Neighborhood-Preserving Translations on Graphs
Discrete Mathematics
2016-06-09 v1 Combinatorics
Abstract
In many domains (e.g. Internet of Things, neuroimaging) signals are naturally supported on graphs. These graphs usually convey information on similarity between the values taken by the signal at the corresponding vertices. An interest of using graphs is that it allows to define ad hoc operators to perform signal processing. Among them, ones of paramount importance in many tasks are translations. In this paper we are interested in defining translations on graphs using a few simple properties. Namely we propose to define translations as functions from vertices to adjacent ones, that preserve neighborhood properties of the graph. We show that our definitions, contrary to other works on the subject, match usual translations on grid graphs.
Keywords
Cite
@article{arxiv.1606.02479,
title = {Neighborhood-Preserving Translations on Graphs},
author = {Nicolas Grelier and Bastien Pasdeloup and Jean-Charles Vialatte and Vincent Gripon},
journal= {arXiv preprint arXiv:1606.02479},
year = {2016}
}