Federated Low-Rank Koopman Learning for Multivariate Time-Series Anomaly Detection in IoT Systems

2026-07-09

AI Summary

This work addresses the challenge of multivariate time series anomaly detection in distributed Internet-of-Things (IoT) environments, where data are non-independent and identically distributed (non-IID), bandwidth is constrained, and edge devices possess limited computational resources. To this end, we propose FedKAD, a novel framework that uniquely integrates low-rank Koopman operators with federated learning. FedKAD employs lightweight sliding windows to capture local temporal dynamics and transmits only compact subspace variables to the central server. A federated Stiefel-ADMM algorithm is devised to enable efficient consensus optimization under orthogonality constraints. Anomalies are detected locally via prediction residuals without sharing raw data. Experiments on four benchmark datasets demonstrate that FedKAD matches or surpasses state-of-the-art federated deep learning baselines while achieving up to 2100× faster training, 80× lower communication overhead, and 79× reduced inference latency.

Abstract

Distributed IoT systems generate multivariate time-series streams for monitoring physical assets, servers, and embedded sensing platforms. Detecting abnormal temporal behavior is critical for fault diagnosis, predictive maintenance, and security. However, practical IoT anomaly detection is hindered by decentralized and non-IID data, limited bandwidth, and the constrained computation and memory of edge devices. This paper proposes FedKAD, a resource-efficient federated Koopman anomaly detection framework for distributed IoT multivariate time series. Unlike deep-learning-based anomaly detectors that require training and communicating large neural models, FedKAD learns normal temporal dynamics through lightweight sliding-window Koopman representations. Federated training is formulated as a low-rank consensus problem, where raw sensor streams and local reduced dynamics remain on device while only compact subspace variables are exchanged with the server. To optimize the shared representation under orthonormality constraints, we develop a federated Stiefel-ADMM algorithm and provide convergence and stationarity analysis under partial client participation. During inference, each client detects anomalies locally by measuring the prediction residual between observed future trajectories and the learned Koopman dynamics. Experiments on four widely used multivariate time-series anomaly detection benchmarks show that FedKAD maintains or improves detection performance compared with federated deep-learning baselines. More importantly for IoT deployment, FedKAD provides up to $2.1\times10^3$ faster training, $80\times$ lower communication, and $79\times$ lower inference latency than neural baselines, confirming its suitability for resource-constrained edge devices.

Problem

• federated learning
• anomaly detection
• multivariate time-series
• IoT systems
• resource-constrained devices

Innovation

• Federated Learning
• Koopman Operator
• Low-Rank Representation
• Multivariate Time-Series Anomaly Detection
• Edge Computing