Kernel PCA
PCA with nonlinear kernel transformations for complex manifold structure
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 PCArbf— radial basis function for smooth nonlinear structurepoly— polynomial kernel for interaction featuressigmoid— 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.