Federated Koopman-Reservoir Learning for Large-Scale Multivariate Time-Series Anomaly Detection

TL;DR

This work addresses anomaly detection in large-scale multivariate time-series data collected by distributed edge devices, where privacy and communication constraints hinder centralized approaches. It introduces FedKO, an unsupervised federated framework that blends Reservoir Computing-based lifted linearization with Koopman operator theory to create a bi-level optimization (ReKo) that learns a global model across devices without sharing raw data. The inner problem learns device-level Koopman operators under a stability constraint, while the outer problem refines the lifted feature map and reconstruction, with momentum-based aggregation to cope with non-IID data. Empirical results on four real-world MVTS datasets show that FedKO outperforms state-of-the-art baselines while substantially reducing communication and memory overhead, demonstrating its suitability for scalable, privacy-preserving anomaly detection in large distributed systems.

Abstract

The proliferation of edge devices has dramatically increased the generation of multivariate time-series (MVTS) data, essential for applications from healthcare to smart cities. Such data streams, however, are vulnerable to anomalies that signal crucial problems like system failures or security incidents. Traditional MVTS anomaly detection methods, encompassing statistical and centralized machine learning approaches, struggle with the heterogeneity, variability, and privacy concerns of large-scale, distributed environments. In response, we introduce FedKO, a novel unsupervised Federated Learning framework that leverages the linear predictive capabilities of Koopman operator theory along with the dynamic adaptability of Reservoir Computing. This enables effective spatiotemporal processing and privacy preservation for MVTS data. FedKO is formulated as a bi-level optimization problem, utilizing a specific federated algorithm to explore a shared Reservoir-Koopman model across diverse datasets. Such a model is then deployable on edge devices for efficient detection of anomalies in local MVTS streams. Experimental results across various datasets showcase FedKO's superior performance against state-of-the-art methods in MVTS anomaly detection. Moreover, FedKO reduces up to 8x communication size and 2x memory usage, making it highly suitable for large-scale systems.

Figures (6)

• Figure 1: Transformation of nonlinear dynamics to a higher-dimensional linear space via Koopman eigenfunctions $\Phi(\cdot): \mathbb{R}^n \rightarrow \mathbb{R}^m$ ($m > n$), where each state $x^{(t)} \in \mathbb{R}^n$ is mapped to an observable $\phi^{(t)} \in \mathbb{R}^m$ that evolves linearly over time with Koopman operator $\mathcal{K}$.
• Figure 2: Illustration of FedKo where devices jointly learning a global ReKo model without data sharing.
• Figure 3: The architecture of lifted linearization component $\Phi$ for ReKo, consisting of an untrainable reservoir$(W_{in}, W_{res})$ for mapping inputs into a high-dimensional space and a trainable readout layer$W$ for pattern analysis from the reservoir states.
• Figure 4: Overview of the FedKO bi-level framework.
• Figure 6: Prediction using FedKO on the PSM dataset