Finite Gaussian Mixture Model (GMM) is a well-known probabilistic clustering algorithm by fitting the following distribution to the data $$f(x; \left\lbrace \mu_k, \Sigma_k \right\rbrace_{k=1}^K) = \sum_{k=1}^K w_k N(x; \mu_k, \Sigma_k)$$ with parameters $$w_k$$'s for cluster weights, $$\mu_k$$'s for class means, and $$\Sigma_k$$'s for class covariances. This function is a wrapper for Armadillo's GMM function, which supports two types of covariance models.

gmm(data, k = 2, ...)

## Arguments

data an $$(n\times p)$$ matrix of row-stacked observations. the number of clusters (default: 2). extra parameters including maxiterthe maximum number of iterations (default: 10). 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.

## Examples

# -------------------------------------------------------------
#            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)$Y ## CLUSTERING WITH DIFFERENT K VALUES cl2 = gmm(X, k=2)$cluster
cl3 = gmm(X, k=3)$cluster cl4 = gmm(X, k=4)$cluster

## VISUALIZATION