Before revision:  This extension, kernel demixed principal component analysis (kdPCA) , relies on kernel least-squares regression techniques, and it resembles kernel-based extensions to standard principal component analysis and canonical correlation analysis. kdPCA includes dPCA as a special case when the kernel is linear.
After revision:  This extension, kernel demixed principal component analysis (kdPCA) as a nonlinear extension of dPCA by applying kernel least-squares regression techniques, and it resembles kernel-based extensions to standard principal component analysis and canonical correlation analysis. kdPCA includes dPCA as a special case when the kernel is linear.