本研究提出一套具備魯棒性的聚類整合框架，以有效應對聯邦學習環境中潛 在的拜占庭攻擊（Byzantine attacks）。本方法將 γ-自我更新程序（γ-Self Update Process, γ-SUP）擴展應用至聯邦式架構，並進一步發展出聯邦 γ-SUP 主成分 分析（Federated γ-SUP PCA）技術。於此架構中，各個客戶端首先透過 γ-SUP PCA 進行本地運算，以萃取潛在資料結構並估計聚類參數，隨後將本地的群中 心及對應的共變異數矩陣傳送至中央伺服器。中央伺服器根據彙集而來的資訊 執行全域聚類與估計精煉，並將更新結果回傳至各客戶端，以進行回歸式的本 地參數校準。該聯邦 γ-SUP PCA 架構不僅強化對惡意客戶端的抵抗能力，亦大 幅提升平均值與共變異數之估計準確性。模擬實驗結果顯示，本方法在面對資 料異質性與對抗性干擾情境時，仍展現高度之穩健性與效能，為聯邦式非監督 學習提供一套具備擴展性與實用性的解決方案。;In this article, we propose a new robust clustering integration framework to address potential Byzantine attacks in federated learning environments. We extend the γ-Self Update Process (γ-SUP) to the federated setting and develop a federated γ-SUP PCA method. In the proposed framework, each client performs local computations using γ- SUP PCA to capture latent structures and estimate clustering parameters. The clients then transmit their local cluster centers and corresponding covariance matrices to a cen- tral server. The server performs global clustering and refines the estimates based on the received centers, then returns the results to each client for local parameter calibration via regression. The federated γ-SUP PCA architecture not only enhances robustness against malicious clients but also significantly improves the accuracy of mean and co- variance estimation. Simulation results demonstrate that the proposed method remains effective and robust even in scenarios with data heterogeneity and adversarial distur- bances, offering a scalable and practical solution for unsupervised learning in federated systems.
