number_regions {shattering}

Computes the maximal number of space regions

Description

This function computes the maximal number of regions an R^n space can be divided using m hyperplanes

Usage

number_regions(m, n)

Arguments

m

number of hyperplanes

n

space dimensionality

Value

Maximal number of space regions

References

de Mello, R.F. (2019) "On the Shattering Coefficient of Supervised Learning Algorithms" arXiv:https://arxiv.org/abs/1911.05461

de Mello, R.F., Ponti, M.A. (2018, ISBN: 978-3319949888) "Machine Learning: A Practical Approach on the Statistical Learning Theory"

https://onionesquereality.wordpress.com/2012/11/23/maximum-number-of-regions-in-arrangement-of-hyperplanes/

Examples

number_regions(m=2, n=2)