Diffusion wavelets - Wikipedia

Abstraction: Adaptive multiscale wavelet basis built from diffusion operator on graphs

Key points:

• Diffusion wavelets extend classical wavelet theory to discrete structures (graphs, manifolds, point clouds) using a diffusion operator T (e.g., heat kernel or random walk) rather than fixed dilation functions.
• Introduced in 2004 by Ronald Coifman and Mauro Maggioni at Yale; basis functions are constructed via dyadic powers T^{2^j} of the operator.
• Algorithm alternates sparse QR decompositions at each dyadic scale to extract orthogonal scaling and wavelet subspaces from T's decaying spectrum.
• Allow direct computation of the Green's function and inverse graph Laplacian.
• Applied to: reinforcement learning value function approximation, Markov decision processes, transfer learning, dimensionality reduction, 3D mesh compression, and document topic modeling.

Connections: Ronald Coifman · Diffusion Wavelets · Graph Laplacian · Multiscale Analysis · Dimensionality Reduction

Source: http://en.wikipedia.org/wiki/Diffusion_wavelets