Approximating signals supported on graphs

Xiaofan Zhu, Michael G. Rabbat

Abstract: In this paper, we introduce the concept of smoothness for signals supported on the vertices of a graph. We provide theoretical explanations when and why the Laplacian eigenbasis can be regarded as a meaningful “Fourier” transform of such signals. Moreover, we analyze the desired properties of the underlying graphs for better compressibility of the signals. We verify our theoretical work by experiments on real world data.