Ubiquitous embedded terminal-oriented asynchronous personalized federal learning method

Through dynamic clustering and energy consumption-aware adaptive communication scheduling strategy optimization model update, the lag and communication efficiency problems in asynchronous federated learning are solved, system performance and robustness are improved, energy consumption is reduced, and model update timeliness and accuracy is improved.

CN120354152APending Publication Date: 2025-07-22NORTHWESTERN POLYTECHNICAL UNIV
View PDF 0 Cites 0 Cited by

Patent Information

Application Number
CN202510391657.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-31
Publication Date
2025-07-22

AI Technical Summary

Technical Problem

The existing asynchronous federated learning methods have lag problems during model update process, which affects model accuracy and training delay, making it difficult to achieve the best balance between model accuracy and training delay.

Method used

A asynchronous personalized federated learning method for ubiquitous embedded terminals is adopted, and the dynamic clustering center model and energy consumption-aware adaptive communication scheduling strategy are combined with the feedback value and energy status of the client, the model update timing is optimized, and the model lag and communication overhead are reduced.

Benefits of technology

It effectively solves the problem of model lag and communication efficiency in asynchronous federated learning, improves the overall performance and robustness of the system, reduces communication energy consumption, and improves the timeliness and accuracy of model updates.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN120354152A_ABST
    Figure CN120354152A_ABST
Patent Text Reader

Abstract

The invention discloses an asynchronous personalized federated learning method for a ubiquitous embedded terminal, and particularly relates to the field of federated learning based on edge intelligence. Comprising the following steps: receiving model parameters uploaded by a client; determining a plurality of initial clustering center models according to an uploading sequence of the model parameters, and determining a client associated with each initial clustering center model; determining a feedback value of each client to the initial clustering center model; establishing a new clustering center model according to the feedback value corresponding to each initial clustering center model; determining the deviation between each new clustering center model and the corresponding initial clustering center model; issuing the new clustering center model to a corresponding client according to the deviation; and receiving model parameters uploaded by the client, and updating and aggregating the model parameters to the corresponding new clustering center model to complete asynchronous personalized federal learning. The problem of model updating hysteresis in an existing asynchronous federal learning method can be solved.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] This application relates to the field of federated learning based on edge intelligence, and particularly to an asynchronous personalized federated learning method for ubiquitous embedded terminals. Background Art

[0002] In recent years, with the rapid development of mobile Internet and Internet of Things (AIoT) technologies, federated learning (FL), as a distributed machine learning paradigm, has gradually become a research hotspot. Its core goal is to train a high-precision deep learning model with low latency through a distributed collaborative training mechanism while ensuring data privacy, so as to quickly adapt to dynamic environments and user personalization needs. However, existing federated learning methods still face many challenges in practical applications, especially in dealing with data heterogeneity and device heterogeneity, and it is difficult to achieve the best balance between model accuracy and training latency.

[0003] On the one hand, traditional federated learning algorithms (such as FedAvg) perform poorly in the cross-device non-independent and identically distributed (non-IID) data scenario, and the unified global model is difficult to adapt to the local data distributions of different devices. For example, sensor data collected by different devices have significant differences in distribution characteristics, noise levels, or semantic contexts, resulting in insufficient model generalization ability. On the other hand, the synchronous mechanism of standard federated learning requires all devices to complete local updates synchronously in each round of training, which makes devices with slower computing speeds become the bottleneck of global model aggregation, significantly increasing the training latency. To address these challenges, personalized federated learning (PFL) and asynchronous federated learning (AFL) have been proposed respectively. Personalized federated learning significantly improves the adaptability and accuracy of the model in a multi-device environment by customizing personalized models for each device or group of devices. However, most existing personalized federated learning methods are based on synchronous mechanisms and are difficult to adapt to asynchronous mobile system environments. Asynchronous federated learning significantly reduces the training latency by allowing devices to complete training and upload updates at their respective speeds, but may lead to model lag problems, affecting model accuracy.

