Diffusion Map — Manifold Learning via Heat Kernel

Diffusion maps embed high-dimensional data by computing eigenvectors of a normalized random walk; geodesic distances are preserved.

Coifman-Lafon (2006): the diffusion distance at time t, D_t(x,y)^2 = sum_l lambda_l^{2t} (phi_l(x)-phi_l(y))^2, approximates geodesic distance on the data manifold. Embedding: (lambda_1^t phi_1, lambda_2^t phi_2, ...).