em

Implementation of the Expectation Maximization (EM) algorithm for finding maximum likelihood estimates of the parameters of a Gaussian Mixture Model (GMM) (i.e. estimates the model parameters for which the observed data are most likely).

Usage

em(x, meantable, membertable, sigmatable, wtable, aposterioritable, minvar, emmaxit, likthresh {, accurate})

x

feature vectors, 1 feature vector per row ((N_vectors x N_dimensions)

meantable

output matrix for estimated mean vectors (N_mixtures x N_dimensions)

membertable

vector with N_vectors elements, defining the feature vector memberships to mixtures, resulting from prior clustering

sigmatable

output matrix for estimated covariance vectors (i.e. diagonal of covariance matrices) of mixture model (N_mixtures x N_dimensions)

wtable

output vector of estimated mixture weights (N_mixtures)

aposterioritable

if a table item is given, it will contain the output a posteriori probabilities of the feature vectors, otherwise (if a number is given) it won't be changed

minvar

minimum variance

emmaxit

maximum number of iterations

liktresh

log-likelihood threshold; if the difference between log-likelihoods of two consecutive iterations is less than this threshold, the algorithm halts

accurate

• if 1, the accurate log-likelihood estimation is used
• otherwise use the Intel IPP fast log. add method

Result

The estimated model parameters are stored in the references meantable, sigmatable, wtable and (optional) aposterioritable. The return value is 10 element vector r containing informations about the estimation process.

r[0]	number of feature vectors
r[1]	number of dimensions
r[2]	number of mixture components
r[3]	number of iterations performed by the algorithm
r[4]	joint log-likelihood of the data in the estimated model
r[5]	-1 (initialisation max. iterations, apparently unused)
r[6]	maximum number of iterations
r[7]	log-likelihood threshold
r[8]	value of the "accurate" parameter
r[9]	0 (= method used is EM for diagonal covariance matrices)

See also

haclust, modclust, density, svd

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