Federated Multi-Center Deep Support Vector Data Description With Lyapunov Convergence Guarantees for Anomaly Detection in IIoT Networks

Abstract

Multi-site Industrial Internet of Things (IIoT) anomaly detection demands cross-site collaboration without sharing raw data. Federated learning enables such collaboration, yet existing methods overlook challenges unique to one-class detectors. We identify a structural conflict that, to our knowledge, has not been characterized in this depth by prior federated anomaly-detection work. When multi-center Deep Support Vector Data Description (Deep SVDD) detectors undergo standard federated aggregation, each site’s hypersphere decision boundary inflates systematically, and the severity escalates with data heterogeneity. The root cause is a structural conflict between SVDD’s geometric objective and federated parameter averaging. We propose Federated Multi-Center Deep SVDD (FMC-SVDD), which employs radius-aware selective aggregation to share encoder representations while preserving per-site hypersphere compactness. Using Lyapunov stability theory, we prove that per-site SVDD loss converges monotonically to a bounded region. To our knowledge, such guarantees have not yet been established for federated anomaly detection. To handle unknown inter-site distribution shift, we incorporate Wasserstein distributionally robust optimization into the aggregation weight design, ensuring that these guarantees remain valid under distributional uncertainty. Experiments on the SWaT and WADI benchmarks confirm that FMC-SVDD suppresses boundary inflation while unlocking federated gains, outperforming existing baselines in detection accuracy and boundary compactness.