Predict mclust cluster membership outside R - r

Question

I've used mclust to find clusters in a dataset. Now I want to implement these findings into external non-r software (predict.Mclust is thus not an option as has been suggested in previous similar Questions) to classify new observations. I need to know how mclust classifies observations.
Since mclust outputs a center and a covariance matrix for each cluster it felt reasonable to calculate mahalanobis distance for every observation and for every cluster. Observations could then be classified to the mahalonobi-nearest cluster. It seems not not to work fully however.
Example code with simulated data (in this example I only use one dataset, d, and try to obtain the same classification as mclust does by the mahalanobi approach outlined above):
set.seed(123)
c1<-mvrnorm(100,mu=c(0,0),Sigma=matrix(c(2,0,0,2),ncol=2))
c2<-mvrnorm(200,mu=c(3,3),Sigma=matrix(c(3,0,0,3),ncol=2))
d<-rbind(c1,c2)
m<-Mclust(d)
int_class<-m$classification
clust1_cov<-m$parameters$variance$sigma[,,1]
clust1_center<-m$parameters$mean[,1]
clust2_cov<-m$parameters$variance$sigma[,,2]
clust2_center<-m$parameters$mean[,2]
mahal_clust1<-mahalanobis(d,cov=clust1_cov,center=clust1_center)
mahal_clust2<-mahalanobis(d,cov=clust2_cov,center=clust2_center)
mahal_clust_dist<-cbind(mahal_clust1,mahal_clust2)
mahal_classification<-apply(mahal_clust_dist,1,function(x){
match(min(x),x)
})
table(int_class,mahal_classification)
#List mahalanobis distance for miss-classified observations:
mahal_clust_dist[mahal_classification!=int_class,]
plot(m,what="classification")
#Indicate miss-classified observations:
points(d[mahal_classification!=int_class,],pch="X")
#Results:
> table(int_class,mahal_classification)
mahal_classification
int_class 1 2
1 124 0
2 5 171
> mahal_clust_dist[mahal_classification!=int_class,]
mahal_clust1 mahal_clust2
[1,] 1.340450 1.978224
[2,] 1.607045 1.717490
[3,] 3.545037 3.938316
[4,] 4.647557 5.081306
[5,] 1.570491 2.193004
Five observations are classified differently between the mahalanobi approach and mclust. In the plots they are intermediate points between the two clusters. Could someone tell me why it does not work and how I could mimic the internal classification of mclust and predict.Mclust?

Answer 1

After formulating the above question I did some additional research (thx LoBu) and found that the key was to calculate the posterior probability (pp) for an observation to belong to a certain cluster and classify according to maximal pp. The following works:
denom<-rep(0,nrow(d))
pp_matrix<-matrix(rep(NA,nrow(d)*2),nrow=nrow(d))
for(i in 1:2){
denom<-denom+m$parameters$pro[i]*dmvnorm(d,m$parameters$mean[,i],m$parameters$variance$sigma[,,i])
}
for(i in 1:2){
pp_matrix[,i]<-m$parameters$pro[i]*dmvnorm(d,m$parameters$mean[,i],m$parameters$variance$sigma[,,i]) / denom
}
pp_class<-apply(pp_matrix,1,function(x){
match(max(x),x)
})
table(pp_class,m$classification)
#Result:
pp_class 1 2
1 124 0
2 0 176
But if someone in layman terms could explain the difference between the mahalanobi and pp approach I would be greatful. What do the "mixing probabilities" (m$parameters$pro) signify?

Answer 2

In addition to Mahalanobis distance, you also need to take the cluster weight into account.
These weight the relative importance of clusters when they overlap.