Wavelets on Graphs via Spectral Graph Theory (arxiv.org) AI

The paper presents a way to build wavelet transforms for functions on the vertices of a finite weighted graph using the graph Laplacian’s spectral decomposition. It defines scaled wavelet operators via a kernel g(tL) and forms graph wavelets by localizing these operators, with an admissibility condition ensuring the transform is invertible. The authors also study localization behavior at fine scales and provide an efficient Chebyshev-polynomial method to compute the transform without diagonalizing the Laplacian.