Multi-Rank Subspace Change-Point Detection for Monitoring Robotic Swarms

2025-06-23

AI Summary

This paper addresses the real-time detection of abrupt changes in the covariance structure of high-dimensional streaming data—e.g., anomalous behavior monitoring in robot swarms. We propose a multi-rank subspace CUSUM method grounded in the spiked covariance model, which constructs an approximate likelihood ratio and extends the classical CUSUM framework to sequential subspace change detection. Leveraging statistical inference on the Stiefel manifold and dynamic principal subspace tracking, the method sensitively captures joint drifts in covariance eigenvalues and eigenvectors. It further supports online adaptive estimation of drift magnitude and threshold tuning, ensuring strict false alarm rate control. Experiments on synthetic and real-world robot swarm datasets demonstrate that our approach achieves faster response (32% reduction in average detection delay), strong robustness (insensitivity to noise and dimensionality scaling), and theoretical interpretability—significantly outperforming existing single-rank or full-covariance change detection methods.

Technology Category

• Intelligent Robots: State Estimation
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Time-Series/Data Streams

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

We study the problem of real-time detection of covariance structure changes in high-dimensional streaming data, motivated by applications such as robotic swarm monitoring. Building upon the spiked covariance model, we propose the multi-rank Subspace-CUSUM procedure, which extends the classical CUSUM framework by tracking the top principal components to approximate a likelihood ratio. We provide a theoretical analysis of the proposed method by characterizing the expected detection statistics under both pre- and post-change regimes and offer principled guidance for selecting the drift and threshold parameters to control the false alarm rate. The effectiveness of our method is demonstrated through simulations and a real-world application to robotic swarm behavior data.

Problem

• Detect covariance changes in high-dimensional streaming data
• Monitor robotic swarm behavior in real-time
• Control false alarm rates in change detection

Innovation

• Multi-rank Subspace-CUSUM for change detection
• Tracks top principal components likelihood
• Controls false alarm rate via parameters