隨著資料分析應用的普及，如何在保障隱私的前提下整合來自多個機構的資料，已成為一項重要課題。為此，聯邦學習（Federated Learning）應運而生，提供一種分散式協作架構，使資料在本地進行運算，僅傳送模型參數至中央伺服器以建構全域模型。另一方面，對比式主成分分析（ContrastivePrincipalComponent Analysis）為傳統主成分分析的延伸方法，透過比較目標資料與背景資料的變異方向，發掘目標資料中特有的低維結構。為因應資料分散於各機構以及隱私保護的雙重需求，本文提出差分隱私（Differential Privacy）結合聯邦對比式主成分分析的方法，在不共享原始資料的情況下，達成跨機構的協作式降維分析。方法上，採用子空間聚合策略，整合各機構所計算之局部對比式主成分分析結果，並透過高斯機制對本地對比共變異矩陣進行擾動，以滿足(ϵ,δ)-差分隱私保護需求。此外，針對對比參數α的選擇問題，設計一套基於 K-medoids 分群方法與輪廓係數的自動化α選取演算法。實驗結果顯示，本方法即便在隱私保護條件下，仍能於多種資料設定中達成清晰且具辨識性的視覺化效果，顯示其具良好之實用性。;With the widespread adoption of data analysis applications, integrating data from multiple institutions while preserving privacy has become a critical issue. To address this, federated learning (FL) has emerged as a distributed collaborative framework that allows data to be processed locally, with only model parameters transmitted to a central server to build a global model. Meanwhile, contrastive principal component analysis (cPCA) extends traditional PCA by comparing variations between a target dataset and a background dataset, enabling the discovery of low-dimensional structures unique to the target data. To meet the needs of distributed data and privacy protection, this study proposes a method that combines differential privacy (DP) with federated cPCA. Without sharing raw data, the proposed method enables collaborative dimensionality reduction across institutions. Specifically, we adopt a subspace aggregation strategy to integrate local cPCA results from each institution and apply the Gaussian mechanism to perturb the local contrastive covariance matrix, ensuring (ϵ,δ)-differential privacy. Furthermore, to address the selection of the contrastive parameter α, we design an automated α selection algorithm based on K-medoids clustering and Silhouette coefficient. Experimental results demonstrate that even under privacy constraints, the proposed method is capable of revealing well-separated structures, highlighting its practical effectiveness.
