E-commerce often refers to commodity trading activities on the Internet, including e-commerce platforms, customers, merchants, advertisers and so on. Domestic e-commerce platforms are represented by Taobao, JD.COM, Suning.cn, Dangdang and other websites with their own characteristics. Global e-commerce platforms are represented by Amazon and eBay. In recent years, cross-border e-commerce such as Koala overseas purchase has been constantly emerging. The number of online shopping customers in China reached 812 million in the first half of 2021, an increase of 29.65 million compared with the end of 2020, of which the number of people purchasing mobile phones was about 650 million, accounting for 80% of all customers (as indicated by the statistics in August 2021); this situation is attributed to the improvement of the social income level and the continuous upgrading of consumption. GMV, an e-commerce website, has also been growing continuously, reaching a 12% increase over 20 years. E-commerce websites first provide customers with shopping services. Then, customers will generate static information data and dynamic behavior data, and then the e-commerce platform will analyze the customer data by portrait, which will not only enhance their experience, but also grasp its own operation and increase the visits and revenue, thus forming a closed loop where the customer portrait is an extremely important part [1, 2].

At present, most methods for building customer portraits rely on a single machine learning algorithm [3–6]. Due to the limitations of a single algorithm, it is not possible to further explore the hidden information among data features, which makes the traditional learning methods inadequate in many cases, such as in predicting customer demographic attribute tags according to customer network behaviour data [7,8]. After pre-processing, the features of customer network behaviour data are often sparse and high-dimensional, which makes it difficult for a single learning method to fully discern the relationship between features, and its prediction effect is usually mediocre.

The deep internal relations among multi-dimensional features are explored by studying the method of feature extraction; low-dimensional features and representative features are extracted by using various machine learning algorithms; and the framework of the prediction algorithm in customer portrait is designed by adopting ensemble learning methods with different strategies, so as to improve the prediction effect of customer portrait labels. Automatically extracting customer features through an algorithm model reduces the time and cost involved in manually processing features, and greatly improves the efficiency of feature processing. Realising the efficient and accurate prediction of customer portrait labels can improve the enterprise recommendation system and boost the marketing revenue, and at the same time, advances customer’s satisfaction and loyalty to the enterprise’s services. To sum up, it is believed that the study of the algorithm of customer portrait based on the data of customer network behaviour is of great practical significance and application value.

According to the different needs, the multi-dimensional collection and analysis of massive data by customer portrait technology are also different [9–11]. Through the integrated analysis of customer portrait technology, the data are labelled, and the system users can have a clear and intuitive knowledge of the various dimensional characteristics of the customers. Customer portrait technology is more than simply mining and analysing customer data since studying customer behaviour is different from traditional market research, and can largely avoid the interference of subjective factors in the process of market research, allowing the data to speak, be closer to the actual situation of customers and improve the accuracy of investigation. In addition, customer portrait technology can narrow the distance between enterprises and customers, instead of leaving enterprises in a simple state of understanding the customers [12–14]. Through corporate customer portrait technology, the market positioning and the response speed to the market can be upgraded to a higher level [15, 16].

Customer portrait system can effectively help marketers find market changes, gain feedback from the market situation in time, adjust product strategies, continuously increase product competitiveness and maintain a strong momentum [17, 18]. Because the transform of products must be caused by the change of market, with the evolution of product life cycle and the change of market demand, the customer’s family structure, asset status and demand level will change, so the product needs to be adjusted in time according to the market and customer situation, otherwise it will eventually decline and fall. Moreover, compared with the traditional marketing model, the results of customer analysis have changed from static to dynamic, and the working mechanism of marketers has changed from post-event remedy to pre-warning, which has greatly improved the work efficiency [19–21].

The amount of data to be processed in data mining is often large. In order to mine valuable information from this low-density and noisy information, certain mining algorithms and tools must be used to filter the source data accordingly and clean it into a unified format [22]. Then, data mining and analysis must be conducted, and thereafter a judgement should be made according to the characteristics of the mined data. There are many tools and algorithms for data mining, while the processing methods are different. The main process of data mining is shown in Figure 1.

