# gmm11R: Regularized GMM by Ruan et al. (2011) In T4cluster: Tools for Cluster Analysis

## Description

Ruan et al. (2011) proposed a regularized covariance estimation by graphical lasso to cope with high-dimensional scenario where conventional GMM might incur singular covariance components. Authors proposed to use λ as a regularization parameter as normally used in sparse covariance/precision estimation problems and suggested to use the model with the smallest BIC values.

## Usage

 1 gmm11R(data, k = 2, lambda = 1, ...) 

## Arguments

 data an (n\times p) matrix of row-stacked observations. k the number of clusters (default: 2). lambda regularization parameter for graphical lasso (default: 1). ... extra parameters including maxiterthe maximum number of iterations (default: 10). nstartthe number of random initializations (default: 5). usediaga logical; covariances are diagonal if TRUE, or full covariances are returned for FALSE (default: FALSE).

## Value

a named list of S3 class T4cluster containing

cluster

a length-n vector of class labels (from 1:k).

mean

a (k\times p) matrix where each row is a class mean.

variance

a (p\times p\times k) array where each slice is a class covariance.

weight

a length-k vector of class weights that sum to 1.

loglkd

log-likelihood of the data for the fitted model.

algorithm

name of the algorithm.

## References

\insertRef

ruan_regularized_2011T4cluster

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 # ------------------------------------------------------------- # clustering with 'iris' dataset # ------------------------------------------------------------- ## PREPARE data(iris) X = as.matrix(iris[,1:4]) lab = as.integer(as.factor(iris[,5])) ## EMBEDDING WITH PCA X2d = Rdimtools::do.pca(X, ndim=2)$Y ## COMPARE WITH STANDARD GMM cl.gmm = gmm(X, k=3)$cluster cl.11Rf = gmm11R(X, k=3)$cluster cl.11Rd = gmm11R(X, k=3, usediag=TRUE)$cluster ## VISUALIZATION opar <- par(no.readonly=TRUE) par(mfrow=c(1,3), pty="s") plot(X2d, col=cl.gmm, pch=19, main="standard GMM") plot(X2d, col=cl.11Rf, pch=19, main="gmm11R: full covs") plot(X2d, col=cl.11Rd, pch=19, main="gmm11R: diagonal covs") par(opar) 

T4cluster documentation built on Aug. 16, 2021, 9:07 a.m.