Frontiers in Computing and Intelligent Systems 
ISSN: 2832-6024 | Vol. 3, No. 1, 2023 

 

1 

Prediction of Telecom Customer Churn Based on 
MIPCA-XGBoost Method 

Chen Zhuo* 

School of Control and Computer Engineering, North China Electric Power University, Beijing 102200, China 

* Corresponding author Email: cherrybombczz@163.com 

 

Abstract: In order to solve the problem that the nonlinear information of data in the field of telecom customer churn prediction 

is not fully used, or even ignored, which leads to inaccurate prediction, this paper introduces the mutual information feature 

selection method (MIPCA) to filter the features and reduce the dimensions of customer data, and proposes an XGBoost method 

based on the mutual information feature selection method(MIPCA-XGBoost), which improves the accuracy of the prediction 

results. By using the data set of telecom industry customers published on Kaggle website, compares the prediction result of this 

method with that of machine learning algorithms commonly used in this field, and proves the accuracy, recall and F_Score of 

MIPCA-XGBoost method is higher than other algorithms. 

Keywords: Customer churn; Telecom customers; Mutual information feature selection; XGBoost algorithm. 

 

1. Introduction 

Nowadays, the market of China's telecom industry is 

becoming increasingly saturated, the competition between 

enterprises is becoming more and more fierce, and the 

customer churn rate is gradually rising. Many enterprises 

focus on how to use novel marketing models to attract new 

customers and further develop them into loyal customers. 

However, studies show that the cost of time and money 

required for a company to develop a new customer is far 

greater than the cost of maintaining an existing customer [1]. 

Therefore, it is imperative for enterprises to build a model that 

can accurately predict the customer churn tendency, 

understand the customer churn tendency in time and adjust 

the customer maintenance strategy to reduce the customer 

churn rate. 

Customer churn is a complex problem, and the prediction 

methods for different industries are different. At present, there 

are a large number of domestic literatures on customer churn, 

involving a wide range of fields. Zhang Lili [2] and others 

used decision tree algorithm to predict airline customer churn, 

and successfully improved the seating rate; Yan Chun [3] and 

others used BP-Adaboost algorithm to predict the clustered 

life insurance industry customers, providing a higher 

prediction accuracy; In the field of e-commerce, Wu 

Yongchun [4] fused multiple methods to establish a prediction 

model, which shortened the prediction time. However, the 

customer data in the telecommunications industry has the 

characteristics of large quantity and high dimension. 

Although the above research has made important 

contributions to the research on customer churn prediction in 

the fields of aviation, life insurance, e-commerce and so on, 

it does not mine the important features of the data set, 

resulting in information redundancy and even dimension 

disaster [5], which will have an impact on the customer churn 

prediction in the telecommunications industry and reduce its 

prediction efficiency and accuracy. 

At present, the data feature selection in the field of 

customer churn prediction is generally based on the 

traditional statistical principal component analysis and linear 

discriminant method [6]. Its advantages are that the 

theoretical basis is solid and the method is simple and easy to 

operate, but the nonlinear relationship between attributes is 

ignored, the information is not fully utilized, and even 

important information is lost. The mutual information feature 

selection method can retain most of the original information 

while effectively reducing the dimension, and take into 

account the nonlinear relationship between variables [7]. In 

addition, XGBoost algorithm has full application in short-

term photovoltaic power generation prediction [8-11], flight 

delay prediction [12-14], food safety risk prediction [15-18] 

and other prediction fields. These studies show that XGBoost 

has the advantages of high flexibility, fast execution speed, 

and high accuracy of prediction results. Based on this, this 

paper proposes an XGBoost prediction method based on 

mutual information feature selection to solve the problem of 

customer churn in the telecommunications industry, and 

compares the accuracy, recall, and F_ Score and other 

indicators, and the analysis proves the effectiveness of the 

method proposed in this paper in telecom customer churn 

prediction. 

2. MIPCA-XGBoost customer churn 
prediction method 

2.1. MIPCA method 

In information theory, mutual information is a measure of 

interdependence between random variables, which can also 

be understood as the amount of information of another 

random variable contained in one random variable [11]. In 

feature selection, the principal component analysis method in 

traditional statistics is to analyze the linear relationship 

between two variables, but cannot reflect the nonlinear 

relationship in the data. Therefore, this paper considers 

introducing mutual information to feature selection, which is 

very helpful for evaluating the interdependence between 

variables, and is no longer limited to the linear relationship. 

