=Paper=
{{Paper
|id=Vol-1492/Paper_20
|storemode=property
|title=Data Integration through Clustering and Finding Statistical Relations - Validation of Approach
|pdfUrl=https://ceur-ws.org/Vol-1492/Paper_20.pdf
|volume=Vol-1492
|dblpUrl=https://dblp.org/rec/conf/csp/JaszukMF15
}}
==Data Integration through Clustering and Finding Statistical Relations - Validation of Approach==
https://ceur-ws.org/Vol-1492/Paper_20.pdf
Data Integration through Clustering and Finding
Statistical Relations - Validation of Approach
Marek Jaszuk, Teresa Mroczek, and Barbara Fryc
University of Information Technology and Management, ul. Sucharskiego 2, Rzeszow, Poland,
{mjaszuk,tmroczek,bfryc}@wsiz.rzeszow.pl
Abstract. The paper analyzes an approach to data integration based on finding
statistical relations between data. The data used for experimenting comes from
surveys collected from student groups. The practical problem that underlies this
research is discovering the model of knowledge about students, which would al-
low for making predictions about their future educational success or failure. The
obstacle is that data collected for different groups over years has different format
and this makes it difficult to reuse the previously collected data. Thus we had to
find a way, to overcome this difficulty and integrate the heterogeneous data. The
paper analyzes the feasibility of integrating data using this method. Although
based on particular application, the model of computations presented in the paper
is of more general nature, and should be applicable in many other domains.
Key words: data integration, clustering, semantic class, correlation, survey
1 Introduction
Increase in popularity of information technologies brought us a large number of inde-
pendently created and managed information systems. Such systems can contain similar
information but coming from disparate sources which leads to information heterogene-
ity. This prevents from interoperability of such systems and their integration. Thus it is
highly demanded to overcome the heterogeneities through some data integration tech-
nique, and data integration is one of the central problems in information systems.
Usually information heterogeneity can be considered on three levels: syntactic,
structural and semantic. Our focus in this paper is on semantic heterogeneity and data
integration on this level. The problem of semantic heterogeneity has been studied in-
tensively in the past years (see e.g. [2, 3, 5, 6, 9]). Automatic identification of semantic
relations between different data sets has been investigated [2] together with represen-
tation and using of identified relations for transferring data and query answering [1,
5, 9]. A prominent part of research is devoted to investigating the role of ontologies,
which represent formally the conceptual structure of a given application domain. The
ontologies are used for identifying and using semantic relations, necessary for repre-
senting information systems to be integrated. In this regard, an ontology works as an
intermediary between heterogeneous data sources.
The main difficulty with using ontologies is that they are usually handcrafted by
domain experts accompanied by ontology engineers. Any modification in an ontology
requires human effort, and thus is inefficient. Another problem is that an ontology for
200
a given domain can be developed in many different ways, and its optimal structure
depends on particular application. Thus a particular ontology is not always suitable for a
specific problem to be solved. In consequence, a method which automatizes integration
of data coming from different sources, is highly desired.
The application example discussed in this paper is integration of different versions
of survey data. Solving this problem using standard ontology based techniques would
require developing ontologies for the survey questions, and then matching the ontolo-
gies to integrate the data. The semantic space for such an ontology is huge, because
changing even a single word in a survey question can change the interpretation of this
question, and thus shifts the meaning of this question. Thus doing the task of data in-
tegration manually can be a challenge. We propose an alternative approach based on
finding statistical relations between data. This technique has been applied to surveys
made on students, but it is more general, and could be applied to many other kinds of
data with similar structure.
The paper is organized as follows. Sec. 2 discusses the practical problem to be
solved. In Sec. 3 we discuss, how the survey questions are formulated. In Sec. 4 the
basic assumptions about statistical data representation and the definition of semantic
space. Then, in Sec. 5, we demonstrate the correlations between two data sets obtained
independently, in order to confirm validity of the presented approach. Finally in Sec. 6
we discuss the way of integrating data coming from different surveys using clustering
techniques.
