Gc3310851089

Silvia Trif, Adrian Visoiu / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.1085-1089
1085 | P a g e
Gene Expression Programming Based Dataset Decoration for
Improved Churn Prediction
Silvia Trif*, Adrian Visoiu**
*(Department of Doctoral Studies of Academy of Economic Studies, Bucharest, Romania)
** (Department of Economic Informatics and Cybernetics, Academy of Economic Studies, Bucharest, Romania)
ABSTRACT
Mobile network operators rely on business
intelligence tools to derive valuable information
regarding their subscribers. A key objective is to
reduce churn rate among subscribers. The mobile
operator needs to know in advance which
subscribers are at risk of becoming churners. This
problem is solved with classification algorithms
having as input data derived from the large
volumes of usage details recorded. For certain
categories of subscribers, available data is limited
to call details records. Using this primary data, a
dataset is created to be conveniently used by a
classification algorithm. Classification quality
using this initial dataset is improved by a proposed
method for dataset decoration. Additional
attributes are derived from the initial dataset
through generation, based on gene expression
programming. Classification results obtained using
the decorated dataset show that the derived
attributes are relevant for the studied problem.
Keywords - business intelligence, churn prediction,
classification, data mining, gene expression
programming
I. INTRODUCTION
Nowadays, due to competition, one major
challenge for service suppliers is to keep their
existing position on market, if not gaining more
market share. For the supplier, this creates the
necessity to find ways to better address customer
needs. The supplier has to understand the customer in
order to model its behavior. Since quantitative
information is objective and may be subject to further
processing, any available customer data is collected
for further analysis. This is also supported by the
existence of information systems and data in
electronic format. Datasets are created and fed to
business intelligence specialized tools in order to
obtain relevant information to support the decision
making process. This processing flow enables a range
of applications such as: churn prediction, suggestion
engine, customer segmentation. Business Intelligence
tools are not standalone, but integrated with the
information system of the organization, such as
CRM, as shown in [1]. Some applications of the
intelligent engine consist in using Business
Intelligence functionality directly from another
system, without human intervention, like the platform
for secure USSD service presented in [2]. The
interactions between Business Intelligence tools and
other systems may become complex. A reference
complex churn prediction system is presented in [3].
II. PROBLEM FORMULATION
One of the problems service providers face
is related to preventing churning. Churning occurs
when a particular subscriber stops using the services
provided by the supplier. The reasons for churning
are various and the service provider may not have
sufficient data to infer them. However, statistical
analysis is able to discover patterns associated to
churning behavior. When performing the analysis,
past data is analyzed and patterns or rules are derived
to identify churners. Statistical methods are used to
estimate the churn risk for each subscriber as
presented in [4]. When using in production, for
existing subscribers, if they match churning patterns
or rules, they are considered as potential churners and
the service provider is able in advance to take
preventive measures to stimulate the subscriber.
Preventive measures include bonuses, discounts, gifts
and other incentives that are likely to convince the
subscriber not to churn and continue the relationship
with the service provider [5].
In the following, we consider the case of a
telecom operator as a service provider. Telecom
operators have: a large number of subscribers of two
main types – prepaid and postpaid - and a large
number of records regarding service usage, stored in
files or databases. An important step in the creation
of the dataset is gathering and transforming primary
data to the format needed by the algorithm used in
analysis. Standard approaches to data mining include
the usage of data warehouses as presented in [6].
Churn analysis results quality is influenced by certain
factors: available data in terms of volume and details
or attributes and algorithms used.
Regarding classification algorithms, the
reference algorithm used in analysis is Naïve Bayes.

