A Preprocessing Design Scheme for Sequential

Pattern Analysis of a Student Database

R. Campagni, D. Merlini and M. C. Verri

Dipartimento di Statistica, Informatica, Applicazioni, Universit`a di Firenze, Viale Morgagni 65, 50134, Firenze, Italia

Keywords:

Educational Data Mining, Sequential Pattern Analysis,

SQL

Preprocessing.

Abstract:

In a data mining project evolved on a relational database often a signiﬁcant effort needs to be done to construct

the data set for the analysis. In fact, usually the database contains a series of normalized tables that need to be

joined, aggregated and processed in an appropriate way to build the data set. This process generates various

SQL

queries that are written independently of each other, in a disordered manner. In this way, the database

grows with tables and views which are not present at the conceptual level and this can yield problems for

the development of the database. In this paper we consider a typical database containing data about students,

courses and exams and illustrate some

SQL

transformations to build a data set to perform a sequential pattern

analysis eventually combined with clustering and classiﬁcation. In particular, we introduce in the student

database some interesting patterns representing relationship between the exams given by students in various

periods and the career of each student. This is achieved by introducing a particular encoding of a the career of

a student. The resulting table can be analyzed with clustering and classiﬁcation algorithms. We present a case

study following this organization.

1 INTRODUCTION

In the ﬁeld of Educational Data Mining, we are often

concerned with transactional data managed by a re-

lational database that needs to be reorganized for the

analysis with data mining algorithms, such as cluster-

ing, classiﬁcation and association rules and frequent

patterns mining. This very expensive preprocessing

phase is crucial for the accuracy of the analysis but

can generate a disorganized growth of the database

(see (Baker, 2014; Pe˜na-Ayala, 2014; Romero et al.,

2014; Romero and Ventura, 2013) for recent surveys

on the state of the art of educational data mining and

on preprocessing educational data). In fact, in order

to apply data mining techniques many join and aggre-

gation operations need to be performed which result

in a de-normalization of the database with new tables

and/or views not present at the conceptual level. The

ideal would be to have already at conceptual level

a clear idea of the information that must be present

in the data set that will be used for the data mining

analysis. At the relational logic level this goal can

be achieved directly through

SQL

language

, organiz-

ing a clean

SQL

script with appropriate queries, views,

In this paper we will refer to the

MySQL

(MySQL) im-

plementation of the standard

SQL

and/or temporary tables that correspond to the cre-

ation of the data set of interest.

The most widely used tools for data mining pro-

vide ﬁlters to transform data for clustering, classi-

ﬁcation and the search of association rules, but as

far as we know, it is less common to ﬁnd features

that allow to prepare data for analysis based on se-

quential patterns (see, e.g., (Dong and Pei, 2007;

Tan et al., 2006)). This kind of analysis has been

used in the context of educational data mining mainly

in computer-based environments (see, e.g., (D’Mello

et al., 2010; Martinez et al., 2011; Soundranayagam

and Yacef, 2010)). A less common application is

the use of sequential patterns to analyze data such

as courses and exams of university students, with

the aim of understanding how the way in which stu-

dents implement their studies inﬂuences their results;

a study of this type has been recently done in (Cam-

pagni et al., 2015a). Similar goals can also be found

in previous work. For example, the analysis of the

paths taken by students has been studied in (Ohland

et al., 2004) to understand the factors that lead stu-

dents to leave their study; this is done by using a

model deﬁned upon checkpoints in the curriculum in

such a way that different curricula can be interpreted

through a common framework. A regression model is

Campagni, R., Merlini, D. and Verri, M.

A Preprocessing Design Scheme for Sequential Pattern Analysis of a Student Database.

In Proceedings of the 8th International Conference on Computer Supported Education (CSEDU 2016) - Volume 2, pages 99-106

ISBN: 978-989-758-179-3

used in (Zhang et al., 2004) to explore the relationship

between graduation and demographic and academic

characteristics.

In this paper, by following an approach similar to

that recently presented in (Ordonez et al., 2014), we

propose a methodology for obtaining a data set for a

sequential pattern analysis, starting from a classical

relational database about students, courses and exams

and working at the

SQL

level.

