Kernel PCA

Kernel PCA applies PCA in a high-dimensional kernel-induced feature space, allowing it to capture nonlinear structure that standard PCA misses. The kernel implicitly defines feature similarities without explicitly constructing the transformed features.

When to use:

• Nonlinear manifolds where linear PCA is insufficient
• When the structure of the data can be captured by a kernel function (RBF, polynomial)
• Preprocessing before a kernel-based classifier

Input: Tabular data with the feature columns defined during training Output: Projected coordinates in the kernel PCA space

Model Settings (set during training, used at inference)

N Components (default: 2) Number of components in the kernel PCA space.

Kernel (default: linear) Kernel function defining the similarity space:

• linear - equivalent to standard PCA
• rbf - radial basis function for smooth nonlinear structure
• poly - polynomial kernel for interaction features
• sigmoid - sigmoid kernel (rarely used)
• cosine - angle-based similarity

Gamma (default: auto) Kernel coefficient for rbf, poly, and sigmoid.

Degree (default: 3) Polynomial degree for the poly kernel.

Inference Settings

No dedicated inference-time settings. The trained kernel matrix and eigenvectors project new data into the kernel PCA space.