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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/2408.11180 |
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| _version_ | 1866917754598064128 |
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| author | Alvarado, Enrique G Belton, Robin Lee, Kang-Ju Palande, Sourabh Percival, Sarah Purvine, Emilie Tymochko, Sarah |
| author_facet | Alvarado, Enrique G Belton, Robin Lee, Kang-Ju Palande, Sourabh Percival, Sarah Purvine, Emilie Tymochko, Sarah |
| contents | The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper parameters such that the output Mapper graph of $X$ is isomorphic to $G$? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11180 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Any Graph is a Mapper Graph Alvarado, Enrique G Belton, Robin Lee, Kang-Ju Palande, Sourabh Percival, Sarah Purvine, Emilie Tymochko, Sarah Algebraic Topology Computational Geometry The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper parameters such that the output Mapper graph of $X$ is isomorphic to $G$? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph. |
| title | Any Graph is a Mapper Graph |
| topic | Algebraic Topology Computational Geometry |
| url | https://arxiv.org/abs/2408.11180 |