EMAlgorithm function

EM algorithm for Gaussian mixture models

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

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

Arguments

• x: A matrix of observations where each row correspond to an observation and each columns to a feature/variable.
• theta: A list of parameters of class theta as described in rtheta. Optional. If not provided m should be given.
• m: numeric. The number of components if theta is not supplied.
• eps: The maximal required difference in successive likelihoods to establish convergence.
• max.ite: The maximum number of iterations.
• trace.theta: Logical. If TRUE, all estimates are stored and returned. Default is FALSE.
• verbose: Set to TRUE for verbose output. Default is FALSE.

Returns

A list of length 3 with elements: - theta: A list of the estimated parameters as described in rtheta.

• loglik.tr: A numeric vector of the log-likelihood trace.

• kappa: A 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. If theta is not given, a k-means clustering is used to determine the initial theta.

Examples

set.seed(3)
true.theta <- rtheta(d = 2, m = 3, method = "old")
true.theta$sigma <- lapply(true.theta$sigma, cov2cor) # Scale
## Not run:

plot(true.theta, nlevels = 20, add.ellipses = TRUE)
## End(Not run)

data <- SimulateGMCMData(n = 1000, theta = true.theta)
start.theta <- rtheta(d = 2, m = 3)
start.theta$mu <- t(kmeans(data$z, 3)$centers) # More sensible location estimates
start.theta <- as.theta(start.theta) # Coerce the matrix to a list
res <- GMCM:::EMAlgorithm(data$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)])

See Also

rtheta, PseudoEMAlgorithm

Author(s)

Anders Ellern Bilgrau anders.ellern.bilgrau@gmail.com