# Predict churn of customers in telecommunications companies

Annual churn rates for telecommunications companies are usually greater than 10%. Customer churn is a big problem for telecommunications companies.

For that reason, it is important that the companies are aware of churn rate to develop strategies that allows them to keep as many clients as possible.

The aim of this example is to use machine learning to understand why customers do churn and what can be done about it. ## 1. Application type

This is a classification project, since the variable to be predicted is binary (churn or loyal customer).

The goal here is to model the probability of churn, conditioned on the customer features.

## 2. Data set

The data file telecommunications_churn.csv contains a total of 19 features for 3333 customers. Each row corresponds to a client of a telecommunications company for whom it has been collected information about the type of plan that they have contracted, the minutes that they have talked or the charge that they pay every month, among others.

The data set includes the following variables:

• account_length
• voice_mail_plan
• voice_mail_messages
• day_mins
• evening_mins
• night_mins
• international_mins
• customer_service_calls
• international_plan
• day_calls
• day_charge
• evening_calls
• evening_charge
• night_calls
• night_charge
• international_calls
• international_charge
• total_charge
• churn: This is the target variable, it is the one that determines whether the client is still in the company or not.

The first step of this analysis is to check the distributions of the variables. The next figure shows a pie chart of churn and loyal customers. As we can see, the annual churn rate in this company is almost 15%. Also, we observe that the dataset is unbalanced.

The inputs-targets correlations might indicate us what factors are most influential for the churn of customers. Here, the most correlated variable with churn is international_plan. A positive correlation here means that a high ratio of customers with international plan are leaving the company.

## 2. Neural network

The second step is to choose a neural network to represent the classification function. For classification problems, it is composed by:

For the scaling layer, the mean and standard deviation scaling method is set.

We set 2 perceptron layers, one hidden layer with 3 neurons as a first guess and one output layer with 1 neuron, both layers having the logistic activation function.

At last, we will set the continuous probabilistic method for the probabilistic layer.

The architecture shown below consists of 18 scaling neurons (yellow), 5 neurons in the first layer (blue) and 1 probabilistic neuron (red). ## 4. Training strategy

The next step is to select an appropriate training strategy, which defines what the neural network will learn. A general training strategy is composed of two concepts:

• A loss index.
• An optimization algorithm.

As we saw before, the data set is unbalanced. In that way, we set the weighted squared error

The next chart shows how the loss decreases during the training process with the iterations of the Quasi-Newton method. As we can see, the final training and selection errors are training error = 0.384 WSE and selection error = 0.455 WSE, respectively.

## 5. Model selection

The objective of model selection is to find the network architecture with best generalization properties, that is, that which minimizes the error on the selection instances of the data set.

More specifically, we want to find a neural network with a selection error less than 0.455 WSE, which is the value that we have achieved so far.

Order selection algorithms train several network architectures with different number of neurons and select that with the smallest selection error.

The incremental order method starts with a small number of neurons and increases the complexity at each iteration. The following chart shows the training error (blue) and the selection error (orange) as a function of the number of neurons. As we can see, the optimal number of perceptrons in the first layer is optimal order = 2, and the optimum error on the selection instances is selection error = 0.455 WSE. ## 6. Testing analysis

The purpose of testing analysis is to evaluate the performance of the trained model on new data that have not been used neither for training nor for selection. For that, we use the testing instances.

The ROC curve measures the discrimination capacity of the classifier between positives and negatives instances. The next chart shows the ROC curve for our problem. The proximity of the curve to the upper left corner means that the model has a good capacity to discriminate between the two classes.

The most important parameter from the ROC curve is the area under the curve (AUC). This value is 0.5 for a random classifier and 1 for a perfect classifier. For this example we have AUC = 0.896, which means that the model is predicting well the churn of our customers.

Predicted positive Predicted negative
Real positive 316 (15.8%) 96 (4.8%)
Real negative 325 (16.3%) 1263 (63.1%)

The binary classification tests are calculated from the values of the confusion matrix.