2 The Problem Formulation
The practical problem that underlies considerations presented in this paper, is integra-
tion of data coming from groups of students. The University of Information Technology
and Management in Rzeszów (UITM), where we conduct the research, collects some
basic data about the students in the computer system, like the date of birth, the gender,
the grades, etc. However, these data are not sufficient when one wants to perform more
sophisticated kind of reasoning about the students. In our case, the main interest are in
the future study results (educational success) of the students, that are beginning their
education. Such information is interesting both for the group as a whole, as well as for
selected individuals. The potential value of such information is both for the university
authorities, as well, as for the teaching stuff, because it allows for early identification
of potential problems, or outstanding individuals, who require special treatment. One
of the factors that indicate the potential success are the results in the preceding stage
of education, like the secondary school. This is, however, not a complete information,
and the educational success is influenced by many other factors. We assume that the
missing information about the factors influencing educational success can be collected
by carrying out surveys, with questions related to socio-economic situation of students,
as well as their motivations and reasons to study. The problem is in itself interesting
from the social sciences perspective, but this aspect will not be discussed here.
There is potentially a large number of details, that could be asked in such a survey.
The problem is thus selection of questions to be included in the survey. Unfortunately,
the survey cannot be to long, otherwise, the students would not be willing to fill it.
201
Thus the choice of the questions should be very careful. The most adequate collection
of questions can be obtained through a trial and error method. Each survey has to be
followed by statistical analysis, which would indicate the questions well correlated with
the educational success categories. After several iterations we should be able collect the
questions delivering desirable information. But even if we identify the questions, there
is always a possibility, that in the future someone would like to incorporate some new
questions in the survey. The reason for such a modification would be changes in the ex-
ternal situation, and identification of possible new factors, that could be relevant. All the
well known reasoning methods are based on unified data sets, i.e. to make predictions
for a new data set, this set should be composed of data in the same format, on which the
reasoning machine has been trained. Any modification in the data, like introducing new
questions, requires retraining of the reasoning machine on the new data. At the same
time, all the previous data which are incompatible with the new format become useless.
This is an important problem, because in this way we loose a huge amount of unique
data, which were difficult to collect.
If one wants to avoid loosing the previously recorded data, it is necessary to match
the data formats in some way. This is usually done through manual effort. One of the
standard approaches to the problem is based on using semantic models (ontologies),
which allow for integrating both the data sets through ontology mapping [9]. The diffi-
culties related to using ontologies, have already been mentioned, and we want to avoid
the direct ontology creation and mapping. The approach demonstrated in this paper tries
to complete the task data integration by generating a set of classes for data automati-
cally. The foundations for this method were described in [4].
3 The Surveys
The questions for the surveys were prepared by social sciences experts according to
their best knowledge. They were not tailored specifically for our experiments, but just to
collect the data about the students, like this is done for other kinds of investigation. The
first survey, that we analyzed, contained 21 questions with different structure depending
on the question specifics. The structure of the questions was organized to make them
clear and understandable. Fig. 1 shows the first question, which is a choice between 10
values from the range 1-10, reflecting the opinion of the questioned person. Some of
1. Are you sas ed with the current study: ( m l lvl f f , 0 g )
|__||__|2 |__|3 |__|4 |__|5 |__|6 |__|7 |__|8 |__|9 |__|
Fig. 1. The question with choice between 10 values
the questions were actually groups of the questions related to the same subject (Fig. 2).
Thus the actual number of questions is much larger than 21, due to subquestions. Yet
another type of questions are multiple choice questions (Fig. 3)
202
2 Why have you choosen to study at the University of Informaon Technology in Rzeszow? ( 1
p , 10 p )
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Fig. 2. The question which is a combination of multiple subquestions
4 The Data Model
4.1 The Survey Representation
As we can see, the questions are of different form, and have to be reduced into a ho-
mogeneous format to allow for treating them in the same way. We do this by separating
each possible outcome of the questions (an answer), and treating it as a separate at-
tribute. In this way, for the first question in Fig. 1, we get 10 different question/answer
pairs i.e:
– 1. Are you satisfied with the current study - 1
– 2. Are you satisfied with the current study - 2
– ...
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Fig. 3. The multiple choice question
203
– 20. Are you satisfied with the current study - 10
The rest of the questions are decomposed in the same way. In consequence the initial
number of 21 questions transforms into the space of more than 500 question/answer
pairs. The survey after completing by a student is a binary vector:
Oi = {Iki : k ∈ 1, . . . M }, (1)
where Oi is the vector representing i-th surveyed student, Iki is the k-th coordinate of
i-th survey vector. M is the number of possible question/answer pairs in the survey. The
vector contains 1-s in positions representing the answers selected by a student, and 0-s
for answers which were not selected.
4.2 Educational Success Categories
Except the surveys, we collected the data about results of education for each of the stu-
dents that filled the survey. These data are available in the university computer system.
