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.

翻译：本文提出了一种通过应用修正核主成分分析（CKPCA）构建所谓中心分布偏差子空间来检测模型结构变化的方法。该方法能够有效识别这些降维子空间中的均值变化和分布变化。我们推导出降维数据子空间中的位置与数量变化与原数据空间中的变化是一致的。同时，我们还解释了使用CKPCA的必要性，因为经典KPCA无法解决这些问题中中心分布偏差子空间的识别问题。此外，我们通过将原始数据嵌入非线性低维空间，将该方法扩展到聚类分析中，从而增强了聚类分析的能力。基于合成数据集和真实数据集的数值研究表明，现有变点检测与聚类方法的降维版本在有限样本场景下显著提升了现有方法的性能。