equivalence_relation {shattering}

Function to compute equivalence relations among input space points.

Description

This function computes the greatest as possible open ball connecting a given input example to every other under the same class label, thus homogeneizing space regions.

Usage

equivalence_relation(
  X,
  Y,
  quantile.percentage = 1,
  epsilon = 0.001,
  chunk = 250
)

Arguments

X

matrix indentifying the input space of variables

Y

numerical vector indentifying the output space of variables

quantile.percentage

real number to define the quantile of distances to be considered (e.g. 0.1 means 10%)

epsilon

a real threshold to be removed from distances in order to measure the open balls in the underlying topology

chunk

number of elements to compute the Euclidean distances at once (if you set a large number, you might have memory limitations to perform the operations)

Value

A list with the equivalence relations in form of a list