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  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  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 . 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 . 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 . 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 . 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 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 .
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 .
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.
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 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 .
The data mining process of e-commerce platform can be divided into six steps, as shown in Figure 4.
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 .
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.
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.
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
Use Eq. (5) to judge the particularity of the decision tree, and the complexity also covers the detailed number and detailed score
Bring Eq. (10) into the above formula to obtain:
The derivative of
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.
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.
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.
|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.
|Optimised XGBoost algorithm||0.9213||0.9412||0.8712|Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x p m− x+ δ) s+ ax p m+ bxover F p2 m Digital marketing solutions based on consumer data and homomorphic encryption The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Paris panxiensis, a new combination of Trilliaceae from Sichuan, China Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic 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 of p-groups The 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