build_classifier {shattering}

Produce a set of SVM classifiers

Description

This function outputs a set of SVM classifiers to perform the supervised learning task based on the topological data analysis

Usage

build_classifier(
  X,
  Y,
  train.size = 0.7,
  quantile.percentage = 1,
  min.points = 3,
  gamma.length = 50,
  cost = 10000,
  weights = c(0.25, 0.75),
  best.stdev.purity = 0
)

Arguments

X

matrix defining the input space of your dataset

Y

numerical vector defining the output space (labels/classes) of your dataset

train.size

fraction of examples used for training

quantile.percentage

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

min.points

minimal number of examples per classification region of the input space

gamma.length

number of possible gamma parameters to test the radial kernel for SVM

cost

the cost for the SVM optimization

weights

weights to be used in our SVM optimization

best.stdev.purity

the stdev to compute data purity

Value

A list of classifiers composing the final classification model

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"

Examples

# require(NMF)
# 
# X = cbind(rnorm(mean=-1, sd=1, n=200), rnorm(mean=-1, sd=1, n=200))
# X = rbind(X, cbind(rnorm(mean=1, sd=1, n=200), rnorm(mean=1, sd=1, n=200)))
# Y = c(rep(-1,200), rep(+1,200))
# plot(X, col=Y+2, pch=20, cex=3, cex.axis=2)
# 
# model = build_classifier(X, Y, train.size=0.5, quantile.percentage=1, 
#		min.points=10, gamma.length=15, cost=10000)
# result = apply_classifier(model, X)
# points(X, col=as.numeric(result$classification.ensembled)+2, pch=20, cex=1.5)
# 
# x = seq(min(X), max(X), length=100)
# z = outer(x, x, function(x,y) { 
#	apply_classifier(model, as.matrix(cbind(x,y)))$classification.ensembled } )
# filled.contour(x,x,z)
# 
# x = seq(min(X), max(X), length=100)
# z = outer(x, x, function(x,y) { 
#	apply_classifier(model, as.matrix(cbind(x,y)), 
#		only.best.classifiers=TRUE)$classification.ensembled } )
# locator(1)
# filled.contour(x,x,z)