Kernel PCA — when and how?

hard

Answer

$Apply the kernel trick to PCA: implicitly map data to a feature space Φ(x) via kernel K(x, y) = ⟨Φ(x), Φ(y)⟩, then do PCA there.$
$Captures non-linear structure without explicit feature construction.$
$Common kernels: RBF, polynomial, cosine.$
$O(n^{2})$
$Modern replacement: autoencoders / UMAP for larger data.$

Check yourself — multiple choice

Same as PCA
Kernel-trick PCA in RKHS via K(x,y); captures non-linear structure without explicit features; $O(n^{2})$ memory → replaced by autoencoders/UMAP at scale
Random
Not real

Kernel PCA: PCA in RKHS via kernel; $O(n^{2})$ memory limits scale.

#dimensionality-reduction#pca

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