Topological signal processing and learning: Recent advances and future challenges

Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges capturing their interactions, leading to the establishment of...

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Vydané v:Signal processing Ročník 233; s. 109930
Hlavní autori: Isufi, Elvin, Leus, Geert, Beferull-Lozano, Baltasar, Barbarossa, Sergio, Di Lorenzo, Paolo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.08.2025
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ISSN:0165-1684
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Abstract Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges capturing their interactions, leading to the establishment of the fields of graph signal processing (GSP) and graph machine learning (GML). Key graph-aware methods include Fourier transform, filtering, sampling, as well as topology identification and spatiotemporal processing. Although versatile, graphs can model only pairwise dependencies in the data. To this end, topological structures such as simplicial and cell complexes have emerged as algebraic representations for more intricate structure modeling in data-driven systems, fueling the rapid development of novel topological-based processing and learning methods. This paper first presents the core principles of topological signal processing through the Hodge theory, a framework instrumental in propelling the field forward thanks to principled connections with GSP-GML. It then outlines advances in topological signal representation, filtering, and sampling, as well as inferring topological structures from data, processing spatiotemporal topological signals, and connections with topological machine learning. The impact of topological signal processing and learning is finally highlighted in applications dealing with flow data over networks, geometric processing, statistical ranking, biology, and semantic communication.
AbstractList Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges capturing their interactions, leading to the establishment of the fields of graph signal processing (GSP) and graph machine learning (GML). Key graph-aware methods include Fourier transform, filtering, sampling, as well as topology identification and spatiotemporal processing. Although versatile, graphs can model only pairwise dependencies in the data. To this end, topological structures such as simplicial and cell complexes have emerged as algebraic representations for more intricate structure modeling in data-driven systems, fueling the rapid development of novel topological-based processing and learning methods. This paper first presents the core principles of topological signal processing through the Hodge theory, a framework instrumental in propelling the field forward thanks to principled connections with GSP-GML. It then outlines advances in topological signal representation, filtering, and sampling, as well as inferring topological structures from data, processing spatiotemporal topological signals, and connections with topological machine learning. The impact of topological signal processing and learning is finally highlighted in applications dealing with flow data over networks, geometric processing, statistical ranking, biology, and semantic communication.
ArticleNumber 109930
Author Isufi, Elvin
Barbarossa, Sergio
Di Lorenzo, Paolo
Leus, Geert
Beferull-Lozano, Baltasar
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  givenname: Elvin
  surname: Isufi
  fullname: Isufi, Elvin
  organization: Faculty of Electrical Engineering Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands
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  givenname: Geert
  surname: Leus
  fullname: Leus, Geert
  organization: Faculty of Electrical Engineering Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands
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  surname: Beferull-Lozano
  fullname: Beferull-Lozano, Baltasar
  organization: SIGIPRO, Department, Simula Metropolitan Center for Digital Engineering, Oslo, Norway
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  givenname: Sergio
  surname: Barbarossa
  fullname: Barbarossa, Sergio
  organization: Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Rome, Italy
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  givenname: Paolo
  orcidid: 0000-0002-4130-3177
  surname: Di Lorenzo
  fullname: Di Lorenzo, Paolo
  email: paolo.dilorenzo@uniroma1.it
  organization: Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Rome, Italy
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Keywords Graph machine learning
Topological signal processing
Hodge theory
Topological data analysis
Graph signal processing
Network science
Topological deep learning
Language English
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Snippet Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs...
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SubjectTerms Graph machine learning
Graph signal processing
Hodge theory
Network science
Topological data analysis
Topological deep learning
Topological signal processing
Title Topological signal processing and learning: Recent advances and future challenges
URI https://dx.doi.org/10.1016/j.sigpro.2025.109930
Volume 233
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