Sequential subspace change point detection

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 assu...

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Bibliographic Details
Published inSequential analysis Vol. 39; no. 3; pp. 307 - 335
Main Authors Xie, Liyan, Xie, Yao, Moustakides, George V.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.07.2020
Taylor & Francis Ltd
Subjects
Change point detection
Control charts
Covariance matrix
Eigenvalues
false alarm control
low rank
Multivariate analysis
online algorithm
Primary 62L10
Secondary 62G10
Seismic activity
spiked covariance model
Subspaces
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Summary: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 postchange distribution is unknown and propose two detection procedures: the largest-eigenvalue Shewhart chart and the subspace-cumulative sum (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 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.
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content type line 14
ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2020.1823191