGIES FOR E-LEARNING ENVIRONMENT.

In Proceedings of the Seventh International Conference on Enterprise Information Systems, pages 386-389

DOI: 10.5220/0002523003860389

Copyright

c

SciTePress

2 ONTOLOGIES

The concept of ontology was taken from philosophy

where it means a systematic explanation of being. In

recent years, however, this concept has been

introduced and used in different contexts, thereby

playing a predominant role in knowledge

engineering and in artificial intelligence. In literature

there are many definitions about what an ontology is

(Gruber,1993). Ontologies could be represented as a

taxonomic trees of conceptualizations: they are

general and domain-independent at a superior level,

but become more and more specific when one goes

down the hierarchy. In other words, when we move

from the highest taxonomic levels to the lowest

ones, characteristics and aspects typical of the

domain under examination are showed. In order to

point out this difference in literature we call them

heavyweight (deeper ontology) and lightweight

(advances taxonomy) ontology respectively. In this

paper we will adopt the last one approach keeping in

mind this definition of ontology: “An ontology may

take a variety of forms, but it will necessarily

include a vocabulary of terms and some

specification of their meaning. This includes

definitions and an indication of how concepts are

inter-related which collectively impose a structure

on the domain and costrain the possible

interpretations of terms”(Uschold,1999). The aim of

this paper is to build ontologies, according the

previously definition, representing the knowledege

domain of university programs.

3 ONTOLOGIES AND BAYESIAN

NETWORKS

In this paragraph we will describe bayesian networks

and as they can map an ontology. Bayesian networks

have been successfully used to model knowledge

under conditions of uncertainty within expert

systems, and methods have been developed from

data combination and expert system knowledge in

order to learn them. The learning process through

Bayesian networks has two important advantages:

first of all they easily encode the knowledge of an

expert. Secondly nodes and arcs of the learnt

Bayesian network represent recognizable links and

causal relationships. So user can understand easily

the knowledge encoded in the representation. A

Bayesian network is a graph-based model encoding

the joint probability distribution of a set of random

variables X ={X

1, …,

X

n

). It consists of a directed

acyclic graph S (called structure) where each node is

associated with one random variable X

i

and each arc

represents the conditional dependence among the

nodes that it joints and a set P of local probability

distributions, each of which is associated with a

random variable X

i

and conditioned by the variables

corresponding to the source nodes of the arcs

entering the node with which X

i

is associated. The

lack of an arc between two nodes involves

conditional independence. On the other hand, the

presence of an arc from the node X

i

to the node X

j

represents that X

i

is considered a direct cause of X

j

.

Given a structure S and the local probability

distributions of each node p(X

i

| Pa

i

), where Pa

i

represents the set of parent nodes of X

i

, the joint

probability distribution p(X) is obtained from:

. In order to construct a

Bayesian network for a given set of variables, we

need to define some arcs from the causal states to

the other ones that represent their direct effects

obtaining a network that accurately describes the

conditional independence relations among the

variables. The aim of this paper is the introduction

of an algorithm, based on the formalism of the

Bayesian networks, able to infer propedeutical

relationships among different subjects (in other

terms the ontology) belonging to the knowledge

domain of an university curricula. The first step of

this algorithm is the introduction of a mapping

between Ontology and Bayesian Network. In our

ontology model nodes represent the subjects

belonging to the course knowledge domain and the

arcs mean a propaedeutical relationship among the

nodes. We can map this ontology graph in a

bayesian network in the following way: the bayesian

networks nodes can model the subjects belonging to

the course Knowledge Domain and the knowledge

of subject by students while arcs in the same way

can mean the propaedeutical relationships among the

nodes. Given the previous mapping strategy our

aim is to define the ontology used by teacher in

his/her course. Obviously we must define data type

and data set for this approach. As previously said

the students answers to the end course evaluation

tests represent a source of implicit evidence. In

fact, teachers through the end-of-course

evaluation tests not only assess students

knowledge for every subjects, but describe the

course ontology and outline the propaedeutic

aspects that relate subjects each other. On the

basis of these considerations, teachers have

designed the final test of the first-level course on

Computer Science at the Electronical Engineering

Faculty of the University of Salerno and the final

1

() ( | )

n

ii

i

pX pX Pa

=

=

∏

A BAYESIAN APPROACH FOR AUTOMATIC BUILDING LIGHTWEIGHT ONTOLOGIES FOR E-LEARNING

ENVIRONMENT

387

test of the first-level course on Introduction to

Computer Science at the Languages Faculty of the

University of Salerno. In order to design the

reference ontologies teachers used the approach

introduced in (Colace, 2004). We must outline

that this process was very long and hard for

teachers. The result of this process is shown in

figure 1. Each node of the networks has two states

and shows the probability that a generic learner

knows the subject associated with the same node.

We have supposed that each node can assume

only the following two states (random

Bernoullian

variable): state ‘Yes’: complete knowledge of the

subject and state ‘Not’: total ignorance on the

subject. The student level of knowledge could be

evaluated on the basis of the answers given to the

questions (a set of questions is proposed for each

subject).

