When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum
arXiv:1701.08401 · doi:10.1109/LSP.2017.2704359
Abstract
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smallest non-zero eigenvalue and plays a key role for graph clustering. Graph signal processing focusses on the analysis of signals that are attributed to the graph nodes. The eigendecomposition of the graph Laplacian allows to define the graph Fourier transform and extend conventional signal-processing operations to graphs. Here, we introduce the design of Slepian graph signals, by maximizing energy concentration in a predefined subgraph for a graph spectral bandlimit. We establish a novel link with classical Laplacian embedding and graph clustering, which provides a meaning to localized graph frequencies.
4 pages, 5 figures, submitted to IEEE Signal Processing Letters
References in corpus (6)
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- Discrete Signal Processing on Graphs
- Discrete Signal Processing on Graphs: Sampling Theory
- Signals on Graphs: Uncertainty Principle and Sampling
- Spatiospectral concentration on a sphere
- A Spectral Graph Uncertainty Principle