Pointsx3 xarbindx1x2x3ind clsxa1 xxa 1

#points(x3)
ind=sample(seq(1,1500,by=1),N,replace=FALSE)
Xa=rbind(x1,x2,x3)[ind,]
cls=Xa[,1]
X=Xa[,-1]
clss=sort(unique(cls))
K=length(clss)
pi=rep(NA,K)
for(k in 1:K)
{
pi[k]=sum(cls==clss[k])/N
}
pi
#X=sample(rbind(x1,x2,x3),N,replace=FALSE)
p=dim(X)[2]
Mu=matrix(NA,K,p)
for(k in 1:K)
{
i=cls==clss[k]
Mu[k,]=colMeans(X[i,])
}
Q.hat=matrix(0,p,p)
for (k in 1:K)
{
i=cls==clss[k]
n=sum(i)
term=X[i,]-t(replicate(n,Mu[k,]))
Q.hat=Q.hat+t(term)%*%term
}
Q.hat=Q.hat/(N-K)
Q.hat
Q.inv=solve(Q.hat)
delta=matrix(NA,N,K)
for (k in 1:K)
{
m=Mu[k,]
d=log(pi[k])-.5*m%*%Q.inv%*%m
for(i in 1:N)
{
delta[i,k]=d+m%*%Q.inv%*%X[i,]
}
}
my.class=apply(delta,1,which.max)
plot(X,col=my.class)
plot(X,col=cls)
Y=data.frame(P1=Xa[,2],P2=Xa[,3])
hft=lda(cls~P1+P2,data=Y)
hft.class=predict(hft,Y)$class
plot(Y,col=hft.class)

#LDA Lab
lda.fit=lda(Direction~Lag1+Lag2,data=Smarket,subset=train)
lda.fit
plot(lda.fit)
lda.pred=predict(lda.fit,Smarket.2005)
names(lda.pred)
lda.class=lda.pred$class
table(lda.class,Direction.2005)
mean(lda.class==Direction.2005)
sum(lda.pred$posterior[,1]>=.5)
sum(lda.pred$posterior[,1]<.5)
lda.pred$posterior[1:20,1]
lda.class[1:20]
sum(lda.pred$posterior[,1]>.9)
#QDA multivariate example
N=500
sigma1=matrix(c(1,0,.1,(1-1/100)),2,2)
mus1=matrix(c(-.5,-.5),2,1)
sigma2=matrix(c(1,0,.25,(1-1/16)),2,2)
mus2=matrix(c(0,-.1),2,1)
sigma3=matrix(c(1,0,0,1),2,2)
mus3=matrix(c(.5,.5),2,1)
x1=mvrnorm(N,mus1,sigma1)
x1=cbind(1,x1)
x2=mvrnorm(N,mus2,sigma2)
x2=cbind(2,x2)
x3=mvrnorm(N,mus3,sigma3)
x3=cbind(3,x3)
#plot(x1,x2)
#points(x3)
ind=sample(seq(1,1500,by=1),N,replace=FALSE)
Xa=rbind(x1,x2,x3)[ind,]
cls=Xa[,1]
X=Xa[,-1]
clss=sort(unique(cls))
K=length(clss)
pi=rep(NA,K)
for(k in 1:K)
{
pi[k]=sum(cls==clss[k])/N
}
pi
p=dim(X)[2]
Mu=matrix(NA,K,p)
for(k in 1:K)
{
i=cls==clss[k]
Mu[k,]=colMeans(X[i,])
}
Q.hat=array(0,dim=c(p,p,K))
for (k in 1:K)
{
i=cls==clss[k]

n=sum(i)
term=X[i,]-t(replicate(n,Mu[k,]))
Q.hat[,,k]=t(term)%*%term/(n-1)