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This paper develops a method to detect model structural changes by applying aCorrected Kernel Principal Component Analysis (CKPCA) to construct theso-called central distribution deviation subspaces. This approach canefficiently identify the mean and distribution changes in these dimensionreduction subspaces. We derive that the locations and number changes in thedimension reduction data subspaces are identical to those in the original dataspaces. Meanwhile, we also explain the necessity of using CKPCA as theclassical KPCA fails to identify the central distribution deviation subspacesin these problems. Additionally, we extend this approach to clustering byembedding the original data with nonlinear lower dimensional spaces, providingenhanced capabilities for clustering analysis. The numerical studies onsynthetic and real data sets suggest that the dimension reduction versions ofexisting methods for change point detection and clustering significantlyimprove the performances of existing approaches in finite sample scenarios.

Corrected kernel principal component analysis for model structural change detection