kernel-methods

Shows how a kernel function k(x,x') replaces explicit inner products <phi(x),phi(x')> to operate in an implicit feature space. The animation alternates between (1) selecting two input points A,B and evaluating similarity via k(A,B) instead of computing phi, and (2) constructing a small Gram matrix and checking positive-semidefiniteness to illustrate Mercer’s condition for valid kernels.

canvasclick to interact

t=0s

practical uses

01.Kernel SVMs: learn nonlinear decision boundaries using k(x,x') instead of explicit features
02.Kernel ridge regression / Gaussian processes: compute predictions from Gram matrices built by k
03.Spectral methods / kernel PCA: perform dimensionality reduction in implicit feature space

technical notes

Pure Canvas2D, grid-snapped blocky drawing with green-on-black palette. Uses time-based phases (4.2s cycle) and an animated scan to depict Gram-matrix construction. Demonstrates PSD vs non-PSD by toggling between an RBF kernel (valid) and an intentionally indefinite similarity (RBF minus constant) and checks PSD via principal minors of a 3x3 Gram matrix.

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