In order to present our preprocessing design

scheme, let us consider a typical relational database

containing data about university students, courses and

exams, as illustrated in Tables 1, 2 and 3. In partic-

ular, table

Students

contains the identiﬁcation code

of a student,

studentid

, the year of enrollment at the

university,

enrollment

, the gender,

gender

, and the

high school grade,

hgrade

; table

Courses

contains

the identiﬁcation code and the description of a course,

courseid

and

description

, as well as the semester

in which the course is given by the teacher,

semester

and the corresponding number of credits,

cfu

; ﬁnally,

table

Exams

contains the information about the date

and grade,

date

and

grade

, each student obtains in

the examinations. Of course, other information could

be added to the tables, for example the evaluation of

courses taken by students and their results in the cor-

responding exams, as recently studied in (Campagni

et al., 2014; Campagni et al., 2015b).

Table 1: A sample

Students

table.

studentid enrollment gender hgrade

10 2012 M 85

20 2012 F 98

30 2012 F 75

Table 2: A sample

Courses

table.

courseid description semester cfu

1 Calculus 1 12

2 Programming 1 12

3 Algorithms 1 9

4 Databases 2 9

5 Statistics 2 6

6 Data Mining 2 6

If we wanted to study the correlations among the

exams given by students through the research of asso-

ciation rules with the

Apriori

algorithm (Tan et al.,

2006), we would probably need to organize data as in

Table 4, for example if we were interested in show-

ing exams conditions that occur frequently together

(e.g., many students who gave exams

Statistics

and

Database

then gave

Data Mining

). The orga-

nization in Table 4 corresponds to the input format

for the

Apriori

implementation in the

Weka

system

Table 3: A sample

Exams

table.

studentid courseid date grade

10 1 2013-06-10 28

10 2 2013-09-24 26

20 1 2013-01-21 28

20 2 2013-02-11 30

20 3 2013-02-25 27

20 5 2013-06-10 28

20 4 2013-07-15 30

20 6 2014-01-22 30

30 2 2013-01-21 24

30 4 2013-09-20 26

Table 4: A sample table for association rule mining. C:

Calculus, P: Programming, A: Algorithms, DB: Databases,

S: Statistics, DM: Data Mining.

studentid C P A DB S DM

10 1 1 0 0 0 0

20 1 1 1 1 1 1

30 0 1 0 1 0 0

(Witten et al., 2011), which provides ﬁlters to menage

the original data. However, such organization can be

achieveddirectly with a quite simple

SQL

query which

performs a natural join among the tables

Students

Exams

and

Courses

and aggregates on each student

by using the appropriate aggregate operator and con-

ditional function. In Table 5 we illustrate the query

which select data for Table 4.

The search of association rules in a table orga-

nized as in Table 4 allows to determine some possible

conditions existing between groups of exams taken by

students. These rules, by their nature, do not take into

account any temporal information and the involved

exams may have been taken by students at any time

and in any order. If we want to monitor the order in

which the exams are taken, it is necessary to search

rules corresponding to sequential patterns by intro-

ducing the temporal information associated with the

events of interest, in our case the exams. As we will

illustrate in the next sections, in order to prepare data

for sequential pattern analysis it is necessary to make

a non trivial preprocessing on the database. We will

show how to achieve this goal by working at

SQL

level

on the original relational scheme. We wish to point

out that the approach presented in this paper could be

easily adapted to contexts different from those of uni-

versity education.

2 THE PREPROCESSING

SCHEME

Before introducing our preprocessing scheme, we

CSEDU 2016 - 8th International Conference on Computer Supported Education

100

Table 5: A

MySQL

query corresponding to Table 4.

select

studentid,

sum

(

(description="Calculus", 1, 0))

Calculus,

sum

(

(description="Programming", 1, 0))

Programming,

sum

(

(description="Algorithms", 1, 0))

Algorithms,

sum

(

(description="Databases", 1, 0))

Databases,

sum

(

(description="Statistics", 1, 0))

Statistics,

sum

(

(description="Data Mining", 1, 0))

DataMining

from

Students

natural join

Exams

natural join

Courses

group by

studentid;

recall the basic concepts related to sequential pat-

terns analysis (see, e.,g., (Tan et al., 2006)). A se-

quence is an ordered list s = hs

. . . s

i, where each

is a collection of one or more events, i.e., s

, e

, . . . , e

). The events in s

correspond to the

same temporal information, that is, they occur at the

same time. We say that sequence s has length m, while

a k-sequence is a sequence that contains k events. A

sequence t is a subsequence of another sequence s if

each ordered element in t is a subset of an ordered el-

ement in s. Given a data set containing one or more

sequences, the support of a sequence s is the frac-

tion of sequences that contain s. The aim of sequential

pattern analysis is to ﬁnd all sequences with support

greatest or equal to a user-speciﬁed minimum support

threshold; those sequences are called frequent pat-

terns. We illustrate these concepts by referring to a

relational database organized as illustrated in Tables

1, 2 and 3.