[0004] In addition, the limitations of existing methods in practical applications have gradually emerged. For example, in typical tasks such as image recognition and human activity recognition, the uneven data distribution and differences in device performance have a significant impact on the convergence and final effect of model training. Experimental results show that although synchronous personalized federated learning is superior to synchronous and asynchronous federated learning in terms of model accuracy, its training latency is longer. Summary of the Invention

[0005] The main objective of this application is to provide an asynchronous personalized federated learning method for ubiquitous embedded terminals, aiming to solve the problem of model update lag in existing asynchronous federated learning methods.

[0006] To achieve the above objective, this application provides an asynchronous personalized federated learning method for ubiquitous embedded terminals, including: receiving the model parameters uploaded by clients; determining multiple initial clustering center models according to the upload order of the model parameters, and determining the clients associated with each initial clustering center model; determining the feedback value of each client to the initial clustering center model; establishing a new clustering center model according to the feedback value corresponding to each initial clustering center model; determining the deviation between each new clustering center model and the corresponding initial clustering center model; sending the new clustering center model to the corresponding client according to the deviation; receiving the model parameters uploaded by the client, and updating and aggregating the model parameters to the corresponding new clustering center model to complete asynchronous personalized federated learning.

[0007] Optionally, after determining the deviation between each new clustering center model and the corresponding initial clustering center model, the method further includes determining the energy status of the client according to the charging status of the client, the usage of local computing task resources, and the communication traffic estimation; sending the new clustering center model to the corresponding client according to the energy status of the client.

[0008] Optionally, sending the new clustering center model to the corresponding client according to the deviation includes: when the deviation is greater than the first preset threshold, sending the model to the corresponding client.

[0009] Optionally, sending the new clustering center model to the corresponding client according to the energy status of the client includes: when the energy status of the client is less than the second preset threshold, sending the model to it.

[0010] Optionally, the method further includes: determining the model remoteness of the client according to the deviation and the energy status; when the model remoteness of the client is greater than the third preset threshold, sending the model to it.

[0011] Optionally, the energy status of the client is determined according to the charging status of the client, the usage of local computing task resources, the communication traffic estimation, and the adjustment parameter.

[0012] Optionally, determining multiple initial clustering center models according to the upload order of the model parameters, and determining the clients associated with each initial clustering center model includes: determining multiple initial clustering centers according to the upload order of the model parameters, and constructing initial clustering center models; respectively determining the distances between the model parameters of the remaining clients and each initial clustering center, and allocating the clients to the initial clustering center with the smallest distance to obtain the clients associated with each initial clustering center model.

[0013] Optionally, determine the feedback value of each client for the initial clustering center model, including: obtaining the predicted label distribution and the actual label distribution corresponding to each client, and determining the variance of the predicted soft label distribution of the corresponding initial clustering center model, and determining the feedback value of the client for the initial clustering center model according to the predicted label distribution, the actual label distribution, and the variance of the predicted soft label distribution.

[0014] Optionally, establish a new clustering center model according to the feedback value corresponding to each initial clustering center model, including: respectively sorting the feedback values of all clients associated with each initial clustering center model in descending order, and allocating the clients ranked in the last preset number to a new cluster; using the model parameters of the initial clustering center model as the initial model parameters of the corresponding clients in the new cluster, and locally fine-tuning the initial model parameters during the training process of the clients, and uploading the fine-tuned model parameters to the server; the server aggregates the model parameters uploaded by all clients in each new cluster to obtain a new clustering center model.

[0015] Optionally, after establishing the new clustering center model, the method further includes: combining the new clustering center model and the initial clustering center model into a model set; when the number of models in the model set is greater than the fourth preset threshold, determining the main model and the auxiliary model in the model set; using the auxiliary model to optimize the main model, and using the attention matrix of the weight granularity to fuse the optimized main model and the auxiliary model to obtain a fused clustering center model; re-determining the main model and the auxiliary model in the model set until the number of models in the model set reaches the fifth preset threshold to obtain the final model set; determining the deviation between each new clustering center model and the corresponding initial clustering center model, including: determining the deviation between the fused clustering center model and the corresponding initial clustering center model in the final model set.

