NormalizationDemo.R

rm(list=ls())

# Manual way to create a grid from x in [-10,10]
# and y in [-5,5]
a<-matrix(rep(seq(-10,10,2),11))
a<-cbind(a,rep(c(-5:5),each=11))

# Assign classes in a linearly separable way
myclass = (a[,1]+a[,2])<5

# myn is for picking the p-norm when we normalize
# So for myn == 2, we're doing Euclidian norm.
# See Section 1.5 in Doug's notes and excercise #7
myn = 2

# mymags is the p-norm
mymags = (abs(a[,1])^myn + abs(a[,2])^myn)^(1/myn)

# Divide by the norm -- verify that the length of each
# row vector in the a matrix is == 1
b = a / mymags

# Here we are scaling each feature independantly by
# dividing each columns by it's standard deviation
# centered around the mean (standardizing)
c<-a
c[,1]<-(a[,1]-mean(a[,1]))/sd(a[,1])
c[,2]<-(a[,2]-mean(a[,2]))/sd(a[,2])

# In matrix 'd', normalizing after scaling.
mymags2 = (abs(c[,1])^myn + abs(c[,2])^myn)^(1/myn)
d = c / mymags2

# PDF divice with 2 x 1 figures and 1 inch outer margin
pdf("normalizationeffect.pdf",width=8.5,height=11)
par(mfrow=c(2,1),omi=c(1,1,1,1))

plot(a,col=ifelse(myclass,'red','green'),pch=16)
title("No normalization")

plot(b,col=ifelse(myclass,'red','green'),pch=16)
title(paste("Normalization ( p =",myn,")"))

# Note what happens when we call plot next. It jumps
# to the next figure which is outside the 2x1 layout.
# This is a pdf device so it starts a new page
plot(c,col=ifelse(myclass,'red','green'),pch=16)
title("Scaled / Standardized features ( mean at the center, sd = 1 )")

plot(d,col=ifelse(myclass,'red','green'),pch=16)
title("Normalization after scaling")
dev.off()