With the rapid development of mobile internet, online social behaviours have shown a strong development trend. The topic of how to make full use of the various elements of information shared by users participating in online society has become popular in recent years. User profiles are built to document users’ social attributes, living habits, consumption behaviours and other characteristics, as abstracted from vast user network behaviour data. These generated profiles are widely used in ecommerce, social networking, internet financing, product development and other fields, providing an important basis for accurate advertising, personalised recommendations and risk control. In practical applications, user network behaviour profiles are built using big data and machine learning technology. To accomplish this, one must collect a vast amount of user network behaviour data. After cleaning and fusing the data, machine learning algorithms are used to model behaviours and build profiles. Existing user network behaviour profiles tend to be domain oriented, focusing on improving the accuracy of the user profiles derived from the user information. Profiles built on single enterprise data usually have difficulty in fully reflecting user characteristics. As the internet society grows and changes, the integration of user network behaviour has become a research trend across multiple fields and enterprises; thus, comprehensive and accurate user profiles are widely used with many network social governance services.
The following key issues exist in the use of large datasets to construct user profiles. First, the requirement for vast amounts of data adds significant performance requirements to central server equipment and networks. If each service provider collects a large quantum of user data for combination and synthesis, the data must be stored and processed centrally. Thus, the centralised method of constructing user profiles poses severe challenges to storage capacity, computing power and network transmission capability. Second, a data island problem is caused by fragmented data storage among enterprises [2]. The behaviour data input by users on the network are collected and stored by different service providers. However, owing to competition, security restrictions and approval processes, a barrier exists that is difficult to overcome regarding network user behavior data collection (i.e., the data island problem). Even if companies intend to exchange data, they may encounter policy accountability issues that prevent it. Splitting stored user network behaviour data obviously does not lead to comprehensive user profile development, resulting in a great discount in its availability and accuracy. Third, there are huge differences in data between different enterprises. Due to the different market positioning of different enterprises, the types of user groups they attract are also different. In addition, the private data of different enterprises are affected by the use behaviour of users under the enterprise. Therefore, the private data distribution of any particular enterprise cannot fully reflect the global data distribution of the entire industry, and it is difficult to build a comprehensive and accurate user profile by relying exclusively on the private data of an enterprise.
Recently, a federated learning architecture proposed by Google [5, 17] has provided inroads to solving data island and load capacity problems. This federated learning architecture ensures that the data of each participant are stored in a decentralised manner without the need for centralisation. It builds a machine learning model of global data without sharing the original data [11]. In the real environment, different from traditional machine learning and distributed machine learning, the data characteristics of participants in the federated learning scenario are mostly no independent and identically distributed (nonIID). Based on this, this paper proposes a global user profile construction method – FedUserPro, which is based on federated learning. The main contributions of this paper are summarised as follows:
This paper proposes, for the first time, a method for constructing user profiles based on unstructured data, and it uses a federated learning architecture to cooperate with multiparty data to construct global user profiles. Compared with user profiles in a single field, it describes user characteristics more comprehensively.
Based on the federated learning architecture, FedUserPro is proposed. Its federated learning architecture employs a horizontal division that is used to construct a global user profile using multiparty data. With this method, a latent Dirichlet allocation (LDA) model is used to mine potential user topic information to obtain a topic probability distribution, and users are grouped by softmax regression multiclassification. This method is extended to the federated learning architecture. When the data of each participant are not independent and identically distributed (IID), the accuracy of the model is improved with parameter transfer and aggregation.
The FedUserPro algorithm was subject to experiments using the Sina Weibo dataset. The experiment verified the accuracy and running time of the algorithm on nonIID data and compared it to the user profile algorithm, UserPro, trained by a single data holder. The results show that the accuracy of the FedUserPro algorithm was significantly higher than that of UserPro. The accuracy was increased by 19.71% in the best case and by 8.69% in the worst case; the running time showed a linear increase with the increase of participants.
Based on the need for federated internet user profiling, this paper provides an improved federated learning algorithm.
User profiles are widely used in recommendation, advertising and marketing services. In recent years, such profiles have been widely used in the construction of smart libraries, smart campuses, emergency public opinion managers and personalised insurance services. With the increasing use of user profiles, the types of data and methods for constructing them are also increasing. In addition to using statistical learning methods to obtain user profile tags, big data machine learning methods can be used to mine detailed and versatile user behaviour information from different sources. Zeng and Sun [12] built user profiles and embedded them into a library's recommendation service by collecting user behaviour information, such as access logs and search keywords in the library, improving user retrieval efficiency and the quality of recommendations. He et al. [13] constructed user profiles by collecting basic realworld information about the urban elderly using a smart elderly care platform to predict their service needs and provide customised services. Ren et al. [14] used crawler technology to obtain the static and dynamic attributes of Weibo users using machine learning methods to analyse their emotional tendencies and build user profiles. They also leveraged user portrait information to predict emotions, helping the platform develop targeted public opinion guidance strategies. Lin and Xie [9] analysed user behaviours based on social identity theory and used an LDA topic model to mine user interests and preferences to construct profiles of Weibo groups.