This stage is mainly to acquire data sets. Some data sets are ready-made and can be downloaded directly, while others need to be actively collected. This stage determines the scope and quality of the data set that the project will eventually study. The quality of data will directly affect the quality of mining and the final result.

Since the acquired data are incomplete, random and noisy with high probability, this stage is particularly important, and it is also thus necessary to carry out preliminary data processing and normalise the data. It mainly includes three steps: data cleaning, data conversion and data integration.

At this stage, it is necessary to select the appropriate data mining model according to the data characteristics and optimise it according to the project characteristics. The selection of an appropriate model can achieve a better mining effect. At the same time, after selection of a suitable model, it may be found that the pre-processed data do not meet the requirements of the model, necessitating a return to the previous stage.

At this stage, the results of data mining are analysed to assess whether the expected goals and tasks have been completed, and whether there is any room for improvement; this would enable the application of the results of data mining in solving practical problems.

After understanding the process of data mining, it is necessary to choose the appropriate data mining methods to model the data according to the problems to be solved. There are many methods of data mining that are suitable for specific problems. Generally, several methods and models need to be tried, so as to select a relatively better model. Clustering is a very common choice in data mining.

The purpose of clustering analysis is to group together data of the same kind. There is little difference between the same kind of data and huge difference between classes, and clustering analysis does not need to know the structure of clustering objects in advance. It classifies the similarity between data variables, and in the process of classification, constructs a symmetric similarity matrix, which is usually a data matrix or a difference matrix. In this paper, the data matrix is used as the data structure of clustering analysis.

The data matrix is a structure with a combination of object and attribute. For example, if there is a customer with j attributes, then the data matrix is expressed by an i*j matrix, as shown in Eq. (1).

The basis of clustering analysis is the similarity between objects, and whether objects are similar or not can be abstracted by ‘distance’. The smaller the distance between two objects, the more similar the two objects are; otherwise, the greater the difference between two objects, the greater the distance between them. For example, each object has one attribute, and x and y are the calculated values of two objects, respectively. So, x and y can be identified by vectors, as shown in Eq. (2).

In this paper, the similarity between two individuals is defined by quoting the Euclidean distance, including the distance calculation of the subsequent customer index system, which adopts this method uniformly. The formula of Euclidean distance is shown in Eq. (3).

With the deepening of research in recent years, clustering algorithms are gradually being divided into five categories, namely partition method, hierarchical method, density-based method, grid-based method and model-based method. However, actually the data mining algorithm not only depends on the which data type to choose, Whether the type is applicable or not can also be the criterion of selection, and the users of the algorithm often combine the ideas of various clustering methods, so it is impossible to completely divide the adopted algorithm into a certain clustering method. Among the many clustering algorithms, the FCM algorithm is one of the most commonly used.

According to the method of establishing the customer portrait system, this paper uses the data from the business analysis system of an e-commerce company [23–25]. First, we investigate the sample data needed for modelling according to the requirements of the portrait system [26]. We then process and clean the obtained customer data, and establish the data model by analysing and mining the customer behaviour data, in order to establish the customer portrait label and store the generated tag data [27, 28]. Finally, the customer portrait system is used to support the marketing of operators. The process is shown in Figure 2.

The basic functional framework of the customer portrait system consists of data collection layer, data model label layer and data basic management layer [29, 30]. The functional framework of the customer portrait is shown in Figure 3:

Among them, the data collection layer realises data pre-processing, customer log processing, text parsing processing, etc., and provides basic data for the preliminary processing of the customer portrait system. The tag layer mainly contains basic attributes, domain attributes, social attributes and purchase attributes of the customers [31]. The basic data management layer includes data storage of customer portrait, metadata management of the system, label life cycle management, query mechanism and update mechanism of the customer portrait system [32, 33].

