EMAlgorithm: EM algorithm for Gaussian mixture models

Description

The regular expectation-maximization algorithm for general multivariate Gaussian mixture models.

Usage

EMAlgorithm(x, theta, eps = 1e-06, max.ite = 1e+05, trace.theta = FALSE,
  verbose = FALSE)

Arguments

A matrix of observations where rows correspond to features and columns to experiments.

theta

A list of parameters as described in rtheta.

eps

The maximal required difference in sucessive likelihoods to establish convergence.

max.ite

The maximum number of interations.

trace.theta

Logical. If TRUE, all estimates are stored and returned. Default is FALSE.

verbose

Set to TRUE for verbose output. Default is FALSE.

Value

A list of length 3 with elements:
thetaA list of the estimated parameters as described in rtheta.
loglik.trA numeric vector of the log-likelihood trace.
kappaA matrix where kappa[i,j] is the probability that x[i, ] is realized from the j'th component.

Details

Though not as versatile, the algorithm can be a faster alternative to Mclust in the mclust-package.

Examples

Run this code

set.seed(10)
data <- SimulateGMCMData(n = 1000, d = 2, m = 3)
start.theta <- rtheta(d = 2, m = 3)
res <- GMCM:::EMAlgorithm(data$z, theta = start.theta)

par(mfrow = c(1,2))
plot(data$z, cex = 0.5, pch = 16, main = "Simulated data",
     col = rainbow(3)[data$K])
plot(data$z, cex = 0.5, pch = 16, main = "GMM clustering",
     col = rainbow(3)[apply(res$kappa,1,which.max)])