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Several other algorithms fit to solve this problem are
decision trees and logistic regression as presented in
[7].
Regarding available data at telecom
operators, for both prepaid subscribers there are call
detail records showing when and how the services
were consumed. There are also differences between
prepaid and postpaid subscribers regarding
supplemental information regarding the subscriber.
Postpaid subscribers consume their service based on
a sign contract and therefore the operator has access
to identification data such as name, gender, age and
similar. This kind of information is important in
churn analysis as it represents additional attributes
helping the algorithm to give better results. On the
other hand, prepaid subscribers are anonymous for
the service provider. The only identification is the
phone number – MSISDN - they have on the prepaid
SIM card. Therefore, churn prediction is a lot more
difficult for prepaid subscribers for which only
service consumption is known. Based on the service
consumption, for each MSISDN, service usage is
summed up for a number of equidistant and
consecutive periods or time in order to build the
initial dataset. A record has the form of MSISDNi,
USGi1, USGi2, …, USGij, …, USGik, STATE,
where:
- MSISDNi is the identifier of the prepaid
subscriber in the system
- USGij is the amount of service consumed by
subscriber i during period j
- STATE is a Boolean value showing if the
subscriber was a churner, based on the amount
consumed by the subscriber i during the k+1
period, if USGik+1>0 then the subscriber is
“active”, if USGik+1=0 then the subscriber is
“inactive”
The set of records defined above constitutes
the initial dataset. In this context, the churn
prediction analysis aims to estimate the value of
STATE variable depending on USG1, USG2, ..,
USGk. This is treated as a classification problem and
classification algorithms are applied. However, it is
observed that simply employing the initial dataset for
analysis leads to poor classification results as shown
in [8]. Dataset decoration is needed to add relevant
attributes that would improve the quality of the
results. In case of poor information available,
decoration is done using derived attributes that are
obtained by transforming the initial attributes such
way to:
- Eliminate unnecessary correlations between
initial attributes
- Improve the dependency between the
derived attributes and the studied variable
- Create meaningful derived attributes, easy to
compute and to interpret
- Gain more information from the derived
attributes than from initial attributes
In [8] a transformation for creating derived attributes
based on predefined basic statistical indicators is
presented. In [9] more attributes are derived by
analyzing the call graph. In our research we
considered only the above defined consumption
indicators.
In the following we investigate a free transformation
of the above initial dataset based on expression
generation using a dedicated evolutionary algorithm,
the gene expression programming.
III. GENE EXPRESSION
PROGRAMMING BASED DATASET
DECORATION
In the following, the simple transformations
made on the initial attributes are extended to a more
general approach. Using simple operators like
addition, subtraction, multiplication, division as well
as operands taken from the attribute set, then a large
number of expressions may be obtained. As the
number of expression forming combinations is very
large, and generating all the possible combinations is
time consuming, a solution taken into account to
obtain a valid result in a short time is to use gene
expression programming as a mean of generating
derived attributes based on the set of initial attributes
and a set of operators to be applied.
Gene expression programming is an
evolutionary algorithm based on the principles
described in [10]. A population of chromosomes
evolves through applying genetic operators
iteratively. Genetic operators include: elitism –
survival of the best chromosomes from a generation,
crossover – exchange of genetic material between
two chromosomes, mutation – random change inside
existing chromosomes. Chromosomes encode,
symbolically, individuals representing solutions of a
problem to be solved. The design and preparation of
the genetic algorithm in general, and of the gene
expression programming, in particular, requires that
specific concepts from the evolutionary algorithm
need to be put in correspondence with elements of the
problem to be solved.
Structurally, chromosomes specific to gene
expression programming are made up of one or more
genes. Genes are made up of symbols. Chromosomes
encode expressions made up of operands and
operators. Due to flexibility needs, chromosomes
allow the encoded expression to be obtained by
combining several sub-expressions encoded by
genes, such way each gene encodes a sub-expression.

1087 | P a g e
A symbol encodes an operand or an operator. Since
the expressions encoded by genes are intended to be
evaluated, there are specific genetic expression
programming rules to correctly form a gene. A gene
is made up of a head having symbols encoding both
operators and operands, and a tail which is made up
only of operands. The length of the head and the
length tail take into account the maximum number of
operands needed by the operators taken into account,
such way the syntax tree associated to the expression
to be well formed, as presented in [11].
In our research, we aim to obtain a dataset
having attributes derived from initial attributes, under
the form of analytical expressions made up of
operands and operators. Taking into account the
structure of the gene expression programming
chromosome, we propose the following mapping
between gene expression programming concepts and
our problem. Each chromosome encodes the list of
derived attributes. Each gene of the chromosome
encodes the expression of the derived attribute. Each
symbol encodes an operator from a predefined set or
an operand taken from the set of initial attributes. In
the following, we consider the initial dataset
containing only usage attributes: USG1, …, USG4..
Table 1 presents a gene encoding for the expression,
while Fig. 1 shows the actual syntax tree inferred
from the encoding, in a top-down, left-to-right
fashion.
E= (USG3-USG2)/USG1
Gene:
Table 1 A gene encoding
Fig. 1 Syntax tree for the gene
For example, a two-gene chromosome, with genes
having a head length of 2 positions and a tail length
of 3 positions is presented in Fig. 2:
Chromosome:
Fig. 2 Two gene chromosome
The preparation of the gene expression programming
approach requires:
1) Setting up the list of operators, OT, and the
list of operands, OD. For example, the list of
operators, OT is OD={+,-,*,/} and the list of
operands, OD is OD={USG1,USG2, USG3, USG4}
Crossover operation that occurs between two
randomly chosen chromosomes enables the exchange
of genetic material in order to obtain new individuals
with new characteristics. Crossover occurs at several
positions inside the chromosome. The crossover
between two single gene chromosomes at a certain
position is presented in figure below:
Chromosome 1, encoding the expression (USG2-
USG3)+USG1 is presented in Fig. 3:
Fig. 3 Chromosome1before crossover
Chromosome 2, encoding the expression
(USG3+USG4)-USG2 is presented in Fig.4:
Fig. 4 Chromosome2 before crossover
After crossover at position 3, chromosome 1’,
encoding the expression: (USG3-USG4)+USG1 is
presented in Fig. 5:
Fig. 5 Chromosome1’ after the crossover
Chromosome 2’, encoding the following expression
(USG2+USG3)-USG2, is presented in Fig. 6:
Fig. 6 Chromosome 2’ after the crossover
The syntax trees associated to the initials
chromosomes before and after crossover are
presented in Fig. 7 and Fig. 8, respectively:
Fig. 7 Expression trees before crossover,
corresponding to chromosomes 1 and 2, respectively.

