# Improving Multivariate Time-Series Anomaly Detection in Industrial Sensor Networks Using Entropy-Based Feature Aggregation

## TL;DR

This paper introduces a new method for detecting anomalies in industrial sensor networks using entropy-based feature aggregation with graph neural networks.

## Contribution

The novelty lies in using a structure-entropy-based attention mechanism to model implicit relationships in multivariate time-series data.

## Key findings

- The method improves anomaly detection performance on industrial datasets like SMAT, MSL, SWaT, and WADI.
- Key adjacent elements are identified by analyzing system entropy, enhancing detection accuracy.
- The approach outperforms baseline methods by modeling multi-element relationships effectively.

## Abstract

Anomaly detection using multivariate time-series data remains a significant challenge for complex industrial systems, such as Cyber–Physical Systems (CPSs), Industrial Control Systems (ICSs), Intrusion Detection Systems (IDSs), the Internet of Things (IoT), and Remote Sensing Monitoring Platforms, including satellite Earth observation systems and Mars Rovers. In these systems, sensors are highly interconnected, and local anomalies frequently affect multiple components. Because these interconnections are often implicit and involve complex interactions, systematic characterization is required. To address this, our study employs graph neural networks with a structure-entropy-based attention mechanism, which models multi-element relationships and formally represents implicit relationships within complex industrial systems using a network-based structural model. Specifically, our method distinguishes the weights of different high-order neighbor nodes based on their locations, rather than treating all nodes equally. Through this formalization, we identify and represent key adjacent elements by analyzing system entropy. We validate our method on SMAT, MSL, SWaT, and WADI datasets, and experimental results demonstrate improved detection performance compared to baseline approaches.