With the individualisation of the customers’ demand for products and the increase of customers, a large number of customer portraits will accumulate in the personalised recommendation system with different demands, which can cause a certain interference and affect the accuracy of system’s recommendation. Based on this, it is necessary to divide the related portraits, and cluster the portraits of value among the customer groups, so as to find customers with similar degree in the group and divide them, and recommend personalised information services according to different customer groups. Combined with the design of the system described above, this paper mainly divides the customer portrait indicators into four dimensions: basic attribute dimension, domain dimension, social acceptability dimension and purchasing power dimension. The basic attributes include e-commerce customer id, contact information, receiving address, purchase amount, etc. Dimensions include the areas where customers buy products or services, such as tourism, food, medicine, clothing, furniture, etc. Social acceptability of customers includes the usage and frequency of social software. Purchasing power is mainly determined according to the disposable income of customers and their willingness to consume.

The construction of customer portraits belonging to multiple categories in the same dimension, and the interests of many customers in the recommendation system, cross and overlap with each other. From the attribute characteristics, customers who are in the same attribute have the same membership degree. From another attribute characteristic, customers in this membership degree represent another category of customers. In this paper, the Fuzzy C-means (FCM) algorithm based on partitioned clustering is selected. Given the data set M = (M1, M2, …, Mi), the data set M is divided into c fuzzy classes, and the clustering centre

Supposing that the customer portrait set is

Through continuous iteration, the best cluster of the fuzzy classification matrix and the best matrix cluster of cluster centre are obtained, in which the values of the principal membership matrix are shown in Eq. (5):

To divide the collection of the customer portrait into k categories (2 < k < _{ji} and _{i}_{i} represents the cluster centre of _{j}_{i}_{j}_{i}_{j}_{j}

The best classification method in the FCM algorithm can be solved through the iterative operation and the infinite nature of the classification matrix

The iterative steps are as follows:

Select k to be classified, and select 2 ≤ k ≤ m: Take the initial fuzzy classification matrix U^{0}:

For ^{(τ)}, calculate the cluster centre matrix.

Among them:

Make auxiliary correction of the fuzzy classification matrix

where j = 1,2,…,m;c = 1,2,…,k.

For U and ^{(τ+1)}, if the accuracy of determination is > 0, then:

If ^{τ+1} and ^{(τ)} are the result of the calculation, stop iteration; otherwise τ = τ + 1, and return to Step 2. Take the obtained classification matrix and central matrix to divide the customer portrait. The solution methods of fuzzy classification cluster centre matrix and optimal cluster centre are as follows:

Fuzzy classification clustering centre matrix

Let the obtained optimal fuzzy classification matrix be:

Then the object _{v}

The best clustering centre matrix clustering

Let the obtained optimal cluster centre matrix be:

Then the object _{v}

From the above algorithms, it can be seen that the FCM algorithm has the following defects: the initial clustering centre needs to be set, the sample data are unbalanced, the initial clustering centre is sensitive and the observation samples do not consider the influence of clustering results in the objective function. Therefore, in this paper, a method of adjusting the influence value of the density function is proposed, which is used to solve the problem that the clustering reliability of the FCM algorithm is reduced due to the sample base, thus improving the stability of the FCM algorithm and increasing the convergence of clustering centre.

Assuming that there are _{i}_{j}_{ij}, _{ij}_{j}_{i}_{j}_{j}_{ij} < 1. It can be concluded from the formula that within a certain range, the more points around, the more sample points surrounding _{j}_{j}_{j}_{j}_{j}_{j}_{j}_{i}

In this paper, data from 120 million customers of Taobao are taken as the sample data, and based on the customer portrait index system, the original data are screened, cleaned and processed from the basic attribute dimension of e-commerce customers in the multi-level customer portrait model. Since the raw data are very important to e-commerce companies, the raw data will not be listed here, and a part of data is randomly selected and normalised according to the norm to obtain new data as shown in Table 1.

