RobustEM (version 1.0)

cluster_em: Clustering Algorithm

Description

This function estimates the mixture model by one of three EM algorithms and clusters observations to the component in which their density is the highest.

Usage

cluster_em(x, k,method=c("reg","rcm","kotz"),iter_max=100)

Arguments

x

This is a matrix or data frame of observations, where rows correspond to n observations and columns correspond to d variables. Categorical variables are not allowed.

k

This is an integer specifying the number of mixture components (clusters).

method

This specifies which of the algorithms is to be used. Presently there are three algorithms that can be used. These are reg(regular-EM), rcm(spatial-EM) and kotz. Regular EM uses sample mean and sample covariance in each M step and hence is sensitive to outliers. Spatial EM utilizes median-based location and rank-based scatter estimators, hence enhancing stability and robustness. It is robust to outliers and initial values. Robustness of Kotz EM is between that of other two.

iter_max

This is a parameter maxiter. It is the maximum number of iterations of the EM algorithm. The default value is 100. If the EM algorithm has not converged at this iteration, the estimates for the 100th iteration are returned and a warning message is presented.

Value

clusters

A factor consisting of cluster labels of observations.

mean

The mean of each component. If there is more than one component, it forms a matrix whose kth row is the mean of kth component of the mixture model.

sigma

A list of variance estimator for each component of the model.

taul

A vector of the mixing proportion for each of the components.

Details

The cluster_em function provides mixture model estimation by one of EM algorithms used and clustering of data. Observations clustered to the component in which their density is highest.

References

Yu, K., Dang, X., Bart Jr, H. and Chen, Y. (2015). Robust Model-based Learning via Spatial-EM Algorithm. IEEE Transactions on Knowledge and Data Engineering, 27(6), 1670-1682.

Examples

x1<-matrix(rnorm(2*200),ncol=2)
x2<-matrix(rnorm(2*200,2,1),ncol=2)
x <- rbind(x1,x2)
k<-2
cluster_em(x,k,"rcm")