The Vapnik-Chervonenkis dimension of cubes in R^d

12/20/2014

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by   Christian J. J. Despres, et al.

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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 R^d is (3d+1)/2.