Here we introduce information entropy H, which is used to 

represent the uncertainty of a random variable. 

Suppose there are random variables X and Y in data set M, 

and there are joint distributions  𝑝(𝑥, 𝑦)  and marginal 

distributions 𝑝(𝑥) and 𝑝(𝑦), then there are 



 

2 

𝐻(𝑋, 𝑌) = 𝐻(𝑋) + 𝐻(𝑌|𝑋) = 𝐻(𝑌) + 𝐻(𝑋|𝑌)    (1) 

Where, 𝐻(𝑋|𝑌) and 𝐻(𝑌|𝑋)  are conditional information 

entropy, which represents the information entropy of its own 

information after deducting other conditions, which can be 

expressed as 

𝐻(𝑋|𝑌) = − ∑ 𝑝(𝑥, 𝑦)𝑙𝑜𝑔𝑝(𝑥|𝑦)𝑥∈𝑋      (2) 

𝐻(𝑌|𝑋) = − ∑ 𝑝(𝑥, 𝑦)𝑙𝑜𝑔𝑝(𝑦|𝑥)𝑦∈𝑌      (3) 

For random variables X and Y, the amount of information 

of another variable contained in one variable can be expressed 

by mutual information [11], which is defined as 

𝐼(𝑋, 𝑌) = 𝐻(𝑋) − 𝐻(𝑋|𝑌) = 𝐻(𝑌) − 𝐻(𝑌|𝑋)   (4) 

The information entropy of random variables X and Y can 

be expressed as 

𝐻(𝑋) = − ∑ 𝑝(𝑥)𝑙𝑜𝑔𝑝(𝑥)𝑥∈𝑋          (5) 

𝐻(𝑌) = − ∑ 𝑝(𝑦)𝑙𝑜𝑔𝑝(𝑦)𝑦∈𝑌        (6) 

Therefore, we can further obtain the mutual information 

𝐼(𝑋, 𝑌) of random variables X and Y as 

𝐼(𝑋, 𝑌) = ∑ ∑ 𝑝(𝑥, 𝑦)𝑙𝑜𝑔
𝑝(𝑥,𝑦)

𝑝(𝑥)𝑝(𝑦)𝑦∈𝑌𝑥∈𝑋       (7) 

In the principal component analysis method, the mutual 

information matrix is used to replace the covariance matrix, 

and the relationship between the eigenvector and the 

eigenvalues of the mutual information feature selection 

method is obtained as 

𝐴𝑇 𝛴𝐼 𝐴= 𝐵                   (8) 

Among them, 𝛴𝐼  is the mutual information matrix 

corresponding to the data set M, 𝐴 is the matrix formed when 

the eigenvector of the mutual information matrix is a column 

vector, and 𝐵  is the eigenvalue matrix of the mutual 

information matrix. In 𝛴𝐼 , the elements on the diagonal 

represent the self-information of variables, while the elements 

on the non-diagonal represent the mutual information of 

variables. When the two variables are not related, the mutual 

information is 0. The principal component 𝑐  of mutual 

information matrix 𝛴𝐼 is 

𝑐𝑘 = 𝛼𝑘
𝑇𝑥                      (9) 

Among them, 𝛼𝑘
𝑇(𝑘 = 1,2, . . . , 𝑛) ∈𝐴𝑇 , is conversion 

coefficient of 𝑐𝑘 . Define the contribution rate of the kTH 

feature as 𝜎𝑘. The formula  

𝜎𝑘 =
𝜇𝑘

∑ 𝜇𝑘
𝑛
𝑘=1

                   (10) 

𝜇𝑘  is the 𝑘 TH largest eigenvalue of the mutual 

information matrix. In this paper, the first m principal 

components whose cumulative contribution rate of 𝛽  is 

about 90% are selected as the output of the feature selection 

results, and the dimensionality reduction of the data set is 

realized. 

2.2. Principles of XGBoost model 

XGBoost algorithm is a model that uses CART tree as the 

base learner for training and combines multiple base learners 

to construct a strong classifier. XGBoost is used to train the 

data set, divide the sample data into each leaf node according 

to different classification characteristics, calculate the gain 

value of the tree model before and after classification, and 

finally obtain a training model with the minimum loss value. 

