Multi-Rank Subspace Change-Point Detection with Application in Monitoring Robotic Swarms

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 performance by characterizing
the expected detection delay (EDD) under a prescribed average run length (ARL), deriving closed-form
asymptotically optimal choices of the window size and drift. We further prove that MRS-C is first-order
asymptotically optimal relative to the oracle Exact CUSUM, with an explicit efficiency constant that
depends on heterogeneity in spike strengths. When the signal rank is unknown, we use a parallel
procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness. This talk is based on recent work Multi-rank subspace change-point detection for monitoring robotic swarms.
Jonghyeok Lee, Yao Xie, Youngser Park, Jason Hindes, Ira Schwartz, Carey Priebe. 2026.