Diffusion Maps — Spectral Embedding

Diffusion maps (Coifman & Lafon 2006) embed high-dimensional data using the geometry of a diffusion process. The kernel matrix K(x,y)=exp(−‖x−y‖²/σ²) defines a random walk; its eigenvectors give coordinates that respect the intrinsic manifold geometry. Unlike PCA, it captures nonlinear structure and is robust to noise.