With the advancement of market economy, entrepreneurs have gradually found that customer resources play an increasingly important role in market competition. Therefore, the ‘customer-centred’ marketing model has gradually replaced the traditional ‘product-centred’ marketing model, and the research on customer resources has become a hot spot of common concern in theoretical and business circles [1, 2]. To maintain its market position and sustainable competitive advantage, the prediction of customer's consumption behaviour is very important. The fundamental purpose of studying the data of daily consumption behaviour among customers is to identify the most valuable customers of the enterprise, and to market their products, so as to increase their profitability. Studies have shown that [3] 80% of an enterprise's total marketing profit comes from enterprise marketing and 20% comes from the contribution of loyal consumers. In addition, some studies have shown that [4] the transaction cost between enterprises and regular customers is only 1/6 of that between them and the total customers. In the existing e-commerce market, apart from the fierce competition between the original e-commerce platforms, in recent years, with the change of social mode, a variety of emerging e-commerce modes are added such as WeChat, Weibo, community, etc., which also makes the e-commerce market more competitive [5, 6].

Customer loyalty is analysed according to the store situation, user psychology and user behaviour data, and the method of predicting repeated purchase behaviour is designed to reflect the importance and attention of customer loyalty [7]. Theoretically, customer loyalty can be discussed from the data generated by consumers’ purchasing behaviour, which can also be discussed from the factors that influence repeated purchase behaviour. However, in the field of academic research, scholars tend to theoretically discuss the factors that influence customer loyalty, thus neglecting the research on behaviour data [8]. At the same time, in the process of studying consumers’ consumption intention and purchasing behaviour, the differences between consumers will be ignored, and the conclusion is usually unreasonable, which leads to insufficient precision of indicators such as accuracy and recall rate [9]. Therefore, it has become an urgent problem to study how to improve the prediction of consumer loyalty.

Customer churn is the basis for effectively judging customer loyalty [10]. In this paper, the concept of e-commerce enterprise customers’ loss is defined as: if e-commerce customers’ consumption behaviour occurs again within a set period of time after consuming on the platform, it is regarded that the customer has not lost, otherwise, if there is no consumption behaviour within a set period of time, it is determined that they have lost. However, the consumption of customers in e-commerce enterprises generally changes periodically, so customers who have no consumption behaviour in a certain period can’t simply and directly judge that the customers are lost. The reasons for the churn of e-commerce customers are shown in Figure 1.

E-commerce customer loyalty can be defined as online consumers’ loyalty to products and services provided by enterprises on the Internet based on past shopping experiences. It refers to the loyalty of online customers to an online store or a brand of products or services on the e-commerce platform [11, 12].

Behaviour and intention of repeated purchase among consumers are the basis of loyalty classification of e-commerce customer. As shown in Figure 2, it can be divided into the following four types: persistent loyalty, potential loyalty, false loyalty and disloyalty.

In this paper, the quantitative index used to measure the loyalty of e-commerce customers is the probability of repeated purchase of a certain merchant on the e-commerce platform, which is divided into the following three parts: >70% are highly loyal, >70–30% are moderately loyal and <30% are low loyal that needs to be maintained by merchants.

Data mining refers to finding out hidden rules and relations from a large amount of data information, which means relying on large-scale original data and pattern analysis of data mining to obtain corresponding knowledge. Based on the perspective of business, data mining needs to extract the data from the huge database, and carry out the corresponding elaboration and analysis through specific rules, so as to achieve the desired modelling effect [13, 14].

The research of data mining technology in prediction of e-commerce customer loyalty mainly includes five tasks as shown in Figure 3.

Classification analysis.

Classification refers to the analysis of data objects with known categories, and then the search for other data by analysing the data and distinguishing their categories or detailed models, which can predict the specific types of unknown objects. By using the matching scheme of data mining in the e-commerce environment, the purchasing activities of multiple age groups and genders can be described effectively. On the basis of classification, it can be referred to the similar characteristics of customers of the same kind and then formulate corresponding marketing measures to provide targetted information services [15].

Prediction and evaluation.

Carry out in-depth collation of the actual data, and further carry out follow-up comprehensive research to ensure the timeliness and regularity of the final model calculation, so as to predict and evaluate the development trend and results of future events [16].

Discover time series patterns.