Each exam is typically associated with the date on

which it was taken by the student, but this temporal

information does not allow to compare the careers of

different students, as, potentially, the exams can be

taken on different dates. We need to perform a time

discretization to give the same temporal information

to exams taken in the same dates interval, taking into

account the organization of the university context un-

der consideration. For example, referring to Tables 1,

2 and 3, we can introduce the discretization illustrated

in Table 6 to associate the interval between the at-

tributes

fromdate

and

todate

to the temporal infor-

mation

semester

. In this way, the exam correspond-

ing to

studentid

10 and

courseid

1 is matched

with the

semester

1 while that of

studentid

20 and

courseid

6 is matched with

semester

3. We wish

to point out that, in this example, the

semester

of the

course in Table 2 corresponds to a value of

semester

in Table 6, that is, these two values correspond to the

same dates interval.

By using the formalism of sequential patterns

just introduced, the exams of students identiﬁed by

10, 20 and 30 correspond to the sequences h(1 2)i,

h(1 2 3)(4 5)(6)i and h(2)(4)i of length 1, 3 and 2,

respectively. This means that student 10 has taken ex-

ams 1 and 2 in the same

semester

, while student 20

has given exams 1, 2 and 3 in the same

semester

then has given exams 4 and 5 in a later

semester

and, ﬁnally, exam 6 in another

semester

. In this data

set, the pattern (1 2) is veriﬁed by two students, that

is, students 10 and 20 gave exams 1 and 2, each in a

same semester. In other words, (1 2) is a subsequence

of sequences h(1 2)i and h(1 2 3)(4 5)(6)i, therefore

it is a frequent pattern with support 66%.

There are several algorithms implementing tech-

niques for ﬁnding frequent patterns based on the Apri-

ori principle (Tan et al., 2006). In this paper, we re-

fer to the

CloSpan

algorithm (CLOSPAN; Yan et al.,

2003) which ﬁnds closed patterns, that is, those pat-

terns containing no super-sequence with the same

support. In the previous example, the algorithm does

not ﬁnd the sequence (1) which is a subsequence of

(1 2) with the same support. These algorithms gener-

ally take as input a data set similar to that illustrated in

Table 7, containing records which correspond, in our

example, to the attributes

studentid

period

and

courseid

. In particular, the blue values correspond

to the discretization of the attribute

date

in Table 3

via Table 6; the red values are an alternative tempo-

ral information, which give the delay with which a

student takes an exam with respect to the period in

which the corresponding course has been given by

the teacher, and can be computed by the difference

between the

period

of the exam and the

semester

of the corresponding course. Once the data set illus-

trated in Table 7 has been processed, we can use the

CloSpan

algorithm specifying a value of support to

ﬁnd the frequent patterns veriﬁed by a percentage of

students greater than the given support. An expert of

Table 6: A sample

Semesters

table.

semester enrollment fromdate todate

1 2012 2012-10-01 2013-02-28

2 2012 2013-03-01 2013-09-30

3 2012 2013-10-01 2014-02-28

4 2012 2014-03-01 2014-09-30

5 2012 2014-10-01 2015-02-28

6 2012 2015-03-01 2015-09-30

A Preprocessing Design Scheme for Sequential Pattern Analysis of a Student Database

101

Table 7: A sample

ExamsSequentialAnalysis

table: in

red the alternative to the blue temporal information.

studentid period courseid

10 2 1 1

10 2 2 1

20 1 1 0

20 1 2 0

20 1 3 0

20 2 5 0

20 2 4 0

20 3 6 1

30 1 2 0

30 2 4 0

the context under examination will be then responsi-

ble to select the most interesting patterns and we will

have to decide how to use this information for data

mining analysis on students.

