gmm: Finite Gaussian Mixture Model

In T4cluster: Tools for Cluster Analysis

Description

Finite Gaussian Mixture Model (GMM) is a well-known probabilistic clustering algorithm by fitting the following distribution to the data

f(x; ≤ft\lbrace μ_k, Σ_k \right\rbrace_{k=1}^K) = ∑_{k=1}^K w_k N(x; μ_k, Σ_k)

with parameters w_k's for cluster weights, μ_k's for class means, and Σ_k's for class covariances. This function is a wrapper for Armadillo's GMM function, which supports two types of covariance models.

Usage

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

Arguments

data	an (n\times p) matrix of row-stacked observations.
k	the number of clusters (default: 2).
...	extra parameters including maxiter the maximum number of iterations (default: 10). usediag a 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
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,4), pty="s")
plot(X2d, col=lab, pch=19, main="true label")
plot(X2d, col=cl2, pch=19, main="gmm: k=2")
plot(X2d, col=cl3, pch=19, main="gmm: k=3")
plot(X2d, col=cl4, pch=19, main="gmm: k=4")
par(opar)

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