Federated learning has been proposed to solve the problem of training and updating local models under privacy constraints. It can train a global model using multiple participants’ data simply by aggregating the gradient or parameter information gathered from each during the model training stage without manipulating the original local data. For the machine learning task, the goal is to find an optimal solution to minimise the loss function. Usually, for complex problems with too many model parameters, optimisation algorithms are used to find the numerical solution of the loss function. The most common optimisation algorithm is the stochastic gradient descent (SGD) method. The FedSGD [19] algorithm applies the SGD algorithm to the federated learning framework for the aggregation optimisation of model parameters. After receiving the current round of global model parameters sent by the central server, the local participants perform a gradient calculation according to all their local data and upload the gradient back to the server to complete the global model aggregation round and update. Although this method is computationally efficient, it requires many communication rounds to reach a satisfactory model. In federated learning, communication cost is a problem that must be solved. There are two optimisation methods for reducing the communication costs of model training [1, 4, 6, 10]. The first reduces the number of communication rounds and the amount of information transmitted in each. Communication round reduction can be achieved by increasing the parallelism of the participants and increasing their local computation power. Information transmission reduction in each round can be achieved through parameter compression. The FedAvg algorithm proposed by McMahan et al. [4] reduces communication costs by increasing the local computation of each participant round. FedAvg has equivalent effects to centralised learning [22]. However, when applied to real data, defects pertaining to equipment heterogeneity arise. For example, participants often lack resources for the current training stage and cannot complete the training task within the specified time; thus, the server abandons them [3]. Consequently, for the problem of equipment heterogeneity, some scholars have proposed the FedProx algorithm [7, 23], which can dynamically adjust the number of local iterative training rounds of participants according to the resource status of the equipment. It improves the stability of federated learning, in which the original data are stored in different places. Owing to factors of time, space and individual differences, it is easy to cause the data to show nonIID characteristics [1, 21]. In response to this problem, Zhao et al. [16] proposed a method of sharing a small amount of data, which helped improve FedAvg performance when the data were nonIID.
In contrast with the above research, this paper examines a more comprehensive user profile that is based on unstructured text data under a horizontally federated learning architecture, with the goal of improving model accuracy by designing parameter transmission and aggregation when the data of each participant are nonIID.
This section provides preparatory knowledge of user profiles and federated learning.
The concept of the user profile was first proposed by Alan Cooper, the “father” of interaction design. He believed that user profiles were virtual representations of real users [8]. The creation of a user portrait requires a vast amount of real user data to obtain usable information through statistical analysis and machine mining. The portrait further describes individuals or groups by establishing tags from different dimensions and forming the prototype of a user group.
User profile
The content posted by Weibo users on their personal accounts reflects their personal characteristics (e.g., hobbies, values and social needs). It is feasible to extract important information from such data to construct user profiles. However, users do not store much content on Weibo, and only the most important aspects of their personalities can be used to identify their behavioural characteristics. Therefore, this article selects only the topk important tags as features.
A federated learning architecture includes servers and
According to the distribution of participants’ local data, federated learning is divided into horizontal, vertical and transfer types [5, 21]. The essence of horizontal federated learning is the collaborative learning of samples. The sample characteristics of each participant are similar, and model training is carried out by combining different data samples among participants. The essence of vertical federated learning is the collaborative learning of features. There is much overlap in user IDs, but the characteristics of user data held by different participants differ. Federated transfer learning solves the problem of each participant having few ID and sample feature overlaps. It can deal with insufficient sample sizes for a certain issue under the premise of ensuring data privacy and security.
Although federated learning uses a distributed learning framework, there are certain differences between it and distributed machine learning. For example, under federated learning, the central server does not have the right to allocate and control all data used for training; it only acts as a curious but credible third party to perform modelling tasks and parameter distributions, as well as local model updating of parameter aggregation operations. In distributed machine learning, the data of each work node are IID, and the number of work nodes is far lower than the number of training data samples. In federated learning, each participant is a work node, and the data are nonIID under the following situations [1]: covariate shift, prior probability shift, concept shift and data imbalance. Among these, a prior probability shift refers to the different distributions of the category labels of different clients. The setting of the nonIID data in this article is based on the prior probability shift, which is expressed as
The problem is that a federated learning architecture is needed to combine the data of multiple participants to construct user profiles during horizontal data segmentation.
The central server holds a uniformly distributed pretraining dataset provided by all participants according to their user category characteristics. The dataset was desensitised to delete user identities, which are only stored on the central server. The data of the pretraining dataset can be expressed as
The symbols used in this article are described in Table 1.
Symbols used in this article and their meanings
Symbols  Meanings 