In this paper, we start from a quite general rela-

tional scheme and describe how to implement, by us-

ing

SQL

, the actions just introduced as well as how

to use the most interesting patterns determined by

the algorithm. Figure 1 illustrates the logical scheme

of our student database. Compared to the example

shown above,we can see that the tables

Students

and

Courses

contain new attributes and that many others

might be considered, as already observed in the In-

troduction. In particular, the attribute

hschool

cor-

responds to the type of high school and the attribute

testgrade

is the grade obtained by a student in the

entrance test at the University. In table

Courses

, the

attribute

number

is a number assigned by an expert

of the domain, taking into account the organization

of the course of study. For example, the courses can

be numbered in the order in which they are given by

teachers and by taking into account the prerequisites

among them. Generally, this number does not match

the identiﬁcation code of the course. For the sake of

simplicity, in the example of Table 2, those attributes

coincide.

In Figure 2 we give the scheme of the tables which

are used for transforming the initial scheme. Table

Semesters

is organized exactly like the sample ta-

ble described in Table 6 and, as already observed, is

important to associate a discrete value to the date of

each exam. Table

ExamsProcessed

adds to the ta-

ble

Exams

the attributes

cfu

period

and

delay

. The

ﬁrst one is the attribute

cfu

of table

Course

and can

be added with a simple join operation. The second at-

tribute correspond to the period of examination and is

computed by using a query similar to that illustrated

in Table 8

. Finally, attribute

delay

is computed as

Tables from now on are displayed at the end of the pa-

per

the difference between the

period

just computed and

the

semester

Courses

. This table could be an-

alyzed on its own, if we want to focus on courses

and their characteristics or can be used as the start-

ing point for computing the next tables of Figure 2.

Table

ExamsSequentialAnalysis

is organized like

the sample table described in Table 7 and can be ob-

tained by a simple join between

ExamsProcessed

and

Courses

followed by a projection. This is the

table used as input for the

CloSpan

algorithm.

After selecting the most signiﬁcant frequent pat-

terns, we want to keep track of such patterns by in-

serting in the

Students

table a Boolean value that

allows to determine if the pattern is veriﬁed by the

student or not. To manage this operation through

SQL

language, we introduce a representation of student ca-

reers that allows us to easily select the students who

verify a certain pattern. For example, the career of

the student corresponding to

studentid

20, is repre-

sented by the string (1: 1 2 3)(2: 4 5)(3: 6) which

highlights the exams taken in semesters 1, 2 and 3.

To achieve this encoding, we use the service table

ExamsInPeriod

, of which we have an example in Ta-

ble 9; in practice, it can be realized through a tempo-

rary table or a view. The encoding for the student ca-

reer can be ﬁnally obtained aggregating data of table

ExamsInPeriod

with respect to the

studentid

and

by concatenating appropriately the sequences of ex-

ams taken in the same period. With

MySQL

this can be

achieved by the

GROUP CONCAT

operator, as described

in Table 10.

The most important table for the analysis is rep-

resented by the

StudentsProcessed

table, that en-

riches

Students

table with the following attributes:

the average grade obtained by the student on all ex-

ams, weighted with respect to the credits,

avggrade

the total number of credits,

credits

, the encoding

of the career in the form just described,

career

, and

one or more attributes associated with one or more

patterns that indicate if the student veriﬁes the pat-

terns or not. In Figure 3, to simplify, we reported

only a

pattern

attribute of this type. In Table 11

we give the

StudentsProcessed

table for our initial

sample tables (a

for i = 1, ··· , 7 are abbreviations for

attributes

studentid

enrollment

gender

hgrade

avggrade

credits

and

career

, respectively, while

corresponds to the pattern (1 2)). The values of

the attribute

pattern

may be calculated using the op-

erator

rlike

, as shown in the query of Table 12. In

particular, the jolly operator . matches any character

and ∗ corresponds to the Kleene star operator for reg-

ular expressions.

We wish to emphasize the step described in Tables

10 which corresponds to a crucial encoding of the ca-

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102

Figure 1: The initial logical schema.

Figure 2: The transformation tables.

Table 8: A

MySQL

query corresponding to Table 7.

select

studentid,

(

select

semester

from

Semesters

where

exams.date>= fromdate

and

exams.date<= todate)

period, courseid

from

Exams;

Table 9: The table

ExamsInPeriod

for Table 7.

studentid period esamslist

10 2 1 2

20 1 1 2 3

20 2 4 5

20 3 6

30 1 2

30 2 4

Table 10: A

MySQL

query corresponding to Table 9.

select

studentid,

group

concat(’(’,convert(period,char(2)),’:’, examslist,’)’

order by

period

SEPARATOR

’ ’)

career

from

ExamsInPeriod

group by

studentid;

Table 11: The sample table

StudentsProcessed

10 2012 M 85 27 24 (2: 1 2) 1

20 2012 F 98 29 54 (1: 1 2 3) (2: 4 5) (3: 6) 1

30 2012 F 75 25 21 (1: 2) (2: 4) 0

reer of a student and the next step described in 12 ,

which allows to search if a given frequent pattern oc-

curs in the career.

