Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Change point analysis of high-dimensional data using random projections

Yi Xu, Yeonwoo Rho

Abstract

This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for univariate time series. We propose applying random projections multiple times and then combining 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.

Change point analysis of high-dimensional data using random projections

Abstract

This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for univariate time series. We propose applying random projections multiple times and then combining 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.
Paper Structure (15 sections, 12 equations, 35 figures, 2 tables, 1 algorithm)

This paper contains 15 sections, 12 equations, 35 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Random projection change point detection method
  3. Step 1: RP Step
  4. Step 2: CUSUM and Combination Step
  5. Simulation
  6. Parameter Choices for the RP method
  7. Comparison of change point methods
  8. Location estimates of the RP method in practice
  9. Application
  10. Conclusion
  11. Additional results for Subsection \ref{['subsection: tuning']}
  12. Result of using the HAC variance estimator
  13. Result of using the variance estimator in horvath2020new
  14. Comparison of different methods using weighted CUSUM
  15. Repeating the procedure in Subsection \ref{['subsec:repeat RP method on one data']} using additional datasets

Figures (35)

  • Figure 8: Estimated change point locations detected by repeating the RP-Bonf method on the temperature dataset 1000 times. The mode of the estimated locations across the 1000 repetitions is marked by a red dot and labeled in the parenthesis under the station.
  • Figure : (a) Setting 1
  • Figure : (a) Setting 1
  • Figure : (a) $SNR=0$
  • Figure : (a) Setting 1
  • ...and 30 more figures