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hum=function(y,d,method="multinom",...){
y_raw=y
y=factor(y)
y_levels=levels(y)
y=as.numeric(y)
d=data.matrix(d)
num=length(unique(y))
pp=pm(y=y,d=d,method=method,...)
if(num==3){
x1=which(y==1) #return the label
x2=which(y==2)
x3=which(y==3)
n=length(y)
#n is the sample size
a=matrix(0,n,3);
one1=a;
one1[,1]=1;
one2=a;
one2[,2]=1;
one3=a;
one3[,3]=1;
#get cr value
dd1=pp-one1;
dd2=pp-one2;
dd3=pp-one3;
jd1=sqrt(dd1[,1]^2+dd1[,2]^2+dd1[,3]^2);
jd2=sqrt(dd2[,1]^2+dd2[,2]^2+dd2[,3]^2);
jd3=sqrt(dd3[,1]^2+dd3[,2]^2+dd3[,3]^2);
jd1=exp(jd1);
jd2=exp(jd2);
jd3=exp(jd3);
mt1=kronecker(jd1[x1]%*%t(jd2[x2]),jd3[x3]);
mt2=kronecker(jd1[x1]%*%t(jd3[x2]),jd2[x3]);
mt3=kronecker(jd2[x1]%*%t(jd1[x2]),jd3[x3]);
mt4=kronecker(jd2[x1]%*%t(jd3[x2]),jd1[x3]);
mt5=kronecker(jd3[x1]%*%t(jd2[x2]),jd1[x3]);
mt6=kronecker(jd3[x1]%*%t(jd1[x2]),jd2[x3]);
cr=sum(mt1==pmin(pmin(pmin(pmin(pmin(mt1, mt2), mt3), mt4), mt5), mt6)); #min of every number of mt1-mt6 is mt1
#hypervolume under ROC manifold value
hum=cr/(length(x1)*length(x2)*length(x3));
result=list(call=match.call(),measure=hum,pm=pp,y=y_raw)
class(result)="mcca.hum"
return(result)
}else if(num==4){
n=length(y)
#n is the sample size
a=matrix(0,n,4);
one1=a;
one1[,1]=1;
one2=a;
one2[,2]=1;
one3=a;
one3[,3]=1;
one4=a;
one4[,4]=1;
x1=which(y==1);
x2=which(y==2);
x3=which(y==3);
x4=which(y==4);
n1=sum(y==1)
n2=sum(y==2)
n3=sum(y==3)
n4=sum(y==4)
dd1=pp-one1;
dd2=pp-one2;
dd3=pp-one3;
dd4=pp-one4;
jd1=sqrt(dd1[,1]^2+dd1[,2]^2+dd1[,3]^2+dd1[,4]^2);
jd2=sqrt(dd2[,1]^2+dd2[,2]^2+dd2[,3]^2+dd2[,4]^2);
jd3=sqrt(dd3[,1]^2+dd3[,2]^2+dd3[,3]^2+dd3[,4]^2);
jd4=sqrt(dd4[,1]^2+dd4[,2]^2+dd4[,3]^2+dd4[,4]^2);
jd1=exp(jd1);
jd2=exp(jd2);
jd3=exp(jd3);
jd4=exp(jd4);
mt1=kronecker(kronecker(jd1[x1]%*%t(jd2[x2]),jd3[x3]),jd4[x4]);
mt7=kronecker(kronecker(jd1[x1]%*%t(jd2[x2]),jd4[x3]),jd3[x4]);
mt2=kronecker(kronecker(jd1[x1]%*%t(jd3[x2]),jd2[x3]),jd4[x4]);
mt8=kronecker(kronecker(jd1[x1]%*%t(jd3[x2]),jd4[x3]),jd2[x4]);
mt9=kronecker(kronecker(jd1[x1]%*%t(jd4[x2]),jd2[x3]),jd3[x4]);
mt10=kronecker(kronecker(jd1[x1]%*%t(jd4[x2]),jd3[x3]),jd2[x4]);
mt3=kronecker(kronecker(jd2[x1]%*%t(jd1[x2]),jd3[x3]),jd4[x4]);
mt11=kronecker(kronecker(jd2[x1]%*%t(jd1[x2]),jd4[x3]),jd3[x4]);
mt4=kronecker(kronecker(jd2[x1]%*%t(jd3[x2]),jd1[x3]),jd4[x4]);
mt12=kronecker(kronecker(jd2[x1]%*%t(jd3[x2]),jd4[x3]),jd1[x4]);
mt13=kronecker(kronecker(jd2[x1]%*%t(jd4[x2]),jd3[x3]),jd1[x4]);
mt14=kronecker(kronecker(jd2[x1]%*%t(jd4[x2]),jd1[x3]),jd3[x4]);
mt5=kronecker(kronecker(jd3[x1]%*%t(jd2[x2]),jd1[x3]),jd4[x4]);
mt15=kronecker(kronecker(jd3[x1]%*%t(jd2[x2]),jd4[x3]),jd1[x4]);
mt6=kronecker(kronecker(jd3[x1]%*%t(jd1[x2]),jd2[x3]),jd4[x4]);
mt16=kronecker(kronecker(jd3[x1]%*%t(jd1[x2]),jd4[x3]),jd2[x4]);
mt23=kronecker(kronecker(jd3[x1]%*%t(jd4[x2]),jd1[x3]),jd2[x4]);
mt24=kronecker(kronecker(jd3[x1]%*%t(jd4[x2]),jd2[x3]),jd1[x4]);
mt17=kronecker(kronecker(jd4[x1]%*%t(jd1[x2]),jd2[x3]),jd3[x4]);
mt18=kronecker(kronecker(jd4[x1]%*%t(jd1[x2]),jd3[x3]),jd2[x4]);
mt19=kronecker(kronecker(jd4[x1]%*%t(jd2[x2]),jd1[x3]),jd3[x4]);
mt20=kronecker(kronecker(jd4[x1]%*%t(jd2[x2]),jd3[x3]),jd1[x4]);
mt21=kronecker(kronecker(jd4[x1]%*%t(jd3[x2]),jd1[x3]),jd2[x4]);
mt22=kronecker(kronecker(jd4[x1]%*%t(jd3[x2]),jd2[x3]),jd1[x4]);
cr=sum(mt1==pmin(mt7,pmin(mt8,pmin(mt9,pmin(mt10,pmin(mt11,pmin(mt12,pmin(mt13,pmin(mt14,pmin(mt15,pmin(mt16,pmin(mt17,pmin(mt18,pmin(mt19,pmin(mt20,pmin(mt21,pmin(mt22,pmin(mt23,pmin(mt24,pmin(pmin(pmin(pmin(pmin(mt1, mt2), mt3), mt4), mt5), mt6))))))))))))))))))));
#hypervolume under ROC manifold
hum=cr/(n1*n2*n3*n4);
result=list(call=match.call(),measure=hum,pm=pp,y=y_raw)
class(result)="mcca.hum"
return(result)
}else if(num==2){
x1=which(y==1) #return the label
x2=which(y==2)
n=length(y)
#n is the sample size
a=matrix(0,n,2);
one1=a;
one1[,1]=1;
one2=a;
one2[,2]=1;
result=list(call=match.call(),measure=as.numeric(pROC::roc(y ~ pp[,1])$auc),pm=pp,y=y_raw)
class(result)="mcca.hum"
return(result)
}
}
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