1088 | P a g e
Fig. 8 Expression trees after crossover, corresponding
to the chromosomes 1’ and 2’. respectively.
This kind of crossover may happen in several
positions, affecting gene contents in both single-gene
and multiple-gene chromosomes. This enables the
evolution of expressions of the derived attributes
through the implied changes.
A special case of crossover is when such exchange of
genetic material occurs only at positions pointing to
the beginning of genes, inside a multiple-gene
chromosome. In this case, entire attributes encoded
by genes will be exchanged, as shown in Fig. 9 and
Fig. 10, respectively.
Fig. 9 Multi-gene chromosomes before crossover at
gene position
After crossover at position 2 the new chromosomes
are the ones presented in Fig. 10:
Fig. 10 Multi-gene chromosomes after crossover at
gene position
Entire gene crossover enables the evolution of
derived attributes lists, through the change they
imply. Both of these two kinds of the same genetic
operator may be applied to the chromosome
population independently.
Mutation is a sudden change in the content of a gene,
randomly changing a symbol. For example, Fig. 11
shows a single gene chromosome before the mutation
of an operator that changes the encoded expression.
Chromosome 1: (USG2-USG3)+USG1
Fig. 11 Chromosome 1 before mutation
After mutation at position 1, changing minus sign
with plus, the chromosome becomes as presented in
Fig.12:
Chromosome 1’: (USG2+USG3)+USG1
Fig. 12 Chromosome 1 after mutation
Using the proposed gene expression programming
approach, an initial population of multi-gene
chromosomes has been evolved in order to obtain a
list of derived attributes corresponding to the best
chromosome after a threshold number of iterations.
The performance criteria was the quality of the
classification with respect to each attribute encoded
by a chromosome.
The list of derived attributes obtained using gene
expression programming is shown in table 2.
Table 2 The list of attributes derived using gene
expression programming
Classifying the subscribers using the whole derived
dataset, the percent of correctly classified instances is
58.56% while the incorrectly classified instances are
41.13% of the set, as obtained from table 3.
Table 3 Correctly and incorrectly classified
subscribers using the list of derived attributes
This is an improvement over the results obtained
using the initial usage attributes. Further
improvement is made by generating combinations of
attributes and asses the quality of the classification
for each individual combination. The combination of
attributes having the best classification quality is
chosen. Table 4 shows the derived attributes chosen
as best combination in our case study.
Table 4 The combination of derived attributes that is
best for the classification
Using the dataset defined by the attributes from table
10, the correctly classified instances are 71.50% of
the total, while incorrectly classified instances are
only 28.50%. The classification details are presented
in table 5.

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Table 5 Correctly and incorrectly classified
subscribers using the best derived attributes
It is also important that the chosen derived attributes
have meaningful expressions with respect to the
domain:
- (USG3+USG4)/USG1 shows the amount of
usage for the last two weeks over the usage during
initial week of the study; this is a relative indicator
showing how many times the usage was higher with
respect to the baseline
- (USG2+USG3)/USG1 is also a relative
indicator showing how many times the usage was
higher in a past period with respect to the baseline
- USG4-USG3 shows the absolute difference
in consumption during consecutive periods.
Therefore, the generated attributes have statistical
meaning, being easy to understand and interpret.
They are also selected from a large set of generated
expressions otherwise hard to assess without the
convergence of evolutionary approach.
As seen, gene expression programming is a powerful
method to use in order to obtain derived attributes
from the original dataset.
IV. CONCLUSION
Dataset decoration is a useful technique for
improving the quality of classification when poor
data is available. We have proposed a dataset
decoration method based on gene expression
programming. For churn prediction analysis
attributes derived using the proposed method are
relevant and their use for classification brings
significant improvement in the results of the
classification.
ACKNOWLEDGEMENTS
This work was co-financed from the
European Social Fund through Sectoral Operational
Programme Human Resources Development 2007-
2013, project number POSDRU/107/1.5/S/77213
„Ph.D. for a career in interdisciplinary economic
research at the European standards”.
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