[0016] Compared with the prior art, the beneficial effects of the present application are as follows: The asynchronous personalized federated learning method for ubiquitous embedded terminals of the present invention first determines the initial clustering center, dynamically clusters the clients according to the distance between the model parameters of the clients and the initial clustering center, and at the same time optimizes the clustering result by combining the feedback of the clients on the initial clustering center model during runtime to adapt to the asynchronous update environment and reduce the model lag; proposes an energy consumption-aware adaptive communication scheduling strategy, and adaptively adjusts the model distribution timing for each clustering center model according to the accumulated model change degree and the energy status of the clients, so as to ensure the timeliness and accuracy of model updates while reducing the communication overhead; through the above method of combining dynamic clustering and model distribution on demand, effectively solves the problems of model lag and communication efficiency in asynchronous federated learning, and improves the overall performance and robustness of the system. Description of the Drawings

[0017] Figure 1 This is a schematic flowchart of an asynchronous personalized federated learning method for ubiquitous embedded terminals in this application; Figure 2 This is a schematic flowchart of the clustering center model merging in the asynchronous personalized federated learning method for ubiquitous embedded terminals in this application.

[0018] The realization, functional features, and advantages of the objectives of this application will be further described with reference to the embodiments and the accompanying drawings. Detailed Embodiments

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in this application will be clearly and completely described below with reference to the accompanying drawings in this application. Obviously, the described embodiments are some, but not all, of the embodiments of this application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this application without making creative efforts shall fall within the protection scope of this application.

[0020] The first embodiment of the present invention provides an asynchronous personalized federated learning method for ubiquitous embedded terminals, as Figure 1 shown, and specifically includes the following steps: Step S1: Receive the model parameters uploaded by the client, determine a plurality of initial clustering center models according to the upload order of the model parameters, and determine the clients associated with each initial clustering center model; the specific steps are as follows: Step S11: Receive the model parameters uploaded by the client; Step S12: Determine a plurality of initial clustering centers according to the upload order of the model parameters, and construct an initial clustering center model; Specifically, according to the upload order of the model parameters, the model parameters of a preset number of clients with earlier upload orders are used as the initial clustering centers, and the initial clustering center model can be obtained according to the model parameters of the initial clustering centers; the preset number can be determined according to the network scale and device heterogeneity, and the preset number is the initial number of clusters C. Initialize the clustering centers, and use the model parameters { } of the first C asynchronously uploaded clients as the initial clustering centers { } respectively; Step S13: Determine the distances between the model parameters of the remaining clients and each initial clustering center respectively, and assign the clients to the initial clustering center with the smallest distance to obtain the clients associated with each initial clustering center model.

[0021] Among them, the remaining clients are the clients u i that upload model parameters later. Calculate the client u iThe distances to all the initial clustering centers are calculated to complete the assignment of clients.

[0022] Step S2: Determine the feedback value of each client for the initial clustering center model. Specifically, obtain the predicted label distribution and the actual label distribution corresponding to each client, and determine the variance of the predicted soft label distribution of the corresponding initial clustering center model. Based on the predicted label distribution, the actual label distribution, and the variance of the predicted soft label distribution, determine the feedback value of the client for the initial clustering center model.

[0023] It can be understood that the predicted label distribution Fc is the predicted probability distribution of each category obtained after inferring the local dataset of the client using the initial clustering center model; the actual label distribution Fi is the distribution of each true category in the local dataset of the client; the variance of the predicted soft label distribution Var(S C ) is the degree of dispersion of the category probability distribution generated by the weights of the initial clustering center model. The formula for determining the feedback value is: .

[0024] Step S3: Based on the feedback value corresponding to each initial clustering center model, establish a new clustering center model. Specifically, in step S31, for each initial clustering center model, sort the feedback values of all associated clients in descending order, and assign the clients ranked in the subsequent preset number to a new cluster; where the preset number can be 20% of the number of clients associated with each initial clustering center model.

