Sequential Subspace Change-Point Detection

TL;DR

This paper introduces two new methods for online detection of subspace changes in multivariate streaming data, with theoretical analysis and applications to gesture and seismic data.

Contribution

It proposes the Largest-Eigenvalue Shewhart chart and Subspace-CUSUM procedures for detecting covariance structure changes, including theoretical performance approximations.

Findings

Methods effectively detect subspace changes in simulations.

Theoretical ARL and EDD approximations are accurate.

Applications demonstrate practical utility in gesture and seismic data.

Abstract

We consider the online monitoring of multivariate streaming data for changes that are characterized by an unknown subspace structure manifested in the covariance matrix. In particular, we consider the covariance structure changes from an identity matrix to an unknown spiked covariance model. We assume the post-change distribution is unknown, and propose two detection procedures: the Largest-Eigenvalue Shewhart chart and the Subspace-CUSUM detection procedure. We present theoretical approximations to the average run length (ARL) and the expected detection delay (EDD) for the Largest-Eigenvalue Shewhart chart and also provide analysis for tuning parameters of the Subspace-CUSUM procedure. The performance of the proposed methods is illustrated using simulation and real data for human gesture detection and seismic event detection.