Topological Signal Processing Over Weighted Simplicial Complexes

Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their (higher order) relationships. Our goal in this paper is to pre...

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Bibliographic Details
Published inICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 1 - 5
Main Authors Battiloro, Claudio, Sardellitti, Stefania, Barbarossa, Sergio, Lorenzo, Paolo Di
Format Conference Proceeding
LanguageEnglish
Published IEEE 04.06.2023
Subjects
algebraic topology
Estimation
Feature extraction
Filtering theory
flow estimation
Harmonic analysis
Laplace equations
Machine learning
metric learning
Signal processing
Topological signal processing
weighted simplicial complexes
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Summary:Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their (higher order) relationships. Our goal in this paper is to present topological signal processing tools for weighted simplicial complexes. Specifically, relying on the weighted Hodge Laplacian theory, we propose efficient strategies to jointly learn the weights of the complex and the filters for the solenoidal, irrotational and harmonic components of the signals defined over the complex. We numerically assess the effectiveness of the proposed procedures.
ISSN:2379-190X
DOI:10.1109/ICASSP49357.2023.10094927