The objective function can be expressed as 

𝑂𝑏𝑗 = ∑ 𝑙(𝑥, 𝑥�̂�) + ∑ Ω(𝑓𝑡)𝑇
𝑡=1

𝑛
𝑖=1   (11) 

Where 𝑙 is the loss function, 𝑥𝑖 is the true value of the i-

th sample data, 𝑥�̂� is the predicted value of the ith sample, n 

is the total number of samples, Ω(𝑓𝑡)  is the penalty term 

controlling the complexity of the model in the t th tree, and T 

is the number of training trees. 

XGBoost is a superposition training model. When training 

the t-th tree, the objective function of the t-th tree is 

𝑂𝑏𝑗𝑡 = ∑ 𝑙 (𝑥𝑖 , 𝑥�̂�
(𝑡−1)

+ 𝑓𝑡(𝑥𝑖)) + Ω(𝑓𝑡) + 𝑐𝑛
𝑖=1    (12) 

𝑓𝑡(𝑥𝑖) = 𝑤𝑞(𝑥𝑖)                 (13) 

Where, 𝑓𝑡(𝑥𝑖) is the weight of sample 𝑥𝑖 in the t-th tree, 

and its formula is shown in Equation (13), c is a constant, 

𝑞(𝑥𝑖) is the position of the ith sample on the t-th tree, which 

is specifically represented by the number of leaf nodes it falls 

on, and 𝑤𝑞(𝑥𝑖) represents the weight of the leaf node. 

The second-order Taylor series is used to expand the loss 

function, and the objective function after processing is 

𝑂𝑏𝑗𝑡 = ∑ [𝐺𝑘𝑤𝑘  +  
1

2
(𝐻𝑘  +  𝜆)𝑤𝑘

2] + 𝛾𝐾𝐾
𝑘=1    (14) 

∑ 𝑔𝑖 = 𝐺𝑘𝑖∈𝐼𝑘
                (15) 

∑ ℎ𝑖𝑖∈𝐼𝑘
= 𝐻𝑘                 (16) 

Where, 𝐼𝑘 represents all samples falling on the kTH leaf 

node, and 𝑔𝑖  and ℎ𝑖  are the replacements of the first and 

second derivatives of the loss function respectively. For each 

sample that has been trained t-1 times, its g and h are known. 

𝐺𝑘  and𝐻𝑘  are the sum of g and h of all samples on k leaf 

nodes respectively. 

By observing the simplified objective function formula, it 

can be seen that this is a quadratic equation with one variable, 

and the extreme value is 

𝑤∗ = −
𝐺𝑘

𝐻𝑘 + 𝜆
                (17) 

By substituting the extreme value into equation (14), the 

expression of leaf nodes in the tree to be trained can be written 

as 

𝑂𝑏𝑗 = −
1

2
∑

𝐺𝑘
2

𝐻𝑘 + 𝜆

𝐾
𝑘=1  +  𝛾𝐾            (18) 

XGBoost model calculates the Gain value by calculating 

𝑂𝑏𝑗𝑂𝐿𝐷 − 𝑂𝑏𝑗𝑁𝐸𝑊: 

𝐺𝑎𝑖𝑛 =  
1

2
[

𝐺𝐿
2

𝐻𝐿 + 𝜆
 +  

𝐺𝑅
2

𝐻𝑅 + 𝜆
 −  

(𝐺𝐿 + 𝐺𝑅)2

𝐻𝐿 + 𝐻𝑅 + 𝜆
] –  𝛾   (19) 

The higher the gain score, the higher the feature importance 

score of the split node, and the more important its 

corresponding feature. 

2.3. MIPCA-XGBoost step 

The procedure is as follows: 

1)Feature screening was performed on the data set by 

MIPCA method, and the first m principal components were 

obtained as new features, and the dimensionality reduction of 

the initial data set was realized; 

2)Randomly divide the new data set after feature selection 

processing, and the divided training set is used as the data 

input of the model, and the test set is used to verify the trained 

model. The flow chart of MIPCA-XGBoost is shown in 

Figure 1. 



