# BreastCancer.R

# change this path for your computer:
Data <- na.omit(read.table("C:/Documents and Settings/steeleb/My Documents//Math 542/BreastCancer.txt",header=FALSE))

names(Data) <- c("Obsvn","ID","thick","uniformSize","uniformShape","adhesion","cellSize","bareNuclei","Chromatin",
	"normalNuclei","Mitoses","Class")

dim(Data)
p <- dim(Data)[2] - 1

head(Data)
cor(Data[,3:p])

library(lattice)
trellis.par.set(canonical.theme(color = FALSE))

attach(Data)

plot(uniformSize,uniformShape)
cor(uniformSize,uniformShape)

x <- (uniformSize - mean(uniformSize))
x <- x/sqrt(sum(x^2))
mean(x)
t(x)%*%x

y <- (uniformShape - mean(uniformShape))
y <- y/sqrt(sum(y^2))
mean(y)
t(y)%*%y

t(x)%*%y

D <- table(uniformSize,uniformShape)
D
z <- as.vector(D)

u <- rep(1:10,time=10)
v <- rep(1:10,each=10)
cbind(u,v,z)

symbols(u,v,circles=z)

plot(uniformShape,thick)
I <- Class=="benign"
sum(I==T)/n
points(uniformShape[I],thick[I],col=2,pch=16)
points(uniformShape[I==F],thick[I==F],col=3,pch=16)


R <- cor(Data[,3:p])
eigen.obj <- eigen(R)
P <- eigen.obj$vectors[,1:2]

P # the projection matrix
t(P)%*%P
X <- matrix(unlist(Data[,3:p]),n,p-2)
cor(X)

Y <- scale(X)%*%P # project X onto 2 new basis vectors P[,1] and P[,2]
plot(Y) 
I <- Class=="benign"
sum(I==T)/n
points(Y[I,1],Y[I,2],col=2,pch=16)
points(Y[I==F,1],Y[I==F,2],col=3,pch=16)

j <- rep(1,n)
X.centered <- X - j%*%t(colMeans(X))
colMeans(X.centered)

Z <- X.centered%*%diag(1/sd(X))/sqrt(n-1)
t(Z)%*%Z