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Contaminated DataSet.R
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Contaminated DataSet.R
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library(MASS)
D<-read.csv("4.3.csv",header=T)
conta=matrix(rep(round(2*as.numeric(apply(D,2,max))+rnorm(9,0,1)),5),5)
DD=rbind(as.matrix(D),conta)
Y<-D[,c(1,5,6)]
X<-D[,c(2,4,8)]
############################## Create correlation matrix
r11<-cor(X)
r22<-cor(Y)
r12<-cor(X,Y)
r21<-t(r12)
#######################
############ squre root matrix for r11
ev1<-eigen(r11)
sev1<-sqrt(ev1$values)
dm1<-diag(1/sev1)
sr11<-ev1$vectors%*%dm1%*%t(ev1$vectors)
################# squre root matrix for r22
ev2<-eigen(r22)
sev2<-sqrt(ev2$values)
dm2<-diag(1/sev2)
sr22<-ev2$vectors%*%dm2%*%t(ev2$vectors)
##################### Define Cross correlation matrix m
m<-sr11%*%r12%*%sr22
############## compute SVD OF m
sd<-svd(m)
##################### canonical correlation
can.corr<-sd$d
l=can.corr^2
################P.Value Calculation of canonical variate paires##########
Y<-D[,c(1,5,6)]
X<-D[,c(2,4,8)]
p=ncol(X);q=ncol(Y);n=nrow(X)
L=PV=df=matrix(rep(0,min(p,q)),nrow=min(p,q))
for(m in 1:min(p,q))
{
df[m]<-(p-m+1)*(q-m+1)
df
X=0
for(k in m:min(p,q))
{
X=X+log(1-l[k])
}
L[m]=-((n-1)-.5*(p+q+1))*X
PV=pchisq(L,df=df,lower.tail=F)
}
L;PV;df
Table=round(data.frame(CanCorr=can.corr,Chisquare=L,df=df,p.value=PV),3)
################## canonical weights
a<-sr11%*%sd$u
a[,colSums(a)<0]=-a[,colSums(a)<0]
b<-sr22%*%sd$v
b[,colSums(b)<0]=-b[,colSums(b)<0]
################### caninical loading
lx<-r11%*%a
ly<-r22%*%b
#hist(lx[,1])
######################## cross loading for x
clx=matrix(rep(0,ncol(X)*ncol(Y)),ncol(X))
for(i in 1:ncol(Y))
{
L<-can.corr[i]*lx[,i]
clx[,i]<-L
}
clx<-clx
####################### cross loading for y
cly=matrix(rep(0,ncol(X)*ncol(Y)),ncol(Y))
for (i in 1:ncol(X))
{
L<-can.corr[i]*ly[,i]
cly[,i]<-L
}
#####################cross loading
clx<-clx
cly<-cly
################ propotion of Explained Variance for x set
pevx=rep(0,min(length(Y),length(X)))
for ( i in 1:min(length(Y),length(X))){
pex<-sum(lx[,i]^2)/length(lx[,i])
pevx[i]<-pex
}
### percent of variance for x set
###########################propotion of Explained Variance for y set
pevy=rep(0,min(length(Y),length(X)))
for ( i in 1:min(length(Y),length(X))){
pey<-sum(ly[,i]^2)/length(ly[,i])
pevy[i]<-pey
}
### percent of variance for y
ppevx<-pevx*100
ppevy<-pevy*100
################Redundency for x
Rx=rep(0,min(p=3,q=3))
for ( i in 1:min(p=3,q=3)){
R1<-can.corr[i]^2*sum(lx[,i]^2)/length(lx[,i])
Rx[i]<-R1
}
#########################Redundency for y
Ry=rep(0,min(p=3,q=3))
for ( i in 1:min(p=3,q=3)){
R2<-can.corr[i]^2*sum(ly[,i]^2)/length(ly[,i])
Ry[i]<-R2
}
Rx
Ry
Table=round(data.frame(Rx,Ry),3)
P.cca=cancor(X,Y)
##================================================================