[0025] To quickly learn the model parameters of the new cluster, the new cluster is regarded as the original cluster with data drift. The transfer learning method for domain adaptation is adopted to fine-tune the model parameters of the new cluster based on the model parameters of the original cluster. However, the newly obtained extended clustering model through transfer learning often encounters overfitting problems. This is because the samples in the new data drift are scarce, which may lead to overfitting of the clustering center model to a small amount of new data, thus reducing the generalization ability of the model. To solve this problem, in this embodiment, local training is performed on each mobile client in the new cluster, and the model is adjusted through partial fine-tuning, focusing on adjusting the output of the final layer rather than performing full training. The specific method is shown in steps S32 - S33.

[0026] Step S32: Use the model parameters of the initial clustering center model as the initial model parameters of the corresponding clients in the new cluster, and during the training process of the clients, perform local fine-tuning on the initial model parameters, and upload the fine-tuned model parameters to the server; where local fine-tuning refers to fine-tuning the model parameters of the final layer.

[0027] Step S33: the server aggregates the model parameters uploaded by all clients in each new cluster to obtain a new cluster center model.

[0028] It is worth noting that after the aggregation is performed in step S33, the restriction of partial fine-tuning in step S32 is lifted and the normal full training mode is switched. In this embodiment, a Boolean index is assigned to the local training mode of each client in the newly expanded cluster to indicate whether the client is performing partial fine-tuning or full training.

[0029] In this embodiment, a data-adaptive personalized client clustering method is used to perform dynamic clustering according to the similarity of the client's local data distribution, and the clustering results are optimized in combination with runtime feedback to adapt to the asynchronous update environment and reduce model lag.

[0030] Furthermore, in order to reduce communication energy consumption and ensure the efficiency of model updating, this embodiment proposes an energy-aware adaptive communication scheduling strategy. The model sending timing is adaptively determined according to the accumulated model change degree to achieve communication energy consumption optimization, as shown in steps S4-S5.

[0031] Step S4, determine each new cluster center model Corresponding to the initial cluster center model Deviation ; According to the deviation, the new cluster center model is sent to the corresponding client; the calculation formula of the deviation is:

[0032] Specifically, when the deviation is greater than a first preset threshold, the model is sent to the corresponding client. Otherwise, the existing model is maintained to reduce invalid communication. Exemplarily, the deviation can be cosine similarity. This strategy can reduce the invalid cluster center model sending process and reduce communication energy consumption while ensuring that the model quality is not reduced.

[0033] In order to further optimize communication energy consumption, the energy-aware adaptive communication scheduling strategy also adaptively determines the timing of model delivery according to the energy status of the user end. The details are as follows.

[0034] Step S5, determining the energy status of the client according to the charging status of the client, the usage of local computing task resources and the communication traffic estimation, and sending the model to the client according to the energy status of the client. Specifically, when the energy status of the client is less than the second preset threshold, sending the model to the client.

[0035] Exemplarily, the charging status of the client is calculated by current power / maximum power; the local computing task resource usage is determined by the current client CPU / GPU usage; the communication traffic estimation is determined by current bandwidth / maximum bandwidth. When the energy status of the client is less than the second preset threshold, the model is sent first, and the model update is avoided as much as possible on the low-energy client.

[0036] Furthermore, the energy status of the client is determined based on the charging status of the client, the usage of local computing task resources and the communication traffic estimation, and the adjustment parameters. The specific formula is as follows:

[0037] In the formula, These are adjustment parameters. is the energy status of the client, Charging status for the client. The resource usage of local computing tasks. Estimate the current communication traffic of the client.

[0038] Furthermore, this embodiment also adaptively adjusts the model sending timing according to the model distance of the client, as shown in step S6.

[0039] Step S6, determining the model distance of the client according to the deviation and energy status; and sending the model to the client according to the model distance. Specifically, when the model distance of the client is greater than a third preset threshold, sending the model to the client. The calculation formula is:

[0040] In this embodiment, for The client with a value greater than the third preset threshold will be given priority for model delivery. For clients whose energy is less than the third preset threshold, a waiting mode is performed when the energy is sufficient. Waiting mode is to perform model delivery as required. In addition, the first preset threshold, the second preset threshold and the third preset threshold can be set according to actual needs.

