Although federated learning has gained prominence as a privacy-preserving framework tailored for distributed Internet of Things (IoT) environments, current federated principal component analysis (PCA) methods lack integration of sparsity, a critical feature for robust anomaly detection. To address this limitation, we propose a novel federated structured sparse PCA (FedSSP) approach for anomaly detection in IoT networks. The proposed model uniquely integrates double sparsity regularization: (1) row-wise sparsity governed by $\ell_{2,p}$-norm with $p\in[0,1)$ to eliminate redundant feature dimensions, and (2) element-wise sparsity via $\ell_{q}$-norm with $q\in[0,1)$ to suppress noise-sensitive components. To efficiently solve this non-convex optimization problem in a distributed setting, we devise a proximal alternating minimization (PAM) algorithm with rigorous theoretical proofs establishing its convergence guarantees. Experiments on real datasets validate that incorporating structured sparsity enhances both model interpretability and detection accuracy.

翻译：尽管联邦学习已成为专为分布式物联网环境设计的隐私保护框架而备受关注，但当前的联邦主成分分析（PCA）方法缺乏对稀疏性的整合，而稀疏性是实现鲁棒异常检测的关键特性。为弥补这一不足，我们提出了一种新颖的联邦结构化稀疏PCA（FedSSP）方法，用于物联网网络中的异常检测。该模型独特地集成了双重稀疏正则化：（1）由 $\ell_{2,p}$-范数（其中 $p\in[0,1)$）控制的行稀疏性，以消除冗余特征维度；（2）通过 $\ell_{q}$-范数（其中 $q\in[0,1)$）实现的元素级稀疏性，以抑制噪声敏感成分。为了在分布式环境中高效求解这一非凸优化问题，我们设计了一种邻近交替最小化（PAM）算法，并提供了严格的理论证明以确立其收敛性保证。在真实数据集上的实验验证了融入结构化稀疏性能够同时提升模型的可解释性与检测精度。