smm_fit_em_GNL08: Estimate Student's t Mixture parameters using Expectation...

In merkys/MixtureFitting: Fitting of Univariate Mixture Distributions to Data using Various Approaches

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

x	data vector
p	initialization vector of 4*n parameters, where n is number of mixture components. Structure of p vector is p = c( A1, A2, ..., An, mu1, mu2, ..., mun, k1, k2, ..., kn, ni1, ni2, ..., nin ), where Ai is the proportion of i-th component, mui is the center of i-th component, ki is the concentration of i-th component and nii is the degrees of freedom of i-th component.
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.
collect.history	logical. If set to TRUE, a list of parameter values of all iterations is returned.
debug	flag to turn the debug prints on/off.
min.sigma	minimum value of sigma
min.ni	minimum value of degrees of freedom
max.df	maximum value of degrees of freedom
max.steps	maximum number of steps, may be infinity
polyroot.solution	polyroot finding method used to approximate digamma function. Possible values are 'jenkins_taub' and 'newton_raphson'.
convergence	function to use for convergence checking. Must accept function values of the last two iterations and return TRUE or FALSE.
unif.component	should a uniform component for outliers be added, as suggested by Cousineau & Chartier (2010)?

Value

A list.

Author(s)

Andrius Merkys

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 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 https://revistas.usb.edu.co/index.php/IJPR/article/view/844

merkys/MixtureFitting documentation built on July 5