Through pattern discovery, other similar time series events can be found, and the corresponding patterns with high probability of recurrence can be further searched. The model helps e-commerce to better predict basic user activities, detect the sequence of user preferences, and further provide more personalised service mechanism.

Cluster analysis.

The main difference between cluster analysis and classification analysis is that data objects do not have corresponding class labels, and cluster analysis can further divide data formation into classes or clusters by referring to specific relationships or attributes, so that data objects in the same class or cluster are highly similar, while data objects in different classes or clusters are quite different from each other.

Association rules.

Association rule refers to finding frequently occurring items from a large amount of historical data, and finding the hidden association data among the data. The specific rules in the e-commerce model are to further explore the detailed number of clicks and the relationship between collection and purchase with reference to the sequential exploration activities of customers [17].

The data mining process of e-commerce platform can be divided into six steps, as shown in Figure 4.

Identify business.

In the data mining carried out by e-commerce, the first procedure is to judge detailed business problems and confirm the core purpose of subsequent data mining, which is difficult to predict its results effectively in real life.

Collect and select data.

The second step in the data mining process of e-commerce platform is to collect and select data, which is to extract information more in line with the goal of data mining through specific data, appropriate data can also reduce the workload of data mining and improve its quality [18].

Data preprocessing.

The third step in the data mining process of e-commerce platform is the basic pretreatment. Pre-processing can pre-process specific data sets, deal with missing data and filter abnormal data, and build feature information as the basis of later model building, which is helpful to improve the accuracy of data mining model.

Build a data mining model.

Refer to the first step to confirm the detailed goal, further select the mining algorithm that meets the requirements, and form the algorithm model that meets the expectations.

Data mining.

Relying on the model built by the previous programme, further research on the basic data of the third step is carried out to obtain ideal information and data.

Analyse and evaluate the results.

This process ensures that the results obtained after mining can be clearly and intuitively displayed after eliminating irrelevant and redundant patterns.

Although there are many methods to predict the customer loyalty, the existing prediction and classification methods have certain limitations to predict the purchase possibility of customers when they hold activities in a shop because the data of different industries and businesses have different characteristics. As the data of customers’ purchasing behaviour on e-commerce platform has the characteristics of limited dimension, abundant data and discrete type, the effective features of data are category data and the logs generated by the past historical records of customers’ purchasing corresponding products in a store on Tmall platform. Therefore, in this study, the classifier model can’t get the ideal effect. So the Boosting algorithm is selected in machine learning to estimate customer loyalty.

XGBoost is a GBDT algorithm and its corresponding generalised algorithm in the Gradient Boosting architecture. Generally, the objective function and the prediction function will be constructed. By applying the training sample to the lowest objective function and making it learn the relevant parameters, detailed samples can be further classified and predicted. Equation (1) shows the specific form.

Specific function

The basic principle of Boosting is to ensure that a specific model remains fixed, and further add new functions

Use Taylor formula to expand and define the objective function approximately, as shown in Eq. (5).

When the constant term is removed, the objective function

Then the specific tree is further divided into a leaf weight _{t}_{q}_{(x)}, where

Use Eq. (5) to judge the particularity of the decision tree, and the complexity also covers the detailed number and detailed score _{2} and its square of the module, the specific formula is shown in the following Eq. (8):
_{2} squared, and

Bring Eq. (10) into the above formula to obtain:

The derivative of _{j}

The research and analysis of customer churn is a classic two-category problem. Due to the deviation of the prediction model itself, the positive and negative cases are often wrongly divided, and the customers who have lost are mistaken for those who have not lost. On the contrary, the customers with higher loyalty are mistaken for those who have lost, which brings a lot of inconvenience to the daily management of enterprises, and even wastes the limited resources of enterprises. Therefore, the definition of loss function of XGBoost algorithm is optimised in this paper to reduce the loss caused by wrong classification.

Logarithmic function is a loss function commonly used in solving classification problems, as shown in Eq. (13):

In the calculation process of XGboost algorithm, it is easy to find out through the loss function, which sets the probability of positive and negative examples being divided into the same. But in fact, there are more cases to divide positive examples into errors. So penalty coefficient

The definition of the loss function after adding the penalty coefficient is shown in Eq. (14), because there are more cases in which the positive examples are wrongly divided. The value range of

This data set mainly describes the sales to customers in Tmall platform and the purchase records of customers in the past 6 months, including the long-term user behaviour logs of customers on Tmall platform. According to the attributes of different data, it can be divided into user information, commodity information and Scenario information. User information includes user ID, province and city; commodity information includes user logo, commodity name, price, category and shelf time; scenario information includes payment time, order quantity and order status.

