Programmer Guide/Command Reference/EVAL/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 r is vector with 10 elements, 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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