What is the $\textit{intrinsic}$ dimension of your binary data? -- and how to compute it quickly

Tom Hanika, Tobias Hille
4/9/2024
cs.LGcs.AI

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Abstract

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.

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Cite this paper

@article{hanika2024what,
  title  = {What is the $\textit{intrinsic}$ dimension of your binary data? -- and how to compute it quickly},
  author = {Tom Hanika and Tobias Hille},
  year   = {2024},
  eprint = {2404.06326},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2404.06326v1}
}

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