 

3 

Telecom customer data 
set

MIPCA decomposition

Deaverage

Build sample mutual 
information matrix

计算特征值与特征向量
Select principal 

components 

Import XGBoost 

Set initial 
parameters

Data training

Test set 
prediction

Output 
results

Whether the maximum 
number of iterations has 

been reached

No
Yes

 
Fig. 1 The flow chart of MIPCA-XGBoost method 

3. Data preparation 

3.1. Experimental data 

The telecom industry customer data set used in this paper 

has 48,712 pieces of data, including 9876 pieces of lost data 

and 38,836 pieces of non-lost data. The amount of lost data is 

about 20% of the total data set. In the experiment, the data set 

is randomly divided into 40% test set and 60% training set, 

which comes from Kaggle website. Each piece of data in the 

data set includes 57 characteristics and attributes, such as 

account opening time, remaining accounts, recharge period, 

online duration, and total call duration. Some attributes are 

shown in Table 1. 

Table 1. Part properties of dataset 

Data classification Data attributes 

Basic Information Customer ID, age, package, 

account opening time 

Billing information Account balance, recharge 

period, credit limit, etc 

Network duration Time spent online, time spent 

online on weekdays, time spent 

online on weekends, etc 

Communication 

information 

Number of calls, total call 

duration, number of calls, number 

of calls, etc 

Network Usage 

information 

Uplink traffic, downlink 

traffic, traffic overflow, etc 

Status of 

complaints 

The number of complaints, the 

response time of complaints, etc 

The data is preprocessed, 0 is used to fill the missing values 

in the data attributes, unique thermal coding is adopted for 

discrete attributes, and standardization is carried out for 

continuous attributes, so that the processed data can meet the 

standard normal distribution. 

3.2. Feature selection 

MIPCA method was used to select the feature of the data 

set, and the feature selection results of the data set were 

compared with the principal component analysis method. The 

comparison results were expressed as the principal 

component characteristic value μ and the cumulative 

contribution rate β, as shown in Table 2. 

Table 2. Principal component eigenvalue and cumulative 
contribution rate 

Principal 

component 

PCA MIPCA 

𝜇 𝛽 𝜇 𝛽 

PC1 16.34 30.07% 22.23 43.30% 

PC2 8.56 46.87% 8.34 56.67% 

PC3 5.23 57.13% 4.27 64.71% 

PC4 4.12 65.22% 3.68 70.35% 

PC5 2.85 69.81% 2.64 76.75% 

PC6 2.21 73.15% 1.93 80.65% 

PC7 1.80 76.68% 1.43 83.77% 

PC8 1.48 79.59% 1.04 86.34% 

PC9 1.23 82.64% 0.84 88.76% 

PC10 1.01 84.76% 0.65 89.93% 

PC11 0.88 85.60% 0.63 91.14% 

PC12 0.76 85.72% 0.57 92.22% 

PC13 0.64 86.43% 0.54 93.27% 

PC14 0.64 87.14% 0.49 94.12% 

PC15 0.62 87.80% 0.44 95.03% 

PC16 0.58 88.47% 0.37 95.87% 

PC17 0.56 89.22% 0.34 96.21% 

PC18 0.55 89.75% 0.32 96.54% 

PC19 0.55 90.28% 0.29 96.84% 

From the extraction results of principal components in 

Table 2, it can be seen that MIPCA has a higher cumulative 

contribution rate when principal components of the same 

dimension are selected. For example, to achieve a cumulative 

contribution rate of 90%, PCA method needs to select 19-

dimensional principal components, while MIPCA method 

reduces the value to 11-dimensional, which indicates that 

MIPCA method can make full use of nonlinear information. 

Thus, the original information can be retained to a greater 

extent, which is helpful to improve the accuracy of 

subsequent prediction. In this paper, when the cumulative 

contribution rate reaches 90%, the first 11 dimensional 

principal components screened by MIPCA method are 

selected for XGBoost customer loss prediction. 

4. Customer churn forecast 

4.1. Evaluation index 

According to the confusion matrix, the prediction accuracy 

𝐸𝑎𝑐𝑐 , the recall rate 𝐸𝑟𝑒𝑐𝑎𝑙𝑙 , and the 𝐹_𝑆𝑐𝑜𝑟𝑒 were calculated 

as the evaluation index of the algorithm. The calculation 

formula of each evaluation index is shown as follows, and the 

classification of customer state prediction results [12] is 

shown in Table 3. 

