David IShuman in " vertix-frequency analysis on graph" claims that,"we generalize one of the most important signal processing tools – windowed Fourier analysis – to the graph setting and When we apply this transform to a signal with frequency components that vary along a path graph, the resulting spectrogram matches our intuition from classical discrete-time signal processing. Yet, our construction is fully generalized and can be applied to analyze signals on any undirected, connected, weighted graph."

in this paper generalized translation operator that allows us to shift a window around the vertex domain so that it is localized around any given vertex, just as we shift a window along the real line to any center point in the classical windowed Fourier transform for signals on the real line.

generalized translation operator:

$$(T_{i}f)(n) := \sqrt{N}(f*\delta_{i})(n) = \sqrt{N}\sum_{\ell=0}^{N-1}\hat{f}(\lambda_{\ell}) \chi^{*}_{\ell}(i)\chi_{\ell}(n) .$$

See the picture enter image description here


  1. How do I understand the motion algorithm on the graph?
  2. How to label irregular graphs with high dimensional data?


  • $\begingroup$ I don't understand your question. What does "How do I understand the motion algorithm on the graph?" Do you have a specific question about it? (Asking us to please re-explain it to you probably isn't a good fit for this site; that's a lot to ask from a single answer here, and if you didn't understand the explanation in the paper, I won't you won't understand another explanation.) Also I don't understand what "How to label irregular graphs with high dimensional?" means. It seems like some words are missing. If you can edit your question to clarify what your question is, please do that. $\endgroup$ – D.W. Sep 18 '18 at 5:28