Typed topology and its application to data set
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913229932855296 |
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| author | Hu, Wanjun |
| author_facet | Hu, Wanjun |
| contents | The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a typically typed topological space. Clusters calculated by the DBSCAN algorithm for data clustering can be well represent in a finite typed topological space. Other concepts such as tracks, port (starting points), type-p-connectedness, p-closure-connectedness, indexing, branches are also introduced for a finite typed topological space. Finally, $left-r$ and $up-left-r$ type open sets are introduced for data sets in $R^2$, so that tracks, port, branches can be calculated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05352 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Typed topology and its application to data set Hu, Wanjun General Topology 05A05, 68P01 The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a typically typed topological space. Clusters calculated by the DBSCAN algorithm for data clustering can be well represent in a finite typed topological space. Other concepts such as tracks, port (starting points), type-p-connectedness, p-closure-connectedness, indexing, branches are also introduced for a finite typed topological space. Finally, $left-r$ and $up-left-r$ type open sets are introduced for data sets in $R^2$, so that tracks, port, branches can be calculated. |
| title | Typed topology and its application to data set |
| topic | General Topology 05A05, 68P01 |
| url | https://arxiv.org/abs/2302.05352 |