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\name{smm_fit_em_GNL08}
\alias{smm_fit_em_GNL08}
\docType{methods}
\title{Estimate Student's t Mixture parameters using Expectation Maximization.}
\description{
Estimates parameters for univariate Student's t mixture using
Expectation Maximization algorithm, according to Eqns. 12--17 of
Gerogiannis et al. (2009).
}
\usage{
smm_fit_em_GNL08( x, p, epsilon = c( 1e-6, 1e-6, 1e-6, 1e-6 ),
collect.history = FALSE, debug = FALSE,
min.sigma = 1e-256, min.ni = 1e-256,
max.df = 1000, max.steps = Inf,
polyroot.solution = 'jenkins_taub',
convergence = abs_convergence,
unif.component = FALSE )
}
\arguments{
\item{x}{data vector}
\item{p}{
initialization vector of 4*\emph{n} parameters, where \emph{n} is
number of mixture components. Structure of p vector is
p = c( A1, A2, ..., A\emph{n}, mu1, mu2, ..., mu\emph{n}, k1, k2, ..., k\emph{n}, ni1, ni2, ..., ni\emph{n} ),
where A\emph{i} is the proportion of \emph{i}-th component,
mu\emph{i} is the center of \emph{i}-th component,
k\emph{i} is the concentration of \emph{i}-th component and
ni\emph{i} is the degrees of freedom of \emph{i}-th component.
}
\item{epsilon}{
tolerance threshold for convergence. Structure of epsilon is
epsilon = c( epsilon_A, epsilon_mu, epsilon_k, epsilon_ni ), where
epsilon_A is threshold for component proportions,
epsilon_mu is threshold for component centers,
epsilon_k is threshold for component concentrations and
epsilon_ni is threshold for component degrees of freedom.
}
\item{collect.history}{
logical. If set to TRUE, a list of parameter values of all
iterations is returned.
}
\item{debug}{
flag to turn the debug prints on/off.
}
\item{min.sigma}{minimum value of sigma}
\item{min.ni}{minimum value of degrees of freedom}
\item{max.df}{maximum value of degrees of freedom}
\item{max.steps}{maximum number of steps, may be infinity}
\item{polyroot.solution}{
polyroot finding method used to approximate digamma function.
Possible values are 'jenkins_taub' and 'newton_raphson'.
}
\item{convergence}{
function to use for convergence checking.
Must accept function values of the last two iterations and return TRUE or FALSE.
}
\item{unif.component}{
should a uniform component for outliers be added, as suggested by Cousineau & Chartier (2010)?
}
}
\value{
A list.
}
\references{
Gerogiannis, D.; Nikou, C. & Likas, A.
The mixtures of Student's t-distributions as a robust framework for rigid registration.
Image and Vision Computing, Elsevier BV, 2009, 27, 1285--1294
\url{https://www.cs.uoi.gr/~arly/papers/imavis09.pdf}
Cousineau, D. & Chartier, S.
Outliers detection and treatment: a review.
International Journal of Psychological Research, 2010, 3, 58--67
\url{https://revistas.usb.edu.co/index.php/IJPR/article/view/844}
}
\author{Andrius Merkys}
|
