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arXiv · 2506.18562

Multi-rank Subspace Change-point Detection with Application in Monitoring Robotic Swarms

Jonghyeok Lee·Yao Xie·Youngser Park·Jason Hindes·Ira Schwartz·Carey Priebe
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Abstract

We study real-time detection of low-rank changes in the covariance structure of high-dimensional streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we propose the Multi-rank Subspace-CUSUM (MRS-C) procedure, which extends classical CUSUM by tracking projection energy onto an estimated signal subspace. We analyze the immediate-change expected detection delay (EDD), deriving closed-form choices of the window size and drift parameter that minimize the leading-order asymptotic EDD approximation. We further establish an oracle-relative asymptotic efficiency result, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we propose a practical parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness.

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Jonghyeok Lee, Yao Xie, Youngser Park, Jason Hindes, Ira Schwartz, Carey Priebe. 2025-06-23. Multi-rank Subspace Change-point Detection with Application in Monitoring Robotic Swarms. https://arxiv.org/abs/2506.18562

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