The 

Data set held by the 

Pretraining data set held by the server  
Total number of participants  
Topic feature tags  
Probability of having topic feature label 

User ID in user data  
Category 

Total categories  
Softmax model parameters  
The total number of documents in the pretraining dataset  
Unstructured data describing user 
This section introduces the FedUserPro algorithm, which is divided into server and client sides.
The serverside algorithm is divided into preprocessing and training subalgorithms. The server holds the pretraining dataset,
The data held by the server are the user's unstructured text data (i.e., all Weibo data published by user
The LDA model is an unsupervised Bayesian generative learning model that includes a text–topic–word distribution. In recent years, it has been widely used for text dimensionality reduction, topic mining and text representation. All user document data contain several topics and probabilities corresponding to different topics. Each topic contains multiple feature tags, and the feature tags have corresponding probability distributions in the topics. Figure 2 shows the process of document generation using the LDA model.
In Figure 2,
According to the LDA probability model, the joint distribution formula of all variables can be known:
The training process of the topic model learns the parameters of the model in the existing document set, and the Gibbs sampling method is most often used to solve the distribution parameters. It randomly assigns a topic number to each feature word in the document set and modifies the topic number of each word by scanning and updating the entire corpus. It repeats the process until convergence to obtain document topic distribution parameters.
On the federated learning server side, the word segmenter is used to preprocess each user's data (e.g., word segmentation and stopword removal) so that each user document becomes a bag of words. It then uses the LDA model for training and obtaining the latent semantic information of the dataset. It then calculates the probability distribution of each user under each topic to realise the vector representation of the original data in the topic feature space.
It is essential that an appropriate number of topics be selected in the LDA model. Presently, most topics are determined through experience and experiments. In this paper, two indicators of perplexity and consistency were used to jointly determine the number of topics. The degree of confusion refers to how uncertain the trained model is about the topic to which the document belongs; hence, the lower the degree of confusion, the better. Generally, however, the higher the number of model topics, the lower the degree of confusion, which leads to model overfitting in the training set and lower topic interpretability. Consistency can reveal the strength of the semantic relationship between words in a topic, and the higher the consistency, the better. Therefore, the score of the comprehensive model for perplexity and consistency determines the number of topics in the model.
The server distributes the trained LDA model to all participants and preprocesses its local data. After preprocessing, all user text data are mapped to the topic feature space so that the server and different participants can start federated learning to jointly construct a global user profile.
The server collects a round of user parameters and updates them as a weighted average according to the proportion of each participant's dataset to the global dataset. It then sends the updated parameters to the participants for the next iteration. The specific algorithm is shown as Algorithm 1.
FedUserPro Serverside training algorithm
1:  Initialise model parameters 
2:  
3:  
4:  
5:  
6: 

7: 

8:  
9: 
This paper uses the softmax multiclass regression algorithm to train the user classification model. Softmax regression is a general form of logistic regression that is used for binary classification tasks and for multiclassification tasks.
The client
The sum of the probability that the sample belongs to all
The algorithm of the FedUserPro client is shown in Algorithm 2.
Client
1:  The client 
2:  Divide 
3: 