The table

StudentsProcessed

can be analyzed

using clustering techniques and/or classiﬁcation algo-

rithms. In the next section we will show an analysis

of this type on a real case study.

A Preprocessing Design Scheme for Sequential Pattern Analysis of a Student Database

103

Table 12: The

MySQL

to insert a value in the attribute

pattern

of Table 11.

update

StudentsProcessed

set

pattern=1

where

studentid

(

select

studentid

from

StudentsProcessed

where

career

rlike

’.*(.*:1 2.*).*’);

Table 13: The 21 careers of students verifying pattern (1 3 4)(11 12).

(2:1 2 3 4 5 6) (3:7 8 9 10) (4:11 12 13 14)

(2:1 2 3 4 5 6) (3:7 8 9 10) (4:11 12 14)

(2:1 2 3 4 5 6) (3:8 9 10) (4:7 11 12 14)

(2:1 2 3 4 5) (3:6 7 8 9 10) (4:11 12 14)

(2:1 2 3 4 5) (3:7 8) (4:9 10 11 12 14)

(2:1 2 3 4 5) (3:8 9 10) (4:7 11 12 13)

(2:1 2 3 4 6) (3:5 7 8 10) (4:9 11 12 14)

(2:1 2 3 4 6) (3:5 8 9) (4:11 12 14)

(2:1 2 3 4 6) (3:8 9 10) (4:5 11 12 14)

(2:1 2 3 4) (3:5) (4:9 11 12)

(2:1 3 4 5 6) (3:2 9) (4:7 10 11 12 13 14)

(2:1 3 4 5 6) (3:8 9 10) (4:11 12 14)

(2:1 3 4 5) (3:2 8 9 10) (4:7 11 12 14)

(2:1 3 4 6) (3:8) (4:10 11 12)

(2:1 3 4) (3:10) (4:11 12)

(2:1 3 4) (3:2 5 8) (4:6 11 12)

(2:1 3 4) (3:2 8 10) (4:9 11 12)

(2:1 3 4) (3:5 10) (4:2 9 11 12 14)

(2:1 3 4) (4:8 11 12)

Figure 3: The ﬁnal table.

3 THE CASE STUDY

Our case study corresponds to a photo shoot in

September 2014 of the students enrolled on 2012 at

the Computer Science degree of an Italian Univer-

sity. This degree is organized into three years and

six semesters, that is, two semesters for year. The

semesters are organized as described in Table 6, there-

fore, we are dealing with students who attended the

courses of the ﬁrst two years, just before the begin-

ning of the third. In the ﬁrst year students have 6

annual courses which are given by teachers from Oc-

tober to May and at the end they can take the corre-

sponding exams; therefore, in practice, students start

to take exams in semester 2, according to Table 6. The

second year includes 4 courses both in the ﬁrst and

second semesters (number 3 and 4 of Table 6, respec-

tively), for a total of 14 courses. In general, with our

choice of semesters, students can start to take an exam

in the same semester in which the course was held by

the teacher, with a null delay, or take the exam in a fol-

lowing semester, accumulating a delay that, in princi-

ple, can grow indeﬁnitely. We numbered the exams

from 1 to 14 according to the year, the semester and

the more or less explicit prerequisites among them.

At the time of the photo, 56 students took at least

an exam and we analyzed their career by using the

methodology illustrated in the previous section. The

data set is not large, however, as focused in (Natek

and Zwilling, 2014), a data mining analysis is useful

also in such small contexts. Moreover, the case study

allows us to describe the methodology on a real situ-

ation.

The data of the students were ﬁrst organized in

a database organized as in Figure 1, then we con-

CSEDU 2016 - 8th International Conference on Computer Supported Education

104

structed table

ExamsSequentialAnalysis

by fol-

lowing the steps previously described and used the

CloSpan

algorithm to identify the possible frequent

patterns existing among the exams taken by students.

