## 3 Research Methodology  
### Personalized Client Models  
This study aims to achieve personalized federated learning and practical division methods based on the characteristics of client neural network models. In this study, all client neural network models are tasked with image recognition, and the data dimensions of the input space \(\mathrm{R}^{\mathrm{x}}\) and prediction output space \(\mathrm{R}^{\mathrm{y}}\) are equal. Therefore, each client's image recognition task can be divided into feature extraction and category prediction tasks. The objective of feature extraction is to map the input data residing in a high-dimensional feature space to a lower-dimensional feature space. In this process, it is necessary to maintain the separability of the input data while achieving dimensionality reduction. In this study, neural networks are used for feature extraction, and the corresponding function is defined as F: \(\mathrm{R}^{\mathrm{x}}\rightarrow\mathrm{R}^{\mathrm{l}}\), where \(\mathrm{R}^{\mathrm{x}}\) is the data input space, and \(\mathrm{R}^{\mathrm{l}}\) is the low-dimensional feature space. Similarly, neural networks will be used for category prediction in this study, and the corresponding function is defined as G: \(\mathrm{R}^{\mathrm{l}}\rightarrow\mathrm{R}^{\mathrm{y}}\), where \(\mathrm{R}^{\mathrm{y}}\) is the category prediction output space. The image recognition task of each client neural network model can be represented as Equation (1), where the input data \(\mathrm{x}_{\mathrm{i}}\in\mathrm{R}^{\mathrm{x}}\), and the model output \(\mathrm{y}_{\mathrm{i}}\)\(\in\mathrm{R}^{\mathrm{y}}\). \[yi=softmax\left(G\left(F\left(xi\right)\right)\right) \tag{1}\]  
In the IID dataset, the data distribution of each client is the same as the global data distribution; therefore, feature extraction F and category prediction G are not affected by client drift. However, individual client data distributions are not representative of the global data distribution, and the direct aggregation of client models can severely affect the learning performance of the neural network owing to client drift. With multitask learning technology, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Characteristic** & **Research Target and Advantages** \\ \hline FedAvg [13] & The first federated learning algorithm proposed by Google. & FedAvg is a collaborative training neural network with data privacy. \\ \hline Mime [15] & It combines control variates and server-level optimizer state. & Mime overcomes the natural client heterogeneity and is faster than any centralized method. \\ \hline FAVOR [16] & It proposes a new method based on Q-learning to select a subset of devices. & FAVOR focuses on validation accuracy and penalizes the use of more communication rounds. \\ \hline FedProx [18] & FedProx allows for the emergence of inadequately trained local models and adds a proximal term to the clients’ loss function. & FedProx reduces the impact of non-IID on federated learning and improves the accuracy relative to FedAvg. \\ \hline FedPer [21] & It separates the client model into two parts and trains each individually. & FedPer demonstrates the ineffectiveness of FedAvg and the effectiveness of modeling personalization tasks. \\ \hline FedTP [24] & It learns personalized self-attention for each client while aggregating the other parameters among the clients. & It combines FedTP with other methods, including FedPer, FedRod, and KNN-Per, to further enhance the model performance. It achieves better accuracy and learning performance. \\ \hline Proposed method & It proposes a personalized federated learning with adaptive feature extraction and category prediction. & The study shows faster convergence speed and lower data loss than the FedProx and the FedPer federated learning algorithms in Fashion-MNIST, CIFAR10, and CIFAR100 datasets. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Review of related work.