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 language | English |
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Title of host publication | 32nd European Signal Processing Conference, EUSIPCO 2024 - Proceedings |
Publisher | European Signal Processing Conference, EUSIPCO |
Pages | 817-821 |
Number of pages | 5 |
ISBN (Electronic) | 9789464593617 |
DOIs | |
Publication status | Published - 2024 |
Event | 32nd European Signal Processing Conference, EUSIPCO 2024 - Lyon, France Duration: 26 Aug 2024 → 30 Aug 2024 https://eusipcolyon.sciencesconf.org/ |
Publication series
Name | European Signal Processing Conference |
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ISSN (Print) | 2219-5491 |
Conference
Conference | 32nd European Signal Processing Conference, EUSIPCO 2024 |
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Abbreviated title | EUSIPCO 2024 |
Country/Territory | France |
City | Lyon |
Period | 26/08/24 → 30/08/24 |
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-careOtherwise 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