# Shapes of Uncertainty in Spectral Graph Theory

arXiv: https://arxiv.org/abs/1909.10865 · HTML: https://mlsanity.com/paper/1909.10865/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2019.

## Built on by (most cited first, 1 of 1)

- [Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization](https://mlsanity.com/paper/2103.01575/) (2021)

## Abstract (arXiv)

We present a flexible framework for uncertainty principles in spectral graph theory. In this framework, general filter functions modeling the spatial and spectral localization of a graph signal can be incorporated. It merges several existing uncertainty relations on graphs, among others the Landau-Pollak principle describing the joint admissibility region of two projection operators, and uncertainty relations based on spectral and spatial spreads. Using theoretical and computational aspects of the numerical range of matrices, we are able to characterize and illustrate the shapes of the uncertainty curves and to study the space-frequency localization of signals inside the admissibility regions.