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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.15419 |
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| _version_ | 1866917008199647232 |
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| author | Hou, Tao Parsa, Salman Wang, Bei |
| author_facet | Hou, Tao Parsa, Salman Wang, Bei |
| contents | The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we introduce a new type of barcode, called the harmonic chain barcode, which tracks the evolution of harmonic chains. In addition, we show that the harmonic chain barcode is stable. Given a filtration of a simplicial complex of size $m$, we present an algorithm to compute its harmonic chain barcode in $O(m^3)$ time. Consequently, the harmonic chain barcode can enrich the family of topological descriptors in applications where a persistence barcode is applicable, such as feature vectorization and machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tracking the Persistence of Harmonic Chains: Barcode and Stability Hou, Tao Parsa, Salman Wang, Bei Computational Geometry 68P01, 55N31 F.2.0 The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we introduce a new type of barcode, called the harmonic chain barcode, which tracks the evolution of harmonic chains. In addition, we show that the harmonic chain barcode is stable. Given a filtration of a simplicial complex of size $m$, we present an algorithm to compute its harmonic chain barcode in $O(m^3)$ time. Consequently, the harmonic chain barcode can enrich the family of topological descriptors in applications where a persistence barcode is applicable, such as feature vectorization and machine learning. |
| title | Tracking the Persistence of Harmonic Chains: Barcode and Stability |
| topic | Computational Geometry 68P01, 55N31 F.2.0 |
| url | https://arxiv.org/abs/2412.15419 |