Corrected kernel principal component analysis for model structural change detection

TL;DR

This paper introduces a corrected kernel PCA method to effectively detect structural changes in models and improve clustering, outperforming classical KPCA in identifying distribution deviations.

Contribution

The paper develops a CKPCA-based approach for change detection and clustering, addressing limitations of classical KPCA in identifying central distribution deviations.

Findings

CKPCA accurately detects mean and distribution changes.

Enhanced clustering performance with nonlinear lower-dimensional embedding.

Significant improvement over existing methods in finite sample scenarios.

Abstract

This paper develops a method to detect model structural changes by applying a Corrected Kernel Principal Component Analysis (CKPCA) to construct the so-called central distribution deviation subspaces. This approach can efficiently identify the mean and distribution changes in these dimension reduction subspaces. We derive that the locations and number changes in the dimension reduction data subspaces are identical to those in the original data spaces. Meanwhile, we also explain the necessity of using CKPCA as the classical KPCA fails to identify the central distribution deviation subspaces in these problems. Additionally, we extend this approach to clustering by embedding the original data with nonlinear lower dimensional spaces, providing enhanced capabilities for clustering analysis. The numerical studies on synthetic and real data sets suggest that the dimension reduction versions of existing methods for change point detection and clustering significantly improve the performances of existing approaches in finite sample scenarios.