The University of Southampton
University of Southampton Institutional Repository

Euclidean distance matrix optimization for sensor network localization

Euclidean distance matrix optimization for sensor network localization
Euclidean distance matrix optimization for sensor network localization
Sensor Network Localization (SNL) is a general framework that generates a set of embedding points in a low-dimensional space so as to preserve given distance information as much as possible. Typical applications include source localization in two or three dimensional space,molecular conformation in three dimensions, graph embedding and data visualization. There are three main difficulties in solving SNL:(i) low-dimensional embedding that gives rise to non-convexity of the problem,coupled with infinitely many local minima;(ii) a large number of lower and upper bounds for certain distances used to improve the embedding quality; and (iii) non-differentiability of some loss functions used to model SNL. There exist a few promising approaches including co-ordinates minimization and semi-definite programming. This survey mainly focus on a recently established approach: Euclidean Distance Matrix (EDM) Optimization. We will give a short but essential introduction how this approach is theoretically well-developed and demonstrate how EDM optimization nicely handles those difficulties through a few widely used loss functions. We also show how regularization terms can be naturally incorporated into EDM optimization. Numerical examples are used to demonstrate the potential of EDM optimization in tackling large scale problems and effect of regularizations.
CRC
Fliege, Joerg
54978787-a271-4f70-8494-3c701c893d98
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Fliege, Joerg
54978787-a271-4f70-8494-3c701c893d98
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee

Fliege, Joerg, Qi, Hou-Duo and Xiu, Naihua (2019) Euclidean distance matrix optimization for sensor network localization. In, Cooperative Localization and Navigation: Theory, Research and Practice. CRC.

Record type: Book Section

Abstract

Sensor Network Localization (SNL) is a general framework that generates a set of embedding points in a low-dimensional space so as to preserve given distance information as much as possible. Typical applications include source localization in two or three dimensional space,molecular conformation in three dimensions, graph embedding and data visualization. There are three main difficulties in solving SNL:(i) low-dimensional embedding that gives rise to non-convexity of the problem,coupled with infinitely many local minima;(ii) a large number of lower and upper bounds for certain distances used to improve the embedding quality; and (iii) non-differentiability of some loss functions used to model SNL. There exist a few promising approaches including co-ordinates minimization and semi-definite programming. This survey mainly focus on a recently established approach: Euclidean Distance Matrix (EDM) Optimization. We will give a short but essential introduction how this approach is theoretically well-developed and demonstrate how EDM optimization nicely handles those difficulties through a few widely used loss functions. We also show how regularization terms can be naturally incorporated into EDM optimization. Numerical examples are used to demonstrate the potential of EDM optimization in tackling large scale problems and effect of regularizations.

Text
EDMSNL - Author's Original
Restricted to Repository staff only
Request a copy

More information

Published date: 2019

Identifiers

Local EPrints ID: 426671
URI: https://eprints.soton.ac.uk/id/eprint/426671
PURE UUID: 670ea04f-5fb7-4916-8ab1-a8fdbe7d5dd3
ORCID for Joerg Fliege: ORCID iD orcid.org/0000-0002-4459-5419
ORCID for Hou-Duo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 10 Dec 2018 17:30
Last modified: 14 Mar 2019 01:43

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×