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#' Caculate the estimator on the MNIPALS method
#'
#' @param data is the orignal data set
#' @param data0 is the missing data set
#' @param real is to judge whether the data set is a real missing data set
#' @param example is to judge whether the data set is a simulation example.
#'
#' @return XMNIPALS, MSEMNIPALS, MAEMNIPALS, REMNIPALS, GCVMNIPALS,timeMNIPALS
#' @export
#'
#' @examples
#' library(MASS)
#' n=100;p=10;per=0.1
#' X0=data=matrix(mvrnorm(n*p,0,1),n,p)
#' m=round(per*n*p,digits=0)
#' mr=sample(1:(n*p),m,replace=FALSE)
#' X0[mr]=NA;data0=X0
#' MNIPALS(data=data,data0=data0,real=FALSE,example=FALSE)
#the MNIPALS method
MNIPALS=function(data=0,data0,real=TRUE,example=FALSE)
#It defaults that the data set is a real data set
{#1
if(real||example){#2
etatol=0.7
}else{#2
etatol=0.9
}#2
lll=0
time=system.time(#2
while(lll==0){#3
X0=data0
n=nrow(X0);p=ncol(X0)
mr=which(is.na(X0)==TRUE)
m=nrow(as.matrix(mr))
cm0=colMeans(X0,na.rm=T)
ina=as.matrix(mr%%n)
jna=as.matrix(floor((mr+n-1)/n))
data0[is.na(data0)]=cm0[ceiling(which(is.na(X0))/n)]
X=as.matrix(data0)
Z0=Z=scale(X,center=TRUE,scale=FALSE)
tol=1e-5;nb=100;niter=0;d=1
t0=matrix(0,n,1);a0=matrix(0,p,1)
t1=matrix(Z[,which.max(diag(t(Z)%*%Z))],,1)
while((d>=tol) & (niter<=nb)){#4
niter=niter+1
thethat=matrix(t(ginv(t(t1)%*%t1)%*%(t(t1)%*%Z)),p,1)
a1hat=matrix(thethat/sqrt(sum(thethat*thethat)),p,1)
t1hat=matrix(t(ginv(t(a1hat)%*%a1hat)%*%(t(a1hat)%*%t(Z))),n,1)
d=sqrt(t(t1hat-t1)%*%(t1hat-t1))
t1=t1hat
}#4
for( i in 1:n){#4
M=is.na(X0[i,])
job=which(M==FALSE);jna=which(M==TRUE)
piob=nrow(as.matrix(job));pina=nrow(as.matrix(jna))
while((piob>0)&(pina>0)){#5
Qi=matrix(0,p,p)
for( u in 1:piob){#6
Qi[job[u],u]=1
}#6
for( v in 1:pina){#6
Qi[jna[v],v+piob]=1
}#6
zi=Z0[i,]
zQi=zi%*%Qi
ZQi=Z0%*%Qi
a1Qi=t(t(a1hat)%*%Qi)
ziob=t(as.matrix(zQi[,1:piob]))
zina=t(as.matrix(zQi[,piob+(1:pina)]))
Ziob=matrix(ZQi[,1:piob],n,piob)
Zina=matrix(ZQi[,piob+(1:pina)],n,pina)
a1iob=matrix(t(a1Qi)[,1:piob],piob,1)
a1ina=matrix(t(a1Qi)[,piob+(1:pina)],pina,1)
zinahat=t1hat[i,]*t(a1ina)
ZQi[i,piob+(1:pina)]=zinahat
Zi=ZQi%*%t(Qi)
Z=Z0=Zi
pina=0
}#5
}#4
XMNIPALS=Xnew=Z+matrix(1,n,p)%*%diag(cm0)
for (j in 1:p){
Mj=is.na(X0[,j])
iob=which(Mj==FALSE)
chj=sum(abs(round(X0[iob,j])-X0[iob,j]))
if (chj==0){
XMNIPALS[,j]=round(XMNIPALS[,j])
}else{
XMNIPALS[,j]= XMNIPALS[,j]
}
}
lll=1
}#3
)#2
if(real){#2
MSEMNIPALS= MAEMNIPALS= REMNIPALS='NULL'
}else{#2
MSEMNIPALS=(1/m)*t(Xnew[mr]-data[mr])%*%(Xnew[mr]-data[mr])
MAEMNIPALS=(1/m)*sum(abs(Xnew[mr]-data[mr]))
REMNIPALS=(sum(abs(data[mr]-Xnew[mr])))/(sum(data[mr]))
}#2
lambdaMNIPALS=svd(cor(XMNIPALS))$d
lMNIPALS=lambdaMNIPALS/sum(lambdaMNIPALS);J=rep(lMNIPALS,times=p);dim(J)=c(p,p)
upper.tri(J,diag=T);J[lower.tri(J)]=0;J;dim(J)=c(p,p)
etaMNIPALS=matrix(colSums(J),nrow = 1,ncol = p,byrow = FALSE)
wwMNIPALS=which(etaMNIPALS>=etatol);kMNIPALS=wwMNIPALS[1]
lambdaMNIPALSpk=lambdaMNIPALS[(kMNIPALS+1):p]
GCVMNIPALS=sum(lambdaMNIPALSpk)*p/(p-kMNIPALS)^2
return(list(XMNIPALS=XMNIPALS,MSEMNIPALS=MSEMNIPALS,MAEMNIPALS=MAEMNIPALS,REMNIPALS=REMNIPALS,GCVMNIPALS=GCVMNIPALS,timeMNIPALS=time))
}#1
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