qclust (version 1.0)

Qclust: Robust Estimation of Gaussian Mixture Models

Description

Robust estimation of Gaussian mixture models and robust model-based clustering.

Usage

Qclust(d, K = NULL, modelNames = NULL, q)

Arguments

d

A data matrix, n by p. n is sample size, p is the dimension.

K

The complexity of the mixture model, an integer.

modelNames

A string indicate the type of "models". The notation is consistent with the package mclust.

q

A tuning parameter, 0

Value

The function returns a list which contains:

parameters

Estimated parameters of Gaussian mixture models

References

Ferrari, D. and Yang, Y., (2010). Maximum Lq-likelihood estimation, Annals of Statistics. Fraley, C., Raftery, A. E., Murphy, T. B., and Scrucca, L., (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington. Fraley, C., and Raftery, A.E., (2002). Model-Based Clustering, Discriminant Analysis, and Density Estimation. Journal of the American Statistical Association, 97, 611-631. McLachlan, G.J., and Peel, D., (2000). Finite Mixture Models, Wiley, ISBN 0-471-00626-2.

Examples

n = 200
set.seed(12345)
true_para=list()
true_para$pro=rep(1/3,3)
true_para$mean=matrix(c(-6,1.5,0,0,6,1.5),2,3)
true_para$variance$sigma=array(c(5,4,4,5,5,-4,-4,5,1.56,0,0,1.56),dim=c(2,2,3))
G=ncol(true_para$mean)
z = sample(1:G,n,true_para$pro,replace=TRUE)
z = sort(z)
X=matrix(NA,n,nrow(true_para$mean))
for (i in 1:G)
{
  X[z==i,]=rmvnorm(sum(z==i),true_para$mean[,i],true_para$variance$sigma[,,i])
}
plot(X,pch=20)
qfit=Qclust(X,K=3,modelNames="VVV",q=0.9)
plot(qfit,what="classification")