Natural Graph Wavelet Packet Dictionaries

We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather than simply using eigenvalue ordering. These dictionaries can be seen as generalizations classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely frequency interpretation eigenvalues. describe algorithms (involving either vector rotations or orthogonalizations) construct these dictionaries, use them efficiently approximate through best search, demonstrate strengths measured sunflower street networks.