CHANGE POINT ANALYSIS IN HIGH-DIMENSIONAL DATA USING RANDOM PROJECTIONS

Author

• Yi Xu, Michigan Technological UniversityFollow

Date of Award

2026

Document Type

Campus Access Dissertation

Degree Name

Doctor of Philosophy in Statistics (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Yeonwoo Rho

Committee Member 1

Qiuying Sha

Committee Member 2

Kui Zhang

Committee Member 3

Sangyoon Han

Abstract

In this thesis, we develop change point detection methods for high-dimensional data, with a focus on changes in the mean. Existing methods for high-dimensional or functional data change point analysis mainly rely on dimension reduction to obtain a low-dimensional representation, direct use of smoothed functional data, or aggregation of coordinate-wise statistics. These approaches may suffer from loss of information, slow computation, or limited applicability to certain data types and forms of mean change. To address these limitations, we propose to use multiple random projections in change point analysis.

The first part of the thesis develops a novel change point identification method for high-dimensional data using random projections, targeting a single change point setting. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for univariate time series. The proposed method applies random projections multiple times and then combines the univariate test results using existing multiple comparison methods. Simulation results suggest that the proposed method tends to have better size and power, with more accurate location estimation. At the same time, random projections may introduce variability in the estimated locations. To enhance stability in practice, we recommend repeating the procedure, and using the mode of the estimated locations as a guide for the final change point estimate. An application to an Australian temperature dataset is presented. This study, though limited to the single change point setting, demonstrates the usefulness of random projections in change point analysis.

The second part of the thesis extends the use of random projections beyond the single change point setting. We develop random projection-based methods for multiple mean change point detection in high-dimensional data. By projecting high-dimensional data into multiple random projections, we aggregate information across projections to identify multiple change points. In particular, we propose binary segmentation-based procedures to detect multiple changes through repeated random projections. Simulation results indicate that the proposed methods perform better in recovering the underlying mean jump pattern. While a single run may be unstable, repeated runs can improve stability and can also capture a gradual change, providing graphical evidence. An application to cell adhesion data is presented. This study demonstrates that random projections offer a flexible and effective framework for multiple change point analysis in high-dimensional data.

Recommended Citation

Xu, Yi, "CHANGE POINT ANALYSIS IN HIGH-DIMENSIONAL DATA USING RANDOM PROJECTIONS", Campus Access Dissertation, Michigan Technological University, 2026.

https://doi.org/10.37099/mtu.dc.etdr/2096