4 AN AUTOMATIC ALGORITHM

FOR BUILDING ONTOLOGIES

FROM DATA

As previously said our aim is the introduction of an

algorithm able to infer automatically propaedeutical

relationships between the different subjects forming

an university program. In the previous section we

defined the general structure of our ontologies and

the way to map them in bayesian networks. In this

section we will describe our automatic algorithm for

building ontologies. The description of the desired

automatic algorithm, able to build an ontology from

data analysis, could be described in the following

steps: to collect data, to collect the nodes of bayesian

networks (also ontology nodes) and to learn the

structure of ontology (relationships and their

strength) through a bayesian statistical inference. In

our scenario an effective approach could be the use

of structural learning algorithms that can build

Bayesian networks (and in our scenario ontologies)

using only data. The main aim of structural learning

algorithms is to point out the relationships between

the entities of a knowledge domain and to specify

the causality relationships starting from the

observation of domain variables values. More details

on structural learning algorithms are in (Neches,

1991). In literature there are many structural

learning algorithms but they are not able to achieve

good results for every data set and structure. In order

to maximize the correct building probability we use

a multiexpert approach (Kittler,1998). We selected

five structural learning algorithms in order to use

them according a majority vote multiexpert

approach. The algorithms are: the Bayesian

algorithm, K2 algorithm, K3 algorithm, PC

algorithm and TPDA algorithm. The main steps of

our algorithm are:

• Insert as inputs of every structural learning

algorithms bayesian networks nodes and data

• Collect the results (bayesian networks) of every

structural learning algorithms and arrange them

in a single networks according to a majority vote

multiexpert approach. In particular we have an

arc between two nodes if and only if three

experts say that. The arc sense of direction is

obtained in the same way (obviously considering

only the experts that point out the arc presence).

We have selected seven networks in order to test the

algorithm effectiveness in the building process. In

table 1 there is a briefly description of all selected

networks and of their related dataset.

Table 1: Analysed Networks.

Network

Name

Nodes

Number

Arcs

Number

Data Set

Samples

Alarm 37 46 10.000

Angina 5 5 10.000

Asia 8 8 5.000

College 5 6 10.000

Led 8 8 5.000

Pregnancy 4 3 10.000

Sprinkler 5 5 400

In order to evaluate the performances of algorithm

we used this index(Colace, 2004):

Global Learning

=

Correctly Oriented Arcs

Correctly Oriented Arcs+ Wrongly Oriented Arcs+ Added Arcs+ Missing Arcs

∑

∑∑∑∑

This index measures the algorithm performance in

the learning correct network topology and correct

arcs orientation. In Table 2 there are the obtained

results of our algorithm compared with the results

obtained by best single expert.

Table 2: Obtained results of multiexpert approach versus

the results of best expert

.

Network

Global Learning

Multi Expert

Global Learning

Best Single Expert

Asia 1 1

Sprinkler

1 0.83

Alarm

1 0.96

Angina

1 1

Led

0.75 0.55

Pregnancy

1 1

College

0.86 0.67

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388

After this first phase we have used our algorithm

on the knowledge domain provideed by teachers

as previously described. For the experimentation

we have used data coming from about nine

hundred questionnaires for the first ontology and

seven hundred questionnaires for the other ones.

Table 3: Obtained results of multiexpert approach versus

the results of best expert in the real cases

.

Network

Global Learning

Multi Expert

Global Learning Best

Single Expert

Ontology#1 0,50 0,18

Ontology#2 0,80 0,43

Ontology#3 0,57 0,29

Ontology#4 1,00 1,00

Analysing the obtained results (table 3) we can

observe as the algorithm offers good results

although we have not furnished any type of “a

priori” knowledge to the system and a low number

of samples that makes worse the performances of

structural learning algorithms. In the case of first-

level course on Computer Science ontology

(figure 2 ontology #1) the system is able to

recognize all the links between nodes that the

teacher defined "strong". The link that is not

recognized has, according to the teacher, the

lowest value. The web ontology (figure 2

ontology #4) is built correctly since the number of

samples is enough to make reliable and strong the

process. Also hardware ontology (figure 2

ontology #2) is built correctly except an arc that,

according to the teacher, expresses one of the

weakest links inside the net. Finally the ontology

Software (figure 2 ontology #2) shows a reverse

orientation of an arc and adds two new arcs. The

reason for these mistakes is the low number of

samples. However, the algorithm offers some

satisfactory results from the point of view of the

determination of the structure of the net

reconstructing all the links defined "strong" by

teacher.

5 CONCLUSION

In this paper, we have described a method for

automatic learning lightweight ontologies that

represent subjects (and their relationships) belonging

to a course program knowledge domain. Our

approach to problem resolution is based on the use

of Bayesian networks. Thanks to their

characteristics, these networks can be used to model

and evaluate the conditional dependencies among

the nodes of ontology on the basis of the data

obtained from student tests. An experimental

evaluation of the proposed method has been

performed using standard datasets and real data. In

the future, we aim to integrate the proposed method

into a distance learning platform, in order to exploit

the inferred ontologies for an adaptive contents

selection.

REFERENCES

Colace, F., De Santo, M., Foggia, P., Vento, M., A Semi

utomatic Bayesian Algorithm for Ontology Learning,

roceedings of ICEIS 04, Porto, 2004

Gruber, T.R, Translation approach to portable ontology

specification, Knowledge Acquisition 5, 1993

Kittler J., Hatef D., Matas J., On Combining Classifiers,

IEEE Trans. On PAMI, vol. 20 n. 3, 1998

Neches R., Fikes R. E., Finin T., Gruber T. R., Senator T.,

Swartout W. R., Enabling Technology for Knowledge

Sharing, AI Magazine, 12(3):36-56, 1991

Uschold M., R. Jasper, A Framework for Understanding

and Classifying Ontology Applications, IJCAI99

Workshop on Ontologies and Problem Solving

Methods, Stockholm, 1999.

Figure 1: Proposed ontology for the first-level course on

Computer Science (Ontology #1) and Introduction to

Computer Science (Ontology #2, Ontology #3 and

Ontology #4)

.

Figure 2: Obtained results. In blue correct arcs, in red

wrongly oriented arcs, in black added arcs.

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ENVIRONMENT

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