Online Structural Change-Point Detection of High-dimensional Streaming Data via Dynamic Sparse Subspace Learning

Abstract

igh-dimensional streaming data are becoming increasingly ubiquitous in many fields. They often lie in multiple low-dimensional subspaces, and the manifold structures may change abruptly on the time scale due to pattern shift or occurrence of anomalies. However, the problem of detecting the structural changes in a real-time manner has not been well studied. To fill this gap, we propose a dynamic sparse subspace learning approach for online structural change-point detection of high-dimensional streaming data. A novel multiple structural change-point model is proposed and the asymptotic properties of the estimators are investigated. A tuning method based on Bayesian information criterion and change-point detection accuracy is proposed for penalty coefficients selection. An efficient Pruned Exact Linear Time based algorithm is proposed for online optimization and change-point detection. The effectiveness of the proposed method is demonstrated through several simulation studies and a real case study on gesture data for motion tracking. Supplementary materials for this article are available online.

Keyword:

• Dynamic learning
• High-dimensional time series
• Manifold learning
• Multiple change-point model
• Subspace clustering

Acknowledgments

The authors would like to thank the editor, associate editor, and anonymous reviewers for many constructive comments which greatly improved the article.

Additional information

Funding

This work is supported in part by the NSFC grant NSFC-72171003, NSFC-71932006 and NSFC-51875003.