What is the $\textit{intrinsic}$ dimension of your binary data? -- and how to compute it quickly
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
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2024
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| _version_ | 1866913811130220544 |
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| author | Hanika, Tom Hille, Tobias |
| author_facet | Hanika, Tom Hille, Tobias |
| contents | Dimensionality is an important aspect for analyzing and understanding (high-dimensional) data. In their 2006 ICDM paper Tatti et al. answered the question for a (interpretable) dimension of binary data tables by introducing a normalized correlation dimension. In the present work we revisit their results and contrast them with a concept based notion of intrinsic dimension (ID) recently introduced for geometric data sets. To do this, we present a novel approximation for this ID that is based on computing concepts only up to a certain support value. We demonstrate and evaluate our approximation using all available datasets from Tatti et al., which have between 469 and 41271 extrinsic dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | What is the $\textit{intrinsic}$ dimension of your binary data? -- and how to compute it quickly Hanika, Tom Hille, Tobias Machine Learning Artificial Intelligence 68T05 06-08 68T01 68T09 Dimensionality is an important aspect for analyzing and understanding (high-dimensional) data. In their 2006 ICDM paper Tatti et al. answered the question for a (interpretable) dimension of binary data tables by introducing a normalized correlation dimension. In the present work we revisit their results and contrast them with a concept based notion of intrinsic dimension (ID) recently introduced for geometric data sets. To do this, we present a novel approximation for this ID that is based on computing concepts only up to a certain support value. We demonstrate and evaluate our approximation using all available datasets from Tatti et al., which have between 469 and 41271 extrinsic dimensions. |
| title | What is the $\textit{intrinsic}$ dimension of your binary data? -- and how to compute it quickly |
| topic | Machine Learning Artificial Intelligence 68T05 06-08 68T01 68T09 |
| url | https://arxiv.org/abs/2404.06326 |