Normalised data

ρ1 | ρ2 | ρ3 | ρ4 | |
---|---|---|---|---|

X1 | 0.38433 | 0.15642 | 0.38430 | 0.19573 |

X2 | 0.70499 | 0.15145 | 0.70497 | 0.18946 |

X3 | 0.19408 | 0.50566 | 0.19506 | 0.64245 |

X4 | 0.39654 | 0.30788 | 0.39696 | 0.37284 |

X5 | 0.10490 | 0.04545 | 0.10485 | 0.056646 |

X6 | 0.18035 | 0.04179 | 0.05144 | 0.18031 |

_{i}_{j}_{jmax}, the minimum value is _{jmin} and the normalised value is

The improved FCM algorithm is used to cluster and divide multi-level customer portraits. The weight coefficient is 2, the clustering data has been set to 4 and 10% of the experimental standard data set was randomly selected for analysis. Considering that the weight ratio of index ρ2 is only 0.1, the attribute characteristic value of e-commerce customers was reduced by three dimensions. They are the basic attribute dimension, purchasing power dimension and customer social dimension, which are represented by ρ1, ρ3 and ρ4, respectively, and the clustering effect is shown in Figure 4.

As can be seen from Figure 4, clustering is carried out according to the basic attribute dimension, purchasing power dimension and customer social dimension, and finally it is divided into four types of customer portrait clustering. Owing to the importance of raw data, it will not be listed and displayed here. According to Figure 4, the improved FCM algorithm proposed in this paper can perform better grouping in space, where the first to fourth categories of customers represent the four categories of key customers, customers to be developed, ordinary customers and worthless customers, respectively. The attribute types of customers mainly include customer loyalty, average profit ratio and profit growth rate, and the classification results as shown in Table 2 can be obtained.

Results after clustering

Cluster centre | Proportion of customers (%) | Proportion of profit (%) | Profit growth rate (%) | Loyalty | Customer type |
---|---|---|---|---|---|

Class I | 17.22 | 14.24 | 295.61 | 0.601 | Key development |

Class II | 25.17 | 69.77 | 48.8 | 0.295 | Key maintenance |

Class III | 38.01 | 10.90 | 98.59 | 0.223 | Ordinary customers |

Class IV | 19.57 | 5.09 | –49.87 | 0.035 | Worthless |

Matrix table of evaluation criteria

Actual/predictive | Negative number | K constant |
---|---|---|

Negative number | ||

K constant | i | j |

According to the results after clustering in Table 1, it can be concluded that the customers with a large degree of membership with cluster centre v2 account for 25.17% of the total customers, and the sum of profits created is 69.77%. These e-commerce customers belong to important e-commerce enterprises. For such e-commerce customers, enterprises should not only meet their basic needs but also provide personalised value-added services according to various individual customer needs, strengthen the daily maintenance between ordinary and e-commerce customers, and improve the loyalty of e-commerce customers. Although the profit share of the key development customers in Table 1 is not very high, the profit growth rate has reached 295.b1%, with high loyalty and great potential value for enterprises. For this kind of e-commerce customers, enterprises should deeply understand their development needs and provide timely support and services. Ordinary customers account for the highest proportion of customers, reaching 38.44% of the total number. The profit growth rate of these customers is lower than that of the key development customers, but higher than that of the other types of customers, and they are regarded as high-quality customers of enterprises. For such customers, companies should do personalised marketing on providing convenient and professional services. For worthless customers, companies should deeply understand the reasons for their choices and turn them into ordinary customers through various forms of personalised customisation.