4:  
5:  
6: 

7:  upload

8:  
9: 
The client
In this study, the FedUserPro method was experimentally verified on a real dataset. This section introduces the experimental environment, parameter settings and experimental results.
This study applied crawler technology to examine the Weibo data published by active users in many articles using 10 Sina Weibo fields (i.e.,
The above data were divided into training and test sets. In each category, 10% of the data were selected and provided to the central server for LDA model pretraining. The data released by 21,000 users were divided horizontally and used as the training set for each participant in federated learning. According to the actual situation, the data of each participant presented a nonIID a priori probability offset that contained 10 categories of data for a total of 4,200 training samples, of which two categories contained 1,500 training samples each, and the remaining eight contained 150 training samples each.
The text data published by 770 users were selected from each category as the test set for federated learning. It was assumed that the central server was credible and that there was no data interaction among the central server and the participants, and no data interaction among the participants during the model training stage, so that the original data information would not be leaked. The number of topics in the LDA model was jointly determined by topic confusion and consistency indicators, and the topic–word distribution was obtained after model training was completed. The user's domain was the category of the user, and the number of topics in the LDA model was the number of user characteristics.
For multiclassification tasks, classification accuracy, recall rate and F1 value are generally used as model evaluation indicators. The calculation formulas for accuracy rate (P) and recall rate (R) are shown in Eq. (6), where TP is true positive, FP is false positive and FN is false negative.
Owing to the differences in the number of samples held by each participant during federated learning, the classification accuracy rate did not reflect the performance of the model in each category. This study measured the macroaveraging index to evaluate the classification performance of the model. The macroaveraging is the arithmetic average of the F1score of each class. The calculation formula is shown in Eq. (7).
The experiment compared and analysed the FedUserPro user profile construction method based on federated learning and the UserPro user profile construction method using singleparty data. The algorithms for constructing user portraits iterated 1,000 rounds each, and the results are shown in Table 2. P1–P5 represent the results of five single parties executing the UsePro algorithm on their respective data. The data of these five single parties were all distributions of prior probability deviations, and the distributions were different, as described in Section 5.1. FedUserPro represents the user profile construction method based on the federated learning proposed in this paper. The experiment analysed the accuracy of the algorithm and the macroaverage. The first (r1), 15th (r15), 25th (r25), 35th (r35), 50th (r50), 100th (r100) and 1,000th (r1,000) round results are presented for comparative analysis. The experimental results show that the accuracy of FedUserPro in the first round of iteration reached 79.77%, which is significantly better than the accuracy of the first round of the single party. After 100 iterations, the accuracy of FedUserPro reached 98.44%, and the accuracy of the single party was 84.32% (best) and 71.12% (worst), showing the advantages of federated learning in terms of accuracy. Similar results can be seen with the macroaverage parameters because the participants uploaded various representative samples to the central server to train the global LDA, which reduced the inaccurate subject distribution in singlepoint learning due to the small number of data samples, poor performance of sample diversity and dimensionality reduction of the test set to the subject feature space. Simultaneously, federated learning cooperated with multiple participants to train together, which increased the number of each type of training data in singlepoint learning and improved the accuracy and macroaverage score of the model in the test set. FedUserPro improved the accuracy by 19.71% in the best case compared with the r1,000 accuracy of P5, and by 8.69% in the worst case compared with the r1,000 accuracy of P3.
Accuracy and macroaverage results of federated learning and singlepoint learning
20.00%  22.45%  49.15%  64.39%  74.31%  77.58%  79.02%  
7.35%  12.19%  49.04%  62.03%  72.01%  74.43%  73.65%  
20.00%  20.00%  38.11%  47.50%  65.53%  79.75%  85.76%  
6.66%  7.31%  37.00%  47.83%  66.10%  79.79%  84.46%  
19.98%  20.00%  35.85%  50.58%  73.49%  84.32%  89.88%  
7.46%  6.71%  33.69%  50.52%  72.17%  83.98%  88.95%  
20.00%  20.64%  41.40%  45.63%  57.89%  75.62%  85.88%  
10.56%  11.92%  45.18%  48.80%  60.73%  77.49%  85.92%  
20.00%  20.19%  35.15%  43.57%  57.37%  71.12%  80.32%  
7.16%  7.54%  32.51%  43.45%  57.59%  69.91%  77.93%  
79.77%  94.85%  97.02%  97.87%  98.20%  98.28%  
73.05%  94.69%  96.97%  97.84%  98.19%  98.28% 
This paper also experimentally verified the performance changes of federated learning when the parameters were changed (i.e., the number of local epochs of participants’ local training iterations, the number of model parameter update samples’ batch size and the number of participants per round participating in parameter updates). Performance testing mainly included algorithm availability (i.e., precision and macroaverage) and efficiency (i.e., runtime). The experimental results are shown in Figures 3–5, and the abscissas all indicate the number of iterations.