Table 3. Customer status classification 

True 

customer status 

Loss of 

prediction results 

The prediction 

result is not churn 

Actual loss TP FN 

Actual non-

churn 

FP TN 

𝐸𝑎𝑐𝑐 =
𝑇𝑃+𝑇𝑁

𝑇𝑃+𝑇𝑁+𝐹𝑃+𝐹𝑁
             (20) 

𝐸𝑟𝑒𝑐𝑎𝑙𝑙 =
𝑇𝑃

𝑇𝑃+𝐹𝑁
               (21) 



 

4 

𝐹_𝑆𝑐𝑜𝑟𝑒 =
2×𝑇𝑃

2×𝑇𝑃+𝐹𝑃+𝐹𝑁
            (22) 

4.2. Important parameter Settings of XGBoost 

algorithm 

The experiment running environment in this paper is a 64-

bit Windows10 operating system, and the specific hardware 

Settings are as follows: 16 GB memory and 12th Gen Intel(R) 

Core(TM) i5-12490F @ 3.00 GHz CPU. python3 and related 

toolkits were used in the experiments. After many 

experiments, the parameters of XGBoost are finally set in 

Table IV. 

Table 4. The important parameters of XGBoost 

Parameter Parameter configuration 

max-depth 5 

min-child-weight 3 

learning-rate 0.3 

gamma 0.1 

subsample 0.76 

n-estimators 200 

4.3. Analysis of prediction results 

In this paper, MIPCA-XGBoost algorithm is applied to 

customer churn prediction in the telecom industry, and 

random forest and logistic regression algorithms commonly 

used in this field are used for comparison experiments. The 

comparison results of precision, recall and 𝐹_𝑆𝑐𝑜𝑟𝑒  of 

related algorithms are shown in Table 5. 

Table 5. Comparison of prediction results of various 
algorithms(%) 

Type of Algorithm  𝐸𝑎𝑐𝑐 𝐸𝑟𝑒𝑐𝑎𝑙𝑙 𝐹_𝑆𝑐𝑜𝑟𝑒 

RF 84.12 84.36 83.25 

LR 81.43 83.03 80.13 

XGBoost 86.37 84.58 84.73 

MIPCA-XGBoost 90.56 90.23 89.64 

Observing the prediction results of various algorithms in 

Table 5, on the whole, the accuracy of three methods of 

random forest, logistic regression and XGBoost is more than 

80%, and the MIPCA-XGBoost algorithm has the highest 

score, with an accuracy of 90.56%, a recall rate of 90.23%, 

and a 𝐹_𝑆𝑐𝑜𝑟𝑒 value of 89.64%. The accuracy of the random 

forest algorithm is 84.12%, and the accuracy of the logistic 

regression algorithm is 81.43%, which indicates that the 

MIPCA-XGBoost method is more suitable for application in 

this field. 

Secondly, through the comparison of the XGBoost 

algorithm MIPCA-XGBoost algorithm, it can be seen that the 

MIPCA feature selection method improves the prediction 

accuracy of the XGBoost algorithm in this experiment, its 

accuracy is increased by 4.19%, the recall rate is increased by 

5.65%, and the 𝐹_𝑆𝑐𝑜𝑟𝑒 value is increased by 4.91%. 

5. Conclusion 

From the perspective of making full use of the original 

information of the data set, this paper introduces the mutual 

information feature selection method in the study of customer 

churn prediction in the telecom industry, and proposes the 

MIPCA-XGBoost method, which successfully improves the 

prediction accuracy. By selecting the telecom customer data 

set from Kaggle website for experiments, the results show that 

the prediction accuracy of MIPCA-XGBoost method is as 

high as 90.56%. It can be seen that the algorithm is helpful for 

the further research of customer churn prediction in the future, 

and provides a new idea for enterprises to solve the problem 

of customer churn, helping enterprises to be more targeted 

and accurate in formulating customer maintenance strategies. 

The research of this paper also has some shortcomings :1) 

At present, the rapid development of Internet communication 

has become an inseparable part of people's communication 

and contact. Under this impact, many users' communication 

behaviors will be affected by instant messaging tools. In the 

future, we will consider the third-party communication 

software and Internet platform data for research. 2) The data 

in this paper are from a single telecom industry customer data, 

and in the future, multiple operators in the same time period 

will be considered for joint research to make the research 

more comprehensive. 

In future research, it is necessary to classify the customers 

who have been predicted to have churn trend, create a 

classification model, and then propose an effective customer 

retention strategy. In addition, in the study of customer churn 

prediction, it is necessary to pay attention to the interaction 

between customers, which may be an important factor 

affecting customer churn, which is of great significance for 

the research in this field. 

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