Before revision:  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.
After revision:  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 algorithm , and demonstrate the strengths of these basis dictionaries for graph signals on sunflower graphs and road traffic networks.