Graph Distribution-valued Signals: A Wasserstein Space Perspective
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912979585335296 |
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| author | Zhao, Yanan Ji, Feng Jian, Xingchao Tay, Wee Peng |
| author_facet | Zhao, Yanan Ji, Feng Jian, Xingchao Tay, Wee Peng |
| contents | We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of classical vector-based GSP, including the assumption of synchronous observations over vertices, the inability to capture uncertainty, and the requirement for strict correspondence in graph filtering. By representing signals as distributions, GDSs naturally encode uncertainty and stochasticity, while strictly generalizing traditional graph signals. We establish a systematic dictionary mapping core GSP concepts to their GDS counterparts, demonstrating that classical definitions are recovered as special cases. The effectiveness of the framework is validated through graph filter learning for prediction tasks, supported by experimental results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph Distribution-valued Signals: A Wasserstein Space Perspective Zhao, Yanan Ji, Feng Jian, Xingchao Tay, Wee Peng Machine Learning Signal Processing We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of classical vector-based GSP, including the assumption of synchronous observations over vertices, the inability to capture uncertainty, and the requirement for strict correspondence in graph filtering. By representing signals as distributions, GDSs naturally encode uncertainty and stochasticity, while strictly generalizing traditional graph signals. We establish a systematic dictionary mapping core GSP concepts to their GDS counterparts, demonstrating that classical definitions are recovered as special cases. The effectiveness of the framework is validated through graph filter learning for prediction tasks, supported by experimental results. |
| title | Graph Distribution-valued Signals: A Wasserstein Space Perspective |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2509.25802 |