# Federated Pseudo-Sample Clustering Algorithm:
## 2 Related Work  
[PERSON] et al. [10] introduced the Federal Average Algorithm (FedAvg) as a means to improve model performance on edge devices without compromising user privacy. In the FedAvg framework, the central server first selects a subset of clients to participate in training and distributes the global model to each selected client. Next, each client trains the model independently using its local data. Finally, the central server aggregates model updates from participating clients to form the global model. In order for federated learning to converge to an optimal solution, it has traditionally relied on the assumption that data are independently and identically distributed (IID) across clients. However, real-world data distributions often deviate from this ideal, leading to suboptimal performance of federated learning models, as demonstrated by experiments conducted by [PERSON] et al. [17], highlighting the challenge posed by non-IID data. As a result, numerous studies have focused on addressing the statistical challenges associated with federated learning. To mitigate the limitations of FedAvg, [PERSON] et al. [18] proposed the FedProx algorithm, which introduces a proximal term to account for system and statistical heterogeneity. Similarly, [PERSON] et al. [19] introduced the SCAFFOLD algorithm, which accounts for data heterogeneity through the use of control variables. Furthermore, [PERSON] et al. [20] presented the FedDC algorithm, which incorporates an auxiliary term to correct weight discrepancies between local and global models, effectively addressing statistical heterogeneity. In addition, [PERSON] et al. [21] proposed the FedMA algorithm,which uses Bayesian nonparametric methods to deal with data heterogeneity. While these approaches collectively mitigate the shortcomings of FedAvg in heterogeneous data settings using different techniques, they still adhere to the global aggregation approach of FedAvg. In practical scenarios, different client requirements and data distributions pose a challenge, making it difficult for a single global model to meet the diverse needs of all clients. In addition, different data distributions further hinder the convergence of a single global model to an optimal solution. Personalized federated learning techniques have emerged as a promising direction to address the diverse needs of customers and the challenges posed by non-IID data. [PERSON] et al. [22] thoroughly analyzed the motivations behind personalized federated learning and identified potential avenues for future research. [PERSON] et al. [23] proposed a local fine-tuning approach for personalized models. After training a global model, they used local data to fine-tune the global model, resulting in a personalized model tailored to the specific needs of each client. [PERSON] et al. [24] investigated the impact of hierarchy in the aggregation process. Their approach assessed the importance of each layer in the model for different clients, enabling personalized model aggregation for clients with statistically heterogeneous data. [PERSON] et al. [25] introduced a personalized cross-silo federated learning technique called FedAMP. This technique differs from traditional global model aggregation by maintaining a cloud model for each client on the central server. By using an attentive message-passing mechanism, the method encourages collaboration between similar clients, ultimately generating personalized models tailored to individual client needs. These personalized federated learning approaches offer valuable insights and techniques for improving model adaptation, accounting for data heterogeneity, and satisfying diverse client requirements. They represent significant contributions to the field and pave the way for further advances in personalized federated learning research. However, the aforementioned methods all require clients to upload their model parameters and ensure model consistency for centralized aggregation, potentially leading to client model leakage.