• Classification accuracy: 91.2% (ratio of correctly classified samples).
• Error rate: 8.8% (ratio of misclassified samples).
• Sensitivity: 76.9% (percentage of actual positive classified as positive).
• Specificity: 93.9% (percentage of actual negative classified as negative).

These binary classification tests show that the model can predict correctly most of the instances.

### 7. Model deployment

Once the generalization performance of the neural network has been tested, it can be saved for future use in the so-called model deployment mode.

We can export the mathematical expression of the neural network to any bank software used for this purpose. This expression is listed below.

```scaled_account_length = (account_length-101.065)/39.8221;
scaled_voice_mail_plan = (voice_mail_plan-0.276628)/0.447398;
scaled_voice_mail_messages = (voice_mail_messages-8.09901)/13.6884;
scaled_day_mins = (day_mins-179.775)/54.4674;
scaled_evening_mins = (evening_mins-200.98)/50.7138;
scaled_night_mins = (night_mins-200.872)/50.5738;
scaled_international_mins = (international_mins-10.2373)/2.79184;
scaled_customer_service_calls = (customer_service_calls-1.56286)/1.31549;
scaled_international_plan = (international_plan-0.0969097)/0.295879;
scaled_day_calls = (day_calls-100.436)/20.0691;
scaled_day_charge = (day_charge-30.5623)/9.25943;
scaled_evening_calls = (evening_calls-100.114)/19.9226;
scaled_evening_charge = (evening_charge-17.0835)/4.31067;
scaled_night_calls = (night_calls-100.108)/19.5686;
scaled_night_charge = (night_charge-9.03932)/2.27587;
scaled_international_calls = (international_calls-4.47945)/2.46121;
scaled_international_charge = (international_charge-2.76458)/0.753773;
scaled_total_charge = (total_charge-59.4498)/10.5023;
y_1_1 = Logistic (-10.0534+ (scaled_account_length*0.837489)+ (scaled_voice_mail_plan*-1.92865)+ (scaled_voice_mail_messages*2.43032)+ (scaled_day_mins*0.619668)+ (scaled_evening_mins*-0.822147)+ (scaled_night_mins*-0.0592015)+ (scaled_international_mins*-0.331996)+ (scaled_customer_service_calls*5.14956)+ (scaled_international_plan*-0.486517)+ (scaled_day_calls*0.247419)+ (scaled_day_charge*-0.844425)+ (scaled_evening_calls*-0.385092)+ (scaled_evening_charge*-0.0288761)+ (scaled_night_calls*0.351411)+ (scaled_night_charge*0.330832)+ (scaled_international_calls*-0.244305)+ (scaled_international_charge*0.175898)+ (scaled_total_charge*-1.06894));
y_1_2 = Logistic (-10.4815+ (scaled_account_length*-0.143055)+ (scaled_voice_mail_plan*-3.90343)+ (scaled_voice_mail_messages*-1.00465)+ (scaled_day_mins*2.01689)+ (scaled_evening_mins*0.674122)+ (scaled_night_mins*1.06811)+ (scaled_international_mins*1.02216)+ (scaled_customer_service_calls*-0.474987)+ (scaled_international_plan*8.85213)+ (scaled_day_calls*-0.106802)+ (scaled_day_charge*2.69922)+ (scaled_evening_calls*-0.0539915)+ (scaled_evening_charge*1.90287)+ (scaled_night_calls*-0.301365)+ (scaled_night_charge*0.201187)+ (scaled_international_calls*0.227339)+ (scaled_international_charge*-0.658305)+ (scaled_total_charge*2.57132));
non_probabilistic_churn = Logistic (-2.085+ (y_1_1*5.50847)+ (y_1_2*4.52172));
churn = probability(non_probabilistic_churn);

logistic(x){
return 1/(1+exp(-x))
}

probability(x){
if x < 0
return 0
else if x > 1
return 1
else
return x
}
```