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 the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary and of classical time-frequency adapted wavelet packets to arbitrary graphs, and does not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to efficiently approximate and compress signals through the best-basis algorithm , and demonstrate the strengths of these basis dictionaries for graph signals  on sunflower graphs and road traffic networks.
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 the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to construct these basis dictionaries, use them to efficiently approximate graph signals through the best basis search , and demonstrate the strengths of these basis dictionaries for graph signals measured on sunflower graphs and street networks.
D
and of classical time-frequency adapted wavelet packets
R
does
do
R
efficiently approximate and compress
construct these basis dictionaries, use them to efficiently approximate graph
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best-basis algorithm
best basis search
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measured
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road traffic
street