Functional Change Point Detection via Adjacent Deviation Subspace

2025-06-18

AI Summary

Detecting change points in functional data is challenging due to information loss inherent in conventional functional principal component analysis (FPCA)-based dimensionality reduction, which compromises detection accuracy in infinite-dimensional settings. Method: This paper proposes the Adjacent Deviation Subspace (ADS) framework—a target-oriented dimensionality reduction operator that preserves change-point structural information entirely in finite-dimensional representations. It further introduces an ADS-based test statistic and the MPULSE criterion for high-precision change-point localization and visualization. Contribution/Results: ADS overcomes the information bottleneck of FPCA by unifying dimensionality reduction and change-point detection into a single analytical paradigm. Simulation studies and empirical applications demonstrate that the method significantly reduces computational complexity and false positive rates, while yielding more robust, interpretable, and accurate change-point identification—outperforming state-of-the-art approaches across all evaluated metrics.

Technology Category

Machine Learning: Dimensionality Reduction/Feature SelectionSearch and Optimization: Mixed Discrete/Continuous SearchData Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsUser Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertisingWeb Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper develops the concept of the Adjacent Deviation Subspace (ADS), a novel framework for reducing infinite-dimensional functional data into finite-dimensional vector or scalar representations while preserving critical information of functional change points. To identify this functional subspace, we propose an efficient dimension reduction operator that overcomes the critical limitation of information loss inherent in traditional functional principal component analysis (FPCA). Building upon this foundation, we first construct a test statistic based on the dimension-reducing target operator to test the existence of change points. Second, we present the MPULSE criterion to estimate change point locations in lower-dimensional representations. This approach not only reduces computational complexity and mitigates false positives but also provides intuitive graphical visualization of change point locations. Lastly, we establish a unified analytical framework that seamlessly integrates dimension reduction with precise change point detection. Extensive simulation studies and real-world data applications validate the robustness and efficacy of our method, consistently demonstrating superior performance over existing approaches.

Problem

• Detects functional change points via dimension reduction
• Overcomes information loss in traditional FPCA methods
• Integrates dimension reduction with precise change detection

Innovation

• Introduces Adjacent Deviation Subspace for dimension reduction
• Proposes MPULSE criterion for change point estimation
• Unifies dimension reduction and change point detection