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

arXiv: https://arxiv.org/abs/2503.11255 · HTML: https://mlsanity.com/paper/2503.11255/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 25 of 25)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Federated Learning for Internet of Things: A Comprehensive Survey](https://mlsanity.com/paper/2104.07914/) (2021)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [Federated Optimization:Distributed Optimization Beyond the Datacenter](https://mlsanity.com/paper/1511.03575/) (2015)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [An Evaluation of Anomaly Detection and Diagnosis in Multivariate Time Series](https://mlsanity.com/paper/2109.11428/) (2021)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Communication-Efficient Adaptive Federated Learning](https://mlsanity.com/paper/2205.02719/) (2022)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder](https://mlsanity.com/paper/2102.01331/) (2021)
- [Reservoir computing approaches for representation and classification of multivariate time series](https://mlsanity.com/paper/1803.07870/) (2018)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Reservoir Transformers](https://mlsanity.com/paper/2012.15045/) (2020)
- [Determination of the edge of criticality in echo state networks through Fisher information maximization](https://mlsanity.com/paper/1603.03685/) (2016)
- [Learning the Koopman Eigendecomposition: A Diffeomorphic Approach](https://mlsanity.com/paper/2110.07786/) (2021)
- [Knowledge-Enhanced Semi-Supervised Federated Learning for Aggregating Heterogeneous Lightweight Clients in IoT](https://mlsanity.com/paper/2303.02668/) (2023)

## Abstract (arXiv)

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.