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find_outmost_points=function(df, kappas){
# Flatten data frame
rownames(df)=1:dim(df)[1]
# Find distances between rows:
dm=as.matrix(dist(df,method = "euclidean", diag = F, upper = F, p = 2))
# Find maximum distance per row and frequency table
outmostrows=max.col(dm, ties.method="first")
di=as.data.frame(table(outmostrows),stringsAsFactors = F)
di=di[order(-di$Freq),]
di$outmostrows=as.integer(di$outmostrows)
di$FreqPerCent=di$Freq/sum(di$Freq)
di$CumFreqPerCent=cumsum(di$FreqPerCent)
rownames(di)=1:dim(di)[1]
rowsmaxall=di$outmostrows
nrowsmaxall=length(rowsmaxall)
#
####################################
# Check if rows are less than kappas
####################################
#
if(nrowsmaxall<kappas){
n1=kappas-nrowsmaxall
r1=setdiff(1:dim(df)[1],rowsmaxall)
rowsmaxall=c(rowsmaxall, sample(setdiff(1:dim(df)[1],rowsmaxall),n1))
}
#
########################################################################
#Find the kappas outmost of outmost if possible
rowsmaxkappas=as.integer(rowsmaxall[1:kappas])
########################################################################
# Return
out=list("outmost"=rowsmaxkappas,"outmostall"=rowsmaxall,"outmostfrequency"=di)
return(out)
}
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