[0041] After the server sends the model in step S6, the client receives the model sent by the server, performs local training, and uploads the trained model parameters; Step S7, the server receives the model parameters uploaded by the client, updates and aggregates the model parameters onto the corresponding new cluster center model, completing asynchronous personalized federated learning. Further, after the server aggregates the model parameters of the received client onto the corresponding cluster center model, it evaluates the aggregated model, and based on the evaluation result, the server decides whether to continue iterative training. If the model performance (such as accuracy) does not meet the requirements, it returns to step S2 to re-determine the feedback values of each client for the corresponding cluster center model (initial cluster center model or new cluster center model), and execute S3 - S7 until the model performance meets the requirements or reaches the preset number of iterations.

[0042] In another embodiment, when the number of cluster center models obtained after step S3 exceeds the preset model number, after establishing a new cluster center model in step S3, the cluster center models need to be merged. The specific merging method is as follows: Step S400, combine the new cluster center model and the initial cluster center model into a model set; when the number of models in the model set is greater than the fourth preset threshold, in the model set, determine the main model and the auxiliary model; use the auxiliary model to optimize the main model, and use the attention matrix of weight granularity to fuse the optimized main model and the auxiliary model to obtain a fused cluster center model; re-determine the main model and the auxiliary model in the model set until the number of models in the model set reaches the fifth preset threshold to obtain the final model set, which is the final cluster center model.

[0043] Specifically, as Figure 2 shown, step S401, combine the new cluster center model and the initial cluster center model into a model set; when the number of models in the model set is greater than the fourth preset threshold, in the model set, take the cluster center model with the largest number of associated clients as the main model, and determine the auxiliary model and the optimization direction according to the distance between the weight vectors of the remaining cluster center models and the weight vector of the main model; Among them, the optimization direction is determined according to the main model and the auxiliary model based on the distance L1 between their weights.

[0044] Step S402, combine the optimization direction and use the model parameters of the auxiliary model to optimize the model parameters of the main model to obtain an optimized main model; Step S403, determine the posterior distribution of the optimization direction, and based on the optimization direction and its posterior distribution, determine the attention matrix of weight granularity for all model parameters; among them, the method for determining the posterior distribution of the optimization direction is: perform training on the local dataset of the main model to obtain an updated main model 。Then, calculate the weight difference between the main model before training and the updated main model to generate the posterior distribution of the optimization direction 。

[0045] Step S404: Aggregate the optimized main model and the auxiliary model using the attention matrix of weight granularity to obtain the fused clustering center model, i.e., the merged model. Among them, the purpose of introducing the attention matrix of weight granularity is to obtain a 01 matrix with the same dimension as the weight of the clustering center model. The calculation method is shown in step 5 of the pseudocode. First, multiply the corresponding positions in the optimization direction and the posterior distribution of the optimization direction to obtain the first result. Then, set the negative numbers in the first result to 0 to prevent negative optimization during aggregation. Next, divide each value of the result of multiplying the corresponding positions in the optimization direction and the posterior distribution of the optimization direction by 1 to obtain the second result. Then, multiply the first result and the second result at the corresponding positions to obtain the attention matrix of weight granularity α。

[0046] Exemplarily, the pseudocode of the fused clustering center model is as follows:

[0047] Step S405: Return to step S401. Among the fused clustering center model and the remaining clustering center models, take the clustering center model with the largest number of associated clients as the main model, and determine the auxiliary model and the optimization direction according to the distance between the weights of each clustering center model; until the number of clustering center models reaches the fifth preset threshold to obtain the final model set. Among them, the fourth preset threshold can be 2C, and the fifth preset threshold can be 1C, where C is a hyperparameter threshold specified manually

[0048] Based on the above merging result, execute step S4. For the deviation between each new clustering center model and the corresponding initial clustering center model determined in step S4, specifically: determine the deviation between the fused clustering center model and the corresponding initial clustering center model in the final model set

[0049] In the asynchronous personalized federated learning method of the present invention, the clustering center model can be models such as RNN, LSTM, CNN, and transformer. RNN is used to process image recognition tasks, RNN and LSTM are used to process time series data tasks, such as human behavior recognition tasks, and transformer is used to process NLP tasks. In order to verify the effect of the asynchronous personalized federated learning method of the present invention, 12 jetson Nano devices were locally deployed to simulate clients. Through experiments, it was found that the asynchronous personalized federated learning method of the present invention reduces energy consumption by 15% compared to the traditional asynchronous federated learning method, and at the same time has an accuracy of up to 90% on the CIFAR10 dataset.

