estimate_number_hyperplanes {shattering}

Function to estimate the number of hyperplanes required to classify such a data sample.

Description

This function estimates the number of hyperplanes

Usage

estimate_number_hyperplanes(
  X,
  Y,
  length = 20,
  quantile.percentage = 0.05,
  epsilon = 1e-07
)

Arguments

X

matrix indentifying the input space of variables

Y

numerical vector indentifying the output space of variables

length

number of data points used to estimate the shattering coefficient

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

Value

A data frame whose columns are: (1) the original sample size; (2) the reduced sample size after connecting homogeneous space regions; (3) the lower bound for the number of hyperplanes required to shatter the input space; and (4) the upper bound for the number of hyperplanes required to shatter the input space

Examples

# Generating some random dataset with 2 classes:
# 50 examples in class 1 and 50 in class 2 (last column)
data = cbind(rnorm(mean=1, sd=1, n=50), rnorm(mean=1, sd=1, n=50), rep(1, 50))
data = rbind(data, cbind(rnorm(mean=-1, sd=1, n=50), rnorm(mean=-1, sd=1, n=50), rep(2, 50)))

# Building up the input and output sets
X = data[,1:2]
Y = data[,3]

# Plotting our dataset using classes as colors
plot(X, col=Y, main="Original dataset", xlab="Attribute 1", ylab="Attribute 2")

# Here we estimate the number of hyperplanes required to shatter (divide) the given sample
# in all possible ways according to the organization of points in the input space
Hyperplanes = estimate_number_hyperplanes(X, Y, length=10, quantile.percentage=0.1, epsilon=1e-7)