The Vapnik-Chervonenkis dimension of cubes in $\mathbb{R}^d$
arXiv:1412.6612v32 citations
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This provides a precise combinatorial result for researchers in discrete geometry and machine learning, addressing a specific theoretical question.
The paper tackled the problem of determining the Vapnik-Chervonenkis (VC) dimension of d-dimensional cubes in ℝ^d, proving it to be ⌊(3d+1)/2⌋.
The Vapnik-Chervonenkis (VC) dimension of a collection of subsets of a set is an important combinatorial concept in settings such as discrete geometry and machine learning. In this paper we prove that the VC dimension of the family of $d$-dimensional cubes in $\mathbb R^d$ is $\lfloor(3d+1)/2\rfloor$.