Hodge-Aware Matched Subspace Detectors

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

Abstract

This paper introduces a hypothesis testing problem to detect whether a noisy simplicial signal lives in some specific Hodge subspaces or not. This is of particular relevance for edge flows in a network since they exhibit, under normal circumstances, different properties in Hodge decomposition. For example, a traffic flow in a road network is often conservative and that can be localized in a particular Hodge subspace. We propose two Neyman-Pearson optimal detectors for this task: the Simplicial Hodge Detector (SHD) and the Constrained Simplicial Hodge Detector (CSHD). They compare the energy of the simplicial embeddings in different Hodge subspaces and distinguish between the two hypotheses. The SHD utilizes the maximum likelihood estimation, while CSHD incorporates signal prior information to estimate the simplicial embeddings. These detectors are validated through numerical simulations on both real-world and synthetic data, indicating great potential in practical applications.

Original languageEnglish
Title of host publication32nd European Signal Processing Conference, EUSIPCO 2024 - Proceedings
PublisherEuropean Signal Processing Conference, EUSIPCO
Pages817-821
Number of pages5
ISBN (Electronic)9789464593617
DOIs
Publication statusPublished - 2024
Event32nd European Signal Processing Conference, EUSIPCO 2024 - Lyon, France
Duration: 26 Aug 202430 Aug 2024
https://eusipcolyon.sciencesconf.org/

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491

Conference

Conference32nd European Signal Processing Conference, EUSIPCO 2024
Abbreviated titleEUSIPCO 2024
Country/TerritoryFrance
CityLyon
Period26/08/2430/08/24
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • detection theory
  • Signal processing over higher-order networks
  • topological signal processing

Fingerprint

Dive into the research topics of 'Hodge-Aware Matched Subspace Detectors'. Together they form a unique fingerprint.

Cite this