[0050] The above are only the preferred embodiments of this application, and do not limit the patent scope of this application accordingly. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of this application, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of this application.

Claims

1. An asynchronous personalized federated learning method for ubiquitous embedded terminals, characterized in that, Including: Receiving model parameters uploaded by a client; Determining a plurality of initial clustering center models according to the upload order of the model parameters, and determining the client associated with each of the initial clustering center models; Determining the feedback value of each client for the initial clustering center model; Establishing a new clustering center model according to the feedback value corresponding to each initial clustering center model; Determining the deviation between each new clustering center model and the corresponding initial clustering center model; Sending the new clustering center model to the corresponding client according to the deviation; Receiving model parameters uploaded by a client, updating and aggregating the model parameters to the corresponding new clustering center model, and completing asynchronous personalized federated learning.

2. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 1, characterized in that, After determining the deviation between each new clustering center model and the corresponding initial clustering center model, the method further includes Determining the energy status of the client according to the charging status, local computing task resource usage, and communication traffic estimation of the client; Sending the new clustering center model to the corresponding client according to the energy status of the client.

3. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 2, characterized in that, The sending the new clustering center model to the corresponding client according to the deviation includes: When the deviation is greater than a first preset threshold, sending the model to the corresponding client.

4. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 3, characterized in that, The sending the new clustering center model to the corresponding client according to the energy status of the client includes: When the energy status of the client is less than a second preset threshold, sending the model to it.

5. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 4, wherein The method further includes: Determining the model remoteness of the client according to the deviation and the energy status; When the model remoteness of the client is greater than a third preset threshold, sending the model to it.

6. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 2, characterized in that The energy status of the client is determined according to the charging status, local computing task resource usage, communication traffic estimation of the client, and adjustment parameters.

7. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 1, characterized in that, The determining a plurality of initial clustering center models according to the upload order of the model parameters, and determining the client associated with each of the initial clustering center models includes: Determining a plurality of initial clustering centers according to the upload order of the model parameters, and constructing initial clustering center models; Respectively determining the distances between the model parameters of the remaining clients and each initial clustering center, and allocating the clients to the initial clustering center with the smallest distance, to obtain the clients associated with each initial clustering center model.

8. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 1, wherein The determining the feedback value of each client for the initial clustering center model includes: Obtaining the predicted label distribution and the actual label distribution corresponding to each client, and determining the variance of the predicted soft label distribution of the corresponding initial clustering center model, and determining the feedback value of the client for the initial clustering center model according to the predicted label distribution, the actual label distribution, and the variance of the predicted soft label distribution.

9. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 1, characterized in that, The establishing a new clustering center model according to the feedback value corresponding to each initial clustering center model includes: Respectively sorting the feedback values of all clients associated with each initial clustering center model in descending order, and allocating the clients ranked in the subsequent preset number to a new cluster; Use the model parameters of the initial clustering center model as the initial model parameters of the corresponding clients in the new clusters, and during the training process of the clients, locally fine-tune the initial model parameters and upload the fine-tuned model parameters to the server; The server aggregates the model parameters uploaded by the clients in each new cluster to obtain a new clustering center model.

10. The asynchronous personalized federated learning method for ubiquitous embedded terminals according to claim 1, characterized in that, After establishing the new clustering center model, the method further includes: Combining the new clustering center model and the initial clustering center model into a model set; When the number of models in the model set is greater than a fourth preset threshold, determine a main model and an auxiliary model in the model set; Use the auxiliary model to optimize the main model, and use the attention matrix at the weight granularity to fuse the optimized main model and the auxiliary model to obtain a fused clustering center model; Redetermine the main model and the auxiliary model in the model set until the number of models in the model set reaches a fifth preset threshold to obtain a final model set; The determination of the deviation between each new clustering center model and the corresponding initial clustering center model includes: Determine the deviation between the fused clustering center model and the corresponding initial clustering center model in the final model set.