Change point analysis of high-dimensional data using random projections

2026-02-23

AI Summary

This study addresses the challenge of change-point detection in high-dimensional time series, where traditional methods suffer from the curse of dimensionality. The authors propose a novel framework that systematically leverages random projections and multiple reuses: high-dimensional data are repeatedly projected onto one-dimensional subspaces, enabling the application of well-established univariate change-point detection techniques. The resulting detections are then aggregated through multiple testing correction and mode-based estimation to yield robust and consistent results. The method achieves a favorable balance between computational efficiency and statistical accuracy, demonstrating superior detection power and localization precision in extensive simulations. Its practical utility is further validated through a successful application to a real-world Australian temperature dataset.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

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.

Problem

• change point analysis
• high-dimensional data
• random projections
• time series

Innovation

• random projections
• change point detection
• high-dimensional time series
• multiple comparisons
• dimensionality reduction