Research on the construction of early warning model of customer churn on e-commerce platform

It reflects the time interval between the customer's last consumption behaviour and the observation point in the observation period. The larger value of indicator R means that customers have not purchased anything on the platform for a long time, and they are in the decline period of life cycle and who are about to be lost, and the customer value of such customers will be lower. On the contrary, the smaller the R value is, the closer the time interval between the customer's last shopping and the observation point, the higher the customer value.

Indicator F is a measure of the number of times customers spend in the inspection period. Generally speaking, the higher the frequency of customers’ consumption, the higher the value. While the shorter the last consumption interval and the higher the consumption frequency in the observation period, the higher the comprehensive value of such customers and the more economic benefits they can bring to enterprises, which should be the focus of the enterprise.

This is the most important measurement index of customer value. The higher the consumption amount, the higher the contribution, and the higher the customer value. By synthesising these three indicators, the value of customers to the enterprise can be described in a multi-dimensional way, and according to the different combination performances of different customer groups with the three indicators, some of their behaviour characteristics can be analysed.

In this period, enterprises explore potential customers from the market by means of marketing, and customers also understand the actual situation of enterprises through various kinds of information, so as to preliminarily understand each other and lay the foundation for the development of follow-up relations.

In this period, with each product or service linkage between the two sides, the satisfaction and cooperation intention between the two sides will accelerate development, and the interdependence relationship will also deepen.

Due to the interaction in the first two stages, enterprises and customers will have more and more understanding in this period, so the relationship between them is further improved where all kinds of contact and cooperation relations are gradually become stable and for enterprises, this is the golden period with customers.

Due to poor communication, or competition from other companies, the established good customer relationship before has deteriorated gradually and the customers showed various negative performances, and the transactions gradually slowed down. However, it should be realised that the deterioration of the relationship may occur at any stage of the whole customer cycle, which is not limited to the last stage of the life cycle.

After the recession stage, customers lose their trust on the enterprise at last, which make them to end the business contact with the enterprise. At this stage, the customers are completely lost.

With the theoretical study of the life cycle, we can intuitively understand the stage of customer churn, and help enterprises to develop better customer retention strategies after the subsequent analysis of customer churn.

It is located at the bottom of the neural network, where neurons in this layer receive pre-selected indicators as input information from the external environment. In the neural network model of this paper, the number of neurons in the input layer is determined by the input amount of index data and 15 normalised index data of early warning of customer churn are respectively input as input samples, which are used to predict the crisis situation of customer churn.

(2) The hidden layer, in which the hidden layer nodes find out the hidden rules from the sample data, and then store the information in the form of connection weights. In summary, the following four formulas can be used to calculate hidden nodes:

Among them m is input layer node, n is the output layer node.

In this paper, the four empirical formulas are used to calculate the number of nodes in the four hidden layers, and the different nodes are put into the neural network for training. Then, the sample data of test set is brought into the neural network for fitting and the prediction accuracy of the output layer data obtained is compared with the expected result of the test set sample. The number of hidden layer nodes with the highest prediction accuracy 8 is selected as the number of hidden layer nodes in the early warning model.

It is located at the highest level of the network. At this level, the neural network transmits the hidden layer data to the output neuron, which in turn transmits the information to the external environment. The data category of the output layer determines the number of neurons in the output layer.

In this paper, when the network output layer is defined, the alert levels are determined in four levels according to different levels of customer churn risk. The result of the first-level warning level corresponding to the output layer is [0001], the second-level warning level corresponding to the output layer is [1000], the third-level warning level corresponding to the output layer is [0100] and the fourth-level warning level corresponding to the output layer is [0010].

Transfer function is usually selected from purelin, tansig and logsig. As there are negative values in the input data, in order to prevent data compression from affecting the accuracy, the tansig function that can map the neuron input range from (−∞, +∞) to (−1,1) is selected as the transfer function of hidden layer, and its expression is:

In addition, as the expected output data of the output layer are [1000], [0100], [0010] and [0001], this paper determines that the transfer function from the hidden layer to the output layer is the logsig function, which maps the input range of neurons from (−∞, +∞) to (0, 1), and its function is (6) log sig(m)=1(1+e−m) {\rm{log}}{\kern 1pt} {\rm{sig}}(m) = {1 \over {\left( {1 + {e^{ - m}}} \right)}}

Trainlm is selected as the training function in this paper. When the number of network weights is small, it can quickly converge, and has strong advantages in improving training speed, which avoids falling into local minimum. It is suitable for the function fitting of small and medium-sized networks, with fast convergence and small error.

In order to ensure the stability of the network, we usually try to choose a small learning rate while ensuring the training duration. The most scientific and reasonable method is to first determine the learning rate of several different values, and then, after the training of neural network, select the most appropriate learning rate according to the descending speed of the error function. Generally, the range of selection is between 0.01 and 0.8. Through the test, the learning rate of 0.01 is chosen.

Usually, the smaller the expected error value is, the more accurate the model. However, if the expected error value is too small, the number of hidden layer nodes will be increased unintentionally, resulting in the extension of the training time of neural network. Meanwhile, it will greatly increase the risk of ‘over-fitting’ of the network in training, which directly leads to the reduction of the universality of the neural network. In this paper, the following indicators are used for calculation:

Mean absolute error (7) MAE=∑|ej|N MAE = {{\sum \left| {{e_j}} \right|} \over N}

Sum square error (8) SSE=∑(ej)2 SSE = \sum {\left( {{e_j}} \right)^2}

Mean square error (9) MSE=∑(ej)2N MSE = {{\sum {{\left( {{e_j}} \right)}^2}} \over N} where e_j represents prediction error (ej=yjk−ojk) \left( {{e_j} = y_j^k - o_j^k} \right) , y_j represents the predicted value of output and o_j represents the actual value.

Generally, the expected error is between 0.0001 and 0.01. The expected error is set to 0.001 with the help the test.