Topological filtering of a signal over a network
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929474458615808 |
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| author | van Lier, Matias de Jong Zurita, Sebastián Elías Graiff Kaji, Shizuo |
| author_facet | van Lier, Matias de Jong Zurita, Sebastián Elías Graiff Kaji, Shizuo |
| contents | Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin by working with signals over general graphs and then extend our approach to what we term signals over graphs with faces. To construct the filter, we introduce a new structure called the Basin Hierarchy Tree, which encodes the persistent homology. We provide an efficient algorithm and demonstrate the effectiveness of our approach through examples with synthetic and real datasets. This work bridges topological data analysis and signal processing, presenting a new application of persistent homology as a topological data processing tool. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14109 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological filtering of a signal over a network van Lier, Matias de Jong Zurita, Sebastián Elías Graiff Kaji, Shizuo Signal Processing Algebraic Topology Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin by working with signals over general graphs and then extend our approach to what we term signals over graphs with faces. To construct the filter, we introduce a new structure called the Basin Hierarchy Tree, which encodes the persistent homology. We provide an efficient algorithm and demonstrate the effectiveness of our approach through examples with synthetic and real datasets. This work bridges topological data analysis and signal processing, presenting a new application of persistent homology as a topological data processing tool. |
| title | Topological filtering of a signal over a network |
| topic | Signal Processing Algebraic Topology |
| url | https://arxiv.org/abs/2408.14109 |