## 1 Introduction  
Artificial intelligence (AI) has rapidly developed with the continuous advancement of technology. Deep learning is one of the most popular AI technologies. The main feature of deep-learning technology is that it can automatically extract features from input data and train efficient neural network models using large amounts of data [1, 2, 3]. However, deep-learning technology requires a large amount of data for training, and these data usually come from different clients. The challenge of effectively training deep-learning models while preserving client data privacy has emerged as a critical issue. Therefore, customer data privacy has become a major concern in deep-learning technology [4, 5]. Federated learning technology has emerged as a solution for avoiding the problem of exposing client data during model training. It is a distributed machine-learning method that can aggregate data for model training while maintaining client privacy [6, 7]. The main concept of federated learning technology is to divide the model training process into multiple stages, each of which involves different clients and transmits only the model parameters. This approach safeguards the confidentiality of client data when using large datasets for model training, resulting in enhanced model accuracy and generalization. Federated learning technology has found extensive applications in various domains, including healthcare, finance, and intelligent transportation [8; 9; 10]. Despite significant progress in federated learning, some technical challenges remain unaddressed. One of the main issues is non-independent and identically distributed (non-IID) data heterogeneity. In real-world applications, data distribution among clients often varies. In federated learning, every device or server has its own data distribution, which can be significantly different from that of other devices. This can lead to poor performance if the model is trained using non-IID data [11; 12]. This study presents a novel approach to federated learning that allows each client to have their own personalized model and preserves local training results during the federated learning process. This approach effectively mitigates the impact of non-IID data on federated learning. To achieve this, the neural network model is divided into two parts: a feature extraction layer and a category prediction layer. During the federated learning process, each client has their own personalized model, which follows the above two-part structure. When the server returns the new global model to the clients, the category prediction layer of each client is unaffected and retains its local training results. The feature extraction layer does not change completely according to the global model. Instead, it is compared with the global model and local training results and then mixed based on the comparison results. Using this approach, this study aims to effectively mitigate the impact of non-IID data on federated learning and improve its performance. The contributions of this study can be summarized as follows:  
1. This study aims to develop a personalized federated learning process to mitigate the impact of data heterogeneity on federated learning. Unlike the conventional federated learning method, which trains a global model for all clients, this study proposes a personalized approach that adjusts the global model based on the data distribution of each client. 2. A neural network model is used to establish personalized models for each client. This study proposes a theoretical basis for client model partitioning based on the properties of neural network models and presents a practical partitioning method that divides client models into feature extraction and category prediction layers. During federated learning training, the feature extraction layers are adjusted in a personalized manner, whereas the category prediction layers serve as elements that give the client models personalized characteristics. 3. This method includes personalized feature extraction for client data.