By running the algorithm with support 30%, we found

66 patterns which we ordered according to the length

and to the number of students verifying them.

As an example, we considered the pattern which

maximizes the product between the number of exams

and the number of students, that is the sequence (1 3

4) (11 12) veriﬁed by 21 students. Numbers 1, 3, 4, 11

and 12 correspond to

Calculus I

Programming

Al-

gorithms

Calculus II

and

Databases

, respectively. In

particular, courses 1, 3 and 4 are annual courses of the

ﬁrst year, while 11 and 12 are two courses of the sec-

ond semester of the second year. The pattern tells us

that the 21 involvedstudents took the exams 1, 3 and 4

in the same semester and exams 11 and 12 in a follow-

ing semester, but it does not tell us nothing about the

semester; in principle, each student could correspond

to a different pair of semesters. However, by coding

the career of the students as described in Table 11 and

adding the pattern to the table

StudentProcessed

we can easily verify that all 21 students gave the ex-

ams 1, 3 and 4 in the semester 2 and exams 11 and 12

in semester 4, that is, without delay, as illustrated in

Table 13.

The pattern shows that courses 1, 3, 4, 11 and 12

seem to be organized in such a way to bring the stu-

dents to take the exams immediately at the end of the

course, while there is a greater dispersion for the ex-

ams of the ﬁrst semester of the second year, as shown

in Table 13. Previous facts also mean that if we used

the delay as temporal information (red values in the

Table 7) we would ﬁnd the pattern (1 3 4 11 12) veri-

ﬁed by 21 students with zero delay.

After choosing the most interesting patterns, with

the help of an expert of the domain, and computing

the table

StudentProcessed

, we proceeded with the

data mining analysis. First, we used the

Weka

imple-

mentation of the

K-means

algorithm, with K = 2, and

obtained the following two clusters, according to at-

tributes

testgrade

avggrade

and

credits

Attribute Full Data 0 1

(56) (29) (27)

============================================

testgrade 14.2321 15.1724 13.2222

avggrade 24.9286 26.1034 23.6667

credits 73.5179 97.6552 47.5926

Cluster 0 contains students which have reached bet-

ter results, in terms of exam grades and number of

credits, than those in cluster 1; moreover, students in

cluster 0 attained a better grade in the entrance test

(with possible values in the range [0..25]).

All students which verify the pattern are in clus-

ter 0; belong to the same cluster also students who do

not verify the pattern but obtained a quite good grade

at the high school, independently from the typology

of the school. Analyzing in more details the careers

of students who do not verify the pattern but belong

to cluster 0 we observed that they had some difﬁcul-

ties with the ﬁrst year exams

Calculus I

and

Program-

ming

, taking them with one semester of delay but then

recovering in the subsequent semesters.

The results obtained in this small case study allow

us to point out that the frequent patterns analysis in-

troduced in this paper can bring out some unusual re-

lationships related to the way in which students face

exams. Obviously, once table

StudentProcessed

has been processed other data mining techniques can

be used to analyse data.

4 CONCLUSIONS

In any data mining project a large part of the work

is related to process the data in order to obtain one

or more data sets on which applying the data min-

ing algorithms. In particular, our attention focused on

the preparation of data for the analysis and the use

of frequent patterns. We presented a preprocessing

design scheme based on

SQL

queries and on a partic-

ular encoding of the student career that, starting from

a traditional university database, allows to obtain the

data set which can later be analyzed by techniques of

clustering and classiﬁcation in order to highlight pos-

sible relations among the exams taken by students;

these relationships take into account the associated

temporal information. The frequent pattern analysis

can highlight some behaviors which may seem coun-

terintuitive, for example, course e

is scheduled be-

fore course e

while many students take exam e

be-

fore e

or can put in evidence which exams tend to be

given with greater delay than others. The introduc-

tion in the database of the Boolean information about

the most signiﬁcant patterns and clustering techniques

can help to understand if students satisfying the pat-

terns have some common characteristics. Another

interesting application could be the identiﬁcation of

patterns corresponding to students at risk of dropping

out. The design scheme and the encoding of the stu-

dent career presented in this paper can help to achieve

these goals. A delicate point remains the selection of

the pattern, for this reason it is crucial the presence of

an expert of the context under analysis, also for the

validation of the models obtained.

A Preprocessing Design Scheme for Sequential Pattern Analysis of a Student Database

105

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