In this experiment, the improved FCM clustering algorithm is used to divide the normalised data into multi-level customer portrait groups, and the accuracy of the recommendation results is measured by calculating the difference between the predicted scores and the actual evaluation data of the target customers. Mean absolute error (MAE) is mainly used to evaluate the accuracy of the recommendation algorithm. When the MAE value is small, the recommendation accuracy of the algorithm is proved to be high, and vice versa. Let the customer forecast score set be expressed as _{i}, _{i},

In order to verify the accuracy of the algorithm’s recommendation in this paper, indices of precision and recall are introduced for comparison.

In the above three evaluation indexes, the higher the MAE value, the worse the recommendation quality. The smaller the accuracy and recall rate, the worse the recommendation quality, and on the contrary, the better the recommendation quality.

On the data set, the improved algorithm in this paper is compared with other algorithms. The results of MAE, accuracy and recall are shown in Table 4.

Comparison of algorithm performance

Precision | Recall | MAE | |
---|---|---|---|

K-Means | 0.61 | 0.35 | 0.95 |

Improvement K-Means | 0.64 | 0.34 | 0.91 |

FCM | 0.66 | 0.36 | 0.89 |

Improvement FCM | 0.71 | 0.32 | 0.82 |

MAE, mean absolute error

From the above table, we can see that the improved FCM clustering algorithm and traditional K-Means; improved K-Means and traditional FCM algorithm have greatly improved the accuracy and recall rate of group customer image classification, and the MAE value has decreased compared with traditional K-Means, improved K-Means and traditional FCM, which greatly improved the accuracy of classification in the e-commerce customer portrait.

In this paper, massive e-commerce sales data are classified according to their characteristics as needed, and four dimensions of customer portrait indicators are finalised. Then, the appropriate algorithm is selected to build the customer portrait system model. Aiming at the problems in the FCM algorithm, such as sensitive initial clustering centre, little consideration about the influence of clustering results in objective function, etc., an improved FCM algorithm with multiple adjustment density function influence values is proposed. Finally, the improved FCM algorithm is compared with the traditional FCM algorithm, traditional K-Means algorithm and improved K-Means algorithm. Based on applied data sets, three performance indexes, MAE, accuracy and recall rate, are selected. The results show that the improved algorithm has excellent performance, which is applied to study the customer portrait system. It can effectively classify e-commerce customers and help e-commerce enterprises to formulate more accurate customer marketing strategies, thus promoting the development of e-commerce enterprises.

#### Comparison of algorithm performance

Precision | Recall | MAE | |
---|---|---|---|

K-Means | 0.61 | 0.35 | 0.95 |

Improvement K-Means | 0.64 | 0.34 | 0.91 |

FCM | 0.66 | 0.36 | 0.89 |

Improvement FCM | 0.71 | 0.32 | 0.82 |

#### Normalised data

ρ1 | ρ2 | ρ3 | ρ4 | |
---|---|---|---|---|

X1 | 0.38433 | 0.15642 | 0.38430 | 0.19573 |

X2 | 0.70499 | 0.15145 | 0.70497 | 0.18946 |

X3 | 0.19408 | 0.50566 | 0.19506 | 0.64245 |

X4 | 0.39654 | 0.30788 | 0.39696 | 0.37284 |

X5 | 0.10490 | 0.04545 | 0.10485 | 0.056646 |

X6 | 0.18035 | 0.04179 | 0.05144 | 0.18031 |

#### Results after clustering

Cluster centre | Proportion of customers (%) | Proportion of profit (%) | Profit growth rate (%) | Loyalty | Customer type |
---|---|---|---|---|---|

Class I | 17.22 | 14.24 | 295.61 | 0.601 | Key development |

Class II | 25.17 | 69.77 | 48.8 | 0.295 | Key maintenance |

Class III | 38.01 | 10.90 | 98.59 | 0.223 | Ordinary customers |

Class IV | 19.57 | 5.09 | –49.87 | 0.035 | Worthless |

#### Matrix table of evaluation criteria

Actual/predictive | Negative number | K constant |
---|---|---|

Negative number | ||

K constant | i | j |

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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 ofp -groupsResearch 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 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