Before the data is imported into R, it is preliminarily sorted out. The steps are divided into four steps, as shown in Figure 5.

Step 1: Use SQL Server software to extract customers’ purchase behaviour from file of text format.

Step 2: Adopt the ifelse() function in R and as the date function to convert it into the format of time data and specifies the format as yyyy-mm-dd.

Step 3: As the independent variables corresponding to individual dependent variables are all empty, delete them directly.

Step 4: Rename the original variables and interpret the variables in the dataset.

Since the data are made ‘dirty’ by missing data, abnormal data and repeated data, we need to clean it.

Process of missing values

In view of the actual gender deficiency, the specific maximum possible number was used to carry out the process of follow-up filling. So that the effective statistics of all genders can be carried out and the maximum value can be filled effectively. In view of the deficiency of the age range, the subsequent filling operation can be carried out through the specific mean value, so that the specific age can be calculated effectively. The corresponding mean value data are obtained to achieve the ideal filling effect.

Outlier handling

Local outlier factor combines anomaly detection and density-based clustering algorithm where any natural number

The calculation of local density of object

Among them, Dist(

Local deviation index: If the object

The local deviation index of object

In this paper, LOF algorithm is used to eliminate the outliers in the preliminary data set. The theoretical basis is to analyse the local density of a point, in order to compare it with the density of points distributed around it. If the comparison shows that the density of the area where this point is located is sparse, it indicates that this point is an abnormal value. In addition, the outlier score is calculated by the lofactor function in DMwR package, and the data with the top five scores are taken as outliers, and then eliminated. In this paper, a total of 200 pieces of abnormal data were eliminated.

Based on the above analysis, in this paper, the xgb.train () function in xgboost package in R language is adopted, and the construction process of e-commerce customer loyalty prediction model proposed in this paper is as follows:

Import data into R, and clean the data.

Store the cleaned data in R software in the format of dataframe, and divide it into training set (70%) and testing set (30%).

Determine that the data in the training set and the test set have the same distribution, and test the homogeneity of the samples by ks.test () function.

Set the parameter variables in xgb.train () function, and obtain different prediction results through different parameter settings, thus select the best prediction result.

Substitute the test set into the model, and use the prediction function to evaluate it.

Establish the confusion matrix, so that the gap between the predicted results and the real values can be obtained to judge the accuracy of the model prediction.

Evaluation and comparison of e-commerce customer loyalty prediction models.

XGBoost algorithm | 0.8689 | 0.6854 | 0.8436 |

Optimised XGBoost algorithm | 0.9213 | 0.9412 | 0.8712 |

After administering the model, it is necessary to evaluate its performance. For the problem of binary classification, the model evaluation based on the confusion matrix is selected in this paper, and the evaluation indexes of the model are calculated, including the values of Accuracy, Precision and Recall of the model prediction, where the higher the index values of these three items, the better the prediction ability of the model, the higher the prediction accuracy. The calculation formula is as follows:

Based on the evaluation indexes of the above models, the e-commerce customer loyalty prediction models based on XGBoost algorithm and improved XGBoost algorithm are compared, and the results are shown in Table 1.

The results shows that the optimised XGBoost model relies on strong feature learning ability, and can better extract user attributes and the information of commodity feature, so as to comprehensively capture the user's’ purchasing interest and get the user's’ shopping loyalty, whose Accuracy, Precision and Recall rates are 0.9213, 0.9412 and 0.8712, respectively. After calculation, the value of

Based on the data mining technology, this paper constructs the prediction model of e-commerce customer loyalty by extracting the purchase records provided by a merchant in the Tmall platform, where the local abnormal factor algorithm is used to eliminate the data for cleaning, and XGBoost algorithm is used for optimisation. The results show that the prediction accuracy for e-commerce customer loyalty in the XGBoost model with improved penalty coefficient is higher, whose value of

#### Evaluation and comparison of e-commerce customer loyalty prediction models.

XGBoost algorithm | 0.8689 | 0.6854 | 0.8436 |

Optimised XGBoost algorithm | 0.9213 | 0.9412 | 0.8712 |

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management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network