The results of education are the grades, or the information that the study has been bro-
ken for some reason. These data is available not earlier, than after the end of the first
semester, while the survey was completed in the beginning of the academic year. The
survey data are collected in the first semester of the university course. In this way we
are able to follow the results of the students from the beginning till the end of the study,
and confront them with the survey answers.
Our method requires dividing the investigated students into a number of groups
related to their educational success. We do this by applying hierarchic clustering [7]1
within the space of grades that the students got. The applied method of clustering was
chosen because it allows for generating different numbers of clusters, depending on the
choice of the cut point on the hierarchy. We performed validation of a number of well
known clustering algorithms, and most of them revealed comparable clustering quality.
So this factor was not crucial for the choice of clustering method.
We had no a priori assumption about the number of clusters, so we decided to choose
the cut point that generated 5 clusters. This number seemed suitable to our experiments,
although we do not exclude the possibility of experimenting also with other numbers of
clusters. There was also a number of students, who filled the survey, but had no grades,
because their study had been broken. This class of students are of particular interest,
because they represent the educational failure. In consequence we got 6 categories of
students - 5 coming from clustering, and one of those, who resigned from study.
4.3 The Semantic Distance
Our purpose is integration of the survey data. To be able to integrate them automati-
cally, we have to start from determining the semantic distance between survey answers.
The context data, which allow for determining the distance, are the educational success
1
Implemented in the R Project [8]
204
categories. The measure of the distance is based on statistical distribution of the survey
answers with respect to the context:
PIk = (Pk1 , Pk2 , . . . , PkN ), (2)
where PIk is the frequency distribution vector of the survey answer Ik with respect to
the N success categories (in our case there are 6 categories). Pkn is the frequency with
which the answer numbered k (Ik ) was found in the success category numbered n,
(n = 1, . . . , N ), i.e. the chance that student belonging to success category n, chooses
the answer k.
The space spanned by the distributions PIk plays the role of semantic space. The
direction of the distribution vector (2) represents the meaning of every survey answer.
The semantic distance between two answers is measured by the angle between respec-
tive distribution vectors. For practical reasons it is more convenient to use the cosine
of the angle between the vectors. The cosine is the semantic similarity measure which
ranges between 0 and 1. This range results from the frequencies, which are non negative
values, and thus the angle between vectors never exceeds π/2. The answers with iden-
tical meaning have the maximal similarity equal to 1, and the answers with completely
different meaning have similarity equal to 0. The semantic similarity Skl between two
answers Ik and Il is calculated as:
P I k · PI l
Skl = cos αkl = , (3)
kPIk k kPIl k
where αkl is the angle between PIk and PIl vectors.
The justification for the thesis, that the semantic distance can be measured using
(3) is the observation, that if there would be two questions in the survey, with iden-
tical meaning, they have to generate the same probability distribution (similarity=1).
Otherwise that would would mean that surveyed persons interpreted the questions dif-
ferently, and thus their meaning is different. The other possibility is that the survey was
filled randomly, but we believe that this is not the case. It should be also noted that the
similarity equal to 1 does not always mean that the human interpretation of the ques-
tions is identical. It is possible, that the interpretation is different, but still generates
similar distribution. In terms of semantic model, this can be interpreted as synonymic
question and answer. No mater which of the synonyms is used in the survey, the result
is the same. So for computational purposes the synonymic questions are not a problem,
because the reasoning based on them will be the same. A more detailed discussion of
motivations for using the space of probabilities as the semantic space can be found in
[4].
5 Correlations of Probability Distributions
The survey data are collected to build a computational model based on the groups of
students that are currently studying, in order to be able to make predictions about the
students recruited in the future. This approach makes sense only when the statistical
distributions are stable for student groups from subsequent years. Thus it is necessary
to verify the stability of distributions.
205
To assess the stability of the frequency distribution (2) for every answer in the sur-
vey, we conducted the survey for two student groups in subsequent years. The two
surveys were not identical. They contained a number of questions that were identical,
and a number of questions that were different. For the purpose of verification, only the
common part of the questions is useful, so the rest of the question/answer pairs is not
used for the stability verification purpose. Computing distributions (2) requires infor-
mation about the grades of the surveyed students, to classify each of them into one of the
6 previously assumed categories of educational success. We clustered the first (older)
of the investigated groups, and used the the same clustering for the second (younger)
group. In this way the have a consistent classification system for students from both of
the groups.
