Signal processing on graphs: Transforms and tomograms
arXiv:1406.2185 · doi:10.1016/j.physa.2016.01.002
Abstract
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presence of noise. Here the notion of tomogram transform is also extended to signals on arbitrary graphs
arXiv comment9 pages, 12 figures
References in corpus (9)
- Finding community structure in networks using the eigenvectors of matrices
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- Discrete Signal Processing on Graphs
- Spectral redemption: clustering sparse networks
- Graph spectra and the detectability of community structure in networks
- A Spectral Graph Uncertainty Principle
- Tomograms and other transforms. A unified view
- Tomographic analysis of reflectometry data II: the phase derivative
- Analysis and separation of time-frequency components in signals with chaotic behavior