########## Robust Correlation Calculation #################
##=================================================================
library(MASS)
D<-read.csv("4.3.csv",header=T)
#conta=matrix(rep(round(5*as.numeric(apply(D,2,max))+rnorm(9,0,1)),5),5)
DD=rbind(as.matrix(D),conta)
Y<-DD[,c(1,5,6)]
X<-DD[,c(2,4,8)]
nDD=cbind(X,Y)
#################@@@ Robust Correlation Making ############
DataR=cov2cor(MeanVar(nDD,Beta=0.1)$V)
r11=DataR[1:3,1:3]
r22=DataR[4:6,4:6]
r12=DataR[1:3,4:6]
r21=DataR[4:6,1:3]
############ squre root matrix for r11
ev1<-eigen(r11)
sev1<-sqrt(ev1$values)
dm1<-diag(1/sev1)
sr11<-ev1$vectors%*%dm1%*%t(ev1$vectors)
################# squre root matrix for r22
ev2<-eigen(r22)
sev2<-sqrt(ev2$values)
dm2<-diag(1/sev2)
sr22<-ev2$vectors%*%dm2%*%t(ev2$vectors)
##################### Define Cross correlation matrix m
m<-sr11%*%r12%*%sr22
############## compute SVD OF m
sd<-svd(m)
##################### canonical correlation
can.corr<-sd$d
l=can.corr^2
#################### test1
################P.Value Calculation of canonical variate paires##########
Y<-DD[,c(1,5,6)]
X<-DD[,c(2,4,8)]
p=ncol(X);q=ncol(Y);n=nrow(X)
L=PV=df=matrix(rep(0,min(p,q)),nrow=min(p,q))
for(m in 1:min(p,q))
{
df[m]<-(p-m+1)*(q-m+1)
df
X=0
for(k in m:min(p,q))
{
X=X+log(1-l[k])
}
L[m]=-((n-1)-.5*(p+q+1))*X
PV=pchisq(L,df=df,lower.tail=F)
}
L;PV;df
Table=round(data.frame(CanCorr=can.corr,Chisquare=L,dd=df,p.value=PV),3)
################## canonical weights
a<-sr11%*%sd$u
a[,colSums(a)<0]=-a[,colSums(a)<0]
b<-sr22%*%sd$v
b[,colSums(b)<0]=-b[,colSums(b)<0]
################### caninical loading
lx<-r11%*%a
ly<-r22%*%b
#hist(lx[,1])
######################## cross loading for x
clx=matrix(rep(0,ncol(X)*ncol(Y)),ncol(X))
for(i in 1:ncol(Y))
{
L<-can.corr[i]*lx[,i]
clx[,i]<-L
}
clx<-clx
####################### cross loading for y
cly=matrix(rep(0,ncol(X)*ncol(Y)),ncol(Y))
for (i in 1:ncol(X))
{
L<-can.corr[i]*ly[,i]
cly[,i]<-L
}
#####################cross loading
clx<-clx
cly<-cly
################ propotion of Explained Variance for x set
pevx=rep(0,min(length(Y),length(X)))
for ( i in 1:min(length(Y),length(X))){
pex<-sum(lx[,i]^2)/length(lx[,i])
pevx[i]<-pex
}
### percent of variance for x set
###########################propotion of Explained Variance for y set
pevy=rep(0,min(length(Y),length(X)))
for ( i in 1:min(length(Y),length(X))){
pey<-sum(ly[,i]^2)/length(ly[,i])
pevy[i]<-pey
}
### percent of variance for y
ppevx<-pevx*100
ppevy<-pevy*100
################Redundency for x
Rx=rep(0,min(p=3,q=3))
for ( i in 1:min(p=3,q=3)){
R1<-can.corr[i]^2*sum(lx[,i]^2)/length(lx[,i])
Rx[i]<-R1
}
#########################Redundency for y
Ry=rep(0,min(p=3,q=3))
for ( i in 1:min(p=3,q=3)){
R2<-can.corr[i]^2*sum(ly[,i]^2)/length(ly[,i])
Ry[i]<-R2
}
Rx
Ry
Table=round(data.frame(Rx,Ry),3)
P.cca=cancor(X,Y)
######################