Given the classification we can compute the distributions (2) for each of the two
groups. Then we can compare the distributions by computing the cosine of the angle
between the distribution vectors for the same answers (semantic distance), but obtained
from two different groups:
12 12
PI1k · PI2k
Skk = cos αkk = , (4)
PI1k PI2k
where P 1 , P 2 are the frequency distributions obtained for group 1 and group 2 of the
students respectively.
Ideally, the similarity (4) should be close to 1 for each of the answers. In reality this
value spreads over the whole range of possible values (Fig. 4(a)). There is an observable
number of answers, which correlate between the groups (semantic similarity close to 1).
But there are also answers, which do not correlate at all.
We were able to identify the reason for low correlations easily - the answers with low
correlation come from the answers rarely chosen by the students. Some of the answers
were chosen by just a few persons, or even by no one. With such small numbers no
reliable statistical distribution can be determined. Luckily one of the significant reasons
for low numbers was easy to eliminate. This was the wide range of possible answers to
particular questions - in many cases this range was set to 10 single choice values, like
in questions in Figs. 1 and 2. The total number of students in each of the investigated
groups was about 200, so statistically the average number of persons that should choose
each of the answers should be 20. However, the students clearly preferred some answers
than the others. Actually we anticipated this situation, and chosen such a wide range
deliberately, because it is easy to reduce the range afterwards, in case if the original
range did not work. So the range was reduced from 10 down to 5 possible choices.
This reduced the number of the considered answers form 401 to 255, and immediately
increased the number of students who chosen each of the answers. After computing the
similarity between groups we got the similarity distribution presented in Fig. 4(b).
As it can be observed, the degree of highly correlated answers increased after re-
ducing the range of answers (e.g. the number of answers with correlation higher than
0.9 increased from about 25% to about 50%). However, there are still answers which do
not correlate well. Despite applying the answer reduction trick, there are still answers,
which are less likely to be chosen by the students. According to our findings, this is the
main reason for low correlations, which result from less statistically reliable distribu-
206
1
0,9
0,8
Semantic similarity
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
1 51 101 151 201 251 301 351 401
a) Survey answers
Semantic similarity
b) Survey answers
Semantic similarity
c) Survey answers
Fig. 4. Similarity distribution for the survey answers: (a) initial range of answers, (b)
reduced range of answers, (c) further reduction of the range of answers
tions. There was still some space for reducing the range of answers, e.g. to 3 or even 2
possible choices, which can increase the level of correlations. Thus we applied further
reduction of the range of answers to 3 possible choices (Fig. 4(c)). The result confirmed
our suspections - the correlations further increased, and the number of uncorrelated an-
swers vanished completely. The lowest similarity between the answers was on the level
of 0.44.
Although the results look much better than the initial, there is still some space for
improvements, which is related to several issues. The first of them are the survey ques-
tions. Not all them have the kind of structure which allow for their easy reduction. Thus
there are still question/answer pairs, which are unlikely to be chosen by the students.
The possible ways of increasing the correlations, would be:
1. eliminate the weakly correlated answers - the risk is, that in this way we will elim-
inate valuable information referring to a relatively small number of students,
2. reformulate the questions in order to force the students, to choose some answers
more frequently - this is something that we consider to do in the future years,
207
3. increase the number of investigated students - we investigated students only from
the Information technology specialization. Due to limited number of students, in-
creasing the number would require extending the research onto other specializa-
tions, which is possible, but we are not sure if students, from very different spe-
cializations, will generate the same probability distributions. This is an interesting
topic for the future research,
4. decrease the number of student success groups - the division into 6 groups might be
too fine grained, thus we consider decreasing it to e.g. 4 groups, which immediately
increases the number of students in each of the groups, and makes the distribution
more reliable.
To summarize the results of correlation investigation, we can state that if the number
of students, who selected a particular answer is sufficiently large, then the frequency
distribution with respect to the educational success categories, in a vast number of cases
remains stable. Thus such an answer can be used as a reliable indicator of the possible
success category.
6 Data Integration through Clustering
As already mentioned, a survey can potentially contain many different questions, and
along time some questions could be replaced by others. This makes it difficult to reuse
the knowledge collected in the previous years, because the evolution of questions could
lead to a potentially large set of questions. Finding relations among such questions
along the timeline is a difficult task. Thus we develop the mechanism, which should
allow for integrating the the old versions of surveys, with the newly created ones. The
basis for this task is the already introduced semantic space of frequency distributions
(2) together with the similarity measure (3).
The basic semantic relation, that can be discovered, among survey answers is the
synonymy relation, i.e. finding answers with the same meaning. This task can be com-
pleted with the clustering technique. We applied the hierarchic clustering again due to
its flexibility, and possibility of selecting various levels of clustering granularity. We
used the cosine distance, to measure the distance between clustered objects (the sur-
vey answers), because this is the assumed semantic similarity measure. Here again it
is interesting to assess, whether the closely related questions indeed fall in the same
category.
There is a number of testing scenarios that can be proposed here. Because we want
to integrate the data coming from surveys obtained from subsequent years, the best ap-
proach is to check, whether the answers belonging to some cluster for one year, belong
to the same cluster in the subsequent year. To verify this, we clustered the answers for
the first of the surveyed groups. Then we calculated the frequency distribution (2) for
each of the answers in the second of the surveyed groups. This allows for determining
the cluster (obtained on the first group), that each of the answers collected in the second
group belongs to.
In the ideal situation, all of the answers for the second group should belong to the
same clusters as for the first group. The results revealed that the situation is more com-
plex to analyze. First of all, there are huge differences in the number of objects in each
208
of the clusters. That of course depends on the cut level in the hierarchy. But in general,
the majority of answers are grouped in several huge clusters. This is illustrated in Fig. 5
for the cut level in the clustering hierarchy equal to 0.1 (the parameter ranges between
0 and 1 - the lower the value, the larger number of clusters). The largest cluster con-
tained 54 answers. The second group are the middle sized clusters (2 to 5), where the
number of answers ranged between 31 and 12. The third group are the smallest clusters
(6 to 14), where the number of answers ranged between 7 and 1. This is an interest-
ing result, because it brings us insight into the nature of the gathered information. We
can see, that the answers grouped in the huge clusters, do not bring much new infor-
mation. In fact, we could resign from using all the question/answer pairs belonging to
such clusters, and leave just one of them for each of the clusters. This would reduce
the survey complexity significantly. More interesting are the answers grouped in small
clusters. Their uniqueness indicate, that they bring some valuable information about
the students, which distinguishes them from the others. This also indicates the possible
regions, in which the survey could be extended to gather more useful information.
60
50
Number of answers
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Clusters
Fig. 5. The distribution of the number of answers in particular clusters
What refers to the basic question, which is the membership of the same questions to
the same clusters, we found that indeed, a huge number of questions belong to the same
clusters. It is no surprise, that the key factor that influences that, is the cosine distance
between the answers, for different sets. The closer the answers between the groups of
students are, the larger chance, that they belong to the same cluster. Uncorrelated an-
swers are unlikely to belong to the same clusters. Thus providing conditions, in which
the collected data are highly correlated for subsequent years, is the key factor to guar-
antee high reliability of the data model. The number of answers, that matches particular
clusters, of course depends of the free parameter - the cut point in the hierarchic clus-
209
tering. The lower the cut point, the more detailed clustering, and the more mismatching
answers. Together with increasing the cut point, the number of matches rises.
7 Conclusions
The paper investigated the problem of data integration on the example of data coming
from student surveys. For this purpose we defined a semantic space, which allows for
computing the similarity between the survey answers. This concept allows for identify-
ing answers with close meaning, which is the first step to integrating the data.
The main focus of this paper was to verify if this approach is reliable, and could
be used for integrating this kind of data. The correlations obtained for two subsequent
years, for which the survey was conducted, indicate that indeed - the statistical distri-
butions for particular questions exhibit high similarities. Thus the approach can be the
basis for data integration. Although there are still some question/answer pairs, which
do not correlate well. We indicated the ways of dealing with the situation to improve
the results.
The other open question is the clustering method to be used to group the answers.
In this paper we used the hierarchic clustering, because of its flexibility in steering the
granularity with the cut point of the clustering hierarchy. But also other methods should
be tested. This is especially important when we realize, that the radius of the clusters
could be an important factor influencing the size of particular clusters. Unfortunately in
hierarchic clustering we have no direct influence on the radius.
The presented methodology of data integration was demonstrated on a particular
application example, but its nature is universal. It can be applied to any kind of data,
where we have information about a group of entities, and the entities can be classified
into a number of categories. This is a very wide category of problems, so there is a lot
of work to do, to analyze the results delivered by our methodology.
Acknowledgments. This work is the result of a project titled “Intelligent meth-
ods of analyzing chances and threats in the educational process” (project no. UDA-
RPPK.01.03.00-18-019/12-00¨), co-financed by the European Union from the European
Regional Development Fund and from the Budget within the Regional Operational Pro-
gramme for the Podkarpackie Region for the years 2007-2013.
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