Nonlinear Component Analysis as a Kernel Eigenvalue Problem (Kernel PCA)

Formulated non-linear PCA using the kernel trick in Reproducing Kernel Hilbert Spaces (RKHS), extracting non-linear principal manifolds.

Serves as canonical technical reference for implementing task-dimensionality-reduction, task-feature-extraction in production systems.

Assumptions

• Underlying data distribution satisfies empirical consistency and regularity assumptions across training domains

Limitations

• Scaling characteristics and accuracy depend on hardware architecture, parameter scale, and dataset quality