<p>Federated learning (FL) is a distributed machine learning paradigm that allows multiple participants to collaboratively train a global model without sharing local data. However, the data of each participant are usually characterized by being non-independent and identically distributed (non-iid), especially in real-world scenarios where label distribution skew is prevalent. This problem can cause the optimization direction of the local model to be inconsistent with the global objective, thus significantly affecting the performance and stability of the global model. Furthermore, this problem can reduce the model’s generalization ability for certain classes and slow down the convergence rate during training. To solve these challenges, this paper proposes a novel FL algorithm via Clustering-Efficient and Knowledge Distillation (FedCK). First, we propose an improved Fuzzy C-Means (FCM) clustering algorithm. An intelligent centroid initialization strategy, inspired by K-Means++, is employed to initialize the cluster centroids. This prevents centroid overlap and mitigates the imbalance in the number of clients across clusters. Additionally, cosine distance is used to capture the similarity in label distributions among clients, thereby enhancing the clustering performance and improving the overall efficiency of the clustered model. Second, to strengthen the feature extraction capability of client-side encoders and accelerate the convergence of the global model, we introduce a knowledge distillation optimization strategy based on a conditional generator. To address the dependency on proxy data during the distillation process, a conditional generator is deployed on the server side, which generates synthetic data that aligns with the label distribution of participating clients. Last, extensive experiments on multiple image classification tasks under various label distribution skew scenarios demonstrate that FedCK achieves significant improvements in both model accuracy and convergence speed.</p>