Figure 3 shows the accuracy and macroaverage score of the FedUserPro algorithm when the local epoch of the participants’ local training iterations was changed. At this time, the number of participants participating in the model update in each round of federated learning was fixed at five, and the experiment was iterated for 1,000 rounds. The figure shows the results of the first 200 rounds. When the local epoch was set to five, the model converged the fastest, and the accuracy reached 97.72% after 20 iterations. When the local epoch was set to one, the accuracy was only 85.33% after 20 iterations. This is because, in each round of global communication, increasing the number of calculations of the local model can reduce the global communication cost, and the model can achieve higher accuracy in fewer communication rounds. Similar results can be seen in the average macro score. When the local epoch was five, the average macro score increased the fastest.
Figure 4 shows the changes in accuracy and macroaverage resultant to changing the batch size of model parameters. When the batch size was 120, the convergence speed of the model was the fastest. When the number of iterations was 20, the accuracy of the model reached 96.27%. However, when the batch size was 600, the accuracy of iteration 20 was only 80.24%. When the batch size was 300, the accuracy was between batch size 120 and batch size 600. Thus, reducing the number of samples for each model parameter update can speed up the convergence of the model. Similar results can be seen with the average macro score, but the convergence was slightly slower. When iterating 20 times and when the batch size was 120, the average macro score was 96.19%, and when the batch size was 600, the average macro score was only 73.78%.
Figure 5 shows the changes in accuracy and macroaverage resultant to changing the number of participants in each update round. It can be seen from the results that when all five participants participated in each round of global model update training, the accuracy of the model on the test dataset and the average macro score steadily improved, and the model converged faster. When the number was three or four, the accuracy and average score of the macro fluctuate greatly, and the smaller the value, the greater the fluctuation. It also required more communication rounds to make the model converge stably because some participants did not participate in the parameter update in a certain round. When they participated in the parameter update again, the accuracy of the model was greatly improved.
To grasp the changes in the differences between the participants’ update parameters during the training process, an experimental test was conducted on the average variance between the various parameters of the participants during federated learning, as shown in Figure 6. The abscissa represents the number of iterations, and the ordinate represents the average squared difference between the participant parameters. Owing to the differences in the amount of various local training data among participants at the beginning of training, each participant focused more on training large local sample categories. Therefore, with the increase in training times, the average variance of parameters among participants also increased. With the advancement of federated learning, the central server aggregated and updated the parameters of all categories in each round, and the average variance of parameters among participants decreased, also improving the accuracy of participants in small sample categories according to the aggregated parameters. This further improved the classification performance of the local model as a whole.
In this paper, the running times of FedUserPro and UserPro algorithms were tested, and the results are shown in Figure 7. Figure 7(a) indicates the time individually required for FedUserPro and UserPro algorithms to run 200 rounds when the model parameters were updated to the batch size and the number of local training iterations was fixed to three. The running time of the algorithm was the longest when the batch size was 120. This is because the number of samples involved in each update was small. Training using local data requires more iterations, and more calculation time is required.
Figure 7(b) shows that when the number of local training iterations of the participants changed, the FedUserPro and UserPro algorithms ran for 200 rounds, and the number of fixed model parameter update samples was 120. Thus, the smaller the number of local participant training iterations, the shorter the algorithm's running time. According to the results in Figure 7, when the number of participants increased, the running time of the FedUserPro algorithm increased linearly, showing good scalability.
User profiling is widely used in ecommerce, social networking, internet financing, product development and other fields. It provides an important basis for accurate advertising, personalised recommendations and risk control. Building a user profile requires a vast amount of data to provide an accurate user portrayal. However, data island problems have become the biggest obstacle to building user profiles in a centralised fashion. The emergence of federated learning allows multiple parties to jointly train machine user portrait models without sharing local data. This paper proposed the FedUserPro federated learning user portrait method based on a multiclassification model, and experimental verification was carried out on a real dataset. Experimental results showed that this method can significantly improve the accuracy of a singleparty training model based on local data. This not only ensures that the data of participants are not shared but also improves model accuracy, which helps build powerful user group profiles.
Notably, FedUserPro has room for improvement, which will motivate future research activities. First, the data privacy of participants needs to be improved, and intermediate parameters need to be handled using encryption or differential privacy. Then, the data need to be combined and sent to the server. The user portrait algorithm also needs improvement, such as by applying an unsupervised clustering algorithm without determining the number of user categories in advance. To summarise, user profile technology under federated learning is still a new research field, and there are many problems worthy of indepth study.
FedUserPro Serverside training algorithm
1:  Initialise model parameters 
2:  
3:  
4:  
5:  
6: 

7: 

8:  
9: 
Client Pk training algorithm ClientUpdate(w)
1:  The client 
2:  Divide 
3: 

4:  
5:  
6: 

7:  upload

8:  
9: 
Symbols used in this article and their meanings
Symbols  Meanings 

The 

Data set held by the 

Pretraining data set held by the server  
Total number of participants  
Topic feature tags  
Probability of having topic feature label 

User ID in user data  
Category 

Total categories  
Softmax model parameters  
The total number of documents in the pretraining dataset  
Unstructured data describing user 
Accuracy and macroaverage results of federated learning and singlepoint learning
20.00%  22.45%  49.15%  64.39%  74.31%  77.58%  79.02%  
7.35%  12.19%  49.04%  62.03%  72.01%  74.43%  73.65%  
20.00%  20.00%  38.11%  47.50%  65.53%  79.75%  85.76%  
6.66%  7.31%  37.00%  47.83%  66.10%  79.79%  84.46%  
19.98%  20.00%  35.85%  50.58%  73.49%  84.32%  89.88%  
7.46%  6.71%  33.69%  50.52%  72.17%  83.98%  88.95%  
20.00%  20.64%  41.40%  45.63%  57.89%  75.62%  85.88%  
10.56%  11.92%  45.18%  48.80%  60.73%  77.49%  85.92%  
20.00%  20.19%  35.15%  43.57%  57.37%  71.12%  80.32%  
7.16%  7.54%  32.51%  43.45%  57.59%  69.91%  77.93%  
79.77%  94.85%  97.02%  97.87%  98.20%  98.28%  
73.05%  94.69%  96.97%  97.84%  98.19%  98.28% 
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techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm} −x +δ )^{s} +ax ^{pm} +bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decisionmaking 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 Antiaging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation 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 Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of Ecommerce Platform 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 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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 LogicalMathematical 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 Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multiarray antennas based on improved genetic algorithm The influence of X fuzzy mathematical 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functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audiovisual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Differenceindifferences test for micro effect of technological finance cooperation pilot in China Application of multiattribute decisionmaking methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanKA New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual 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An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multisource heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listedcompanies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the BSM model in the pricing of derivatives in financial markets FedUserPro: A user profile construction method based on federated learning A multifactor Regression Equationbased Test of Fitness Maximal Aerobic Capacity in Athletes 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 Multifeature 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 FirstOrder 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 EnglishChinese CrossLanguage 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 horizontaltorsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations 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 A mathematical model of PCNN for image fusion with nonsampled contourlet transform Nonlinear Differential Equations in ComputerAided 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 DiamondSquare 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 Crossborder Ecommerce 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 Timedelay 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 watersaving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of AirConditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the winlose 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 Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on shortterm human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Crossborder Ecommerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model 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 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 edgebased finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of ecommerce 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 Research on threat assessment problems of island air defence system based on the leaderfollower model 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 ecommerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long shortterm memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSRAHP model A study of local smoothnessinformed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H_{2}N_{2} atmosphere Algorithm of overfitting avoidance in CNN based on maximum pooled and weight decay 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 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 Crossborder Ecommerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model ChineseEnglish Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model