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.

翻译：我们引入了一套新型的多尺度基质变换图纸上的信号,这些变换通过将图 Laplacian 电子元体之间的“自然”距离纳入图解 Laplacian 电子元体,而不是简单地使用电子元值定序。 这些基词典可以被视为古典香农波子包字典对任意图的概括,而并不依赖对Laplacian 电子元值的频率解释。 我们描述了构建这些基词典的算法(涉及矢量旋转或正方位化),通过最佳的基础搜索将其用于高效近似图形信号,并展示了这些基词典在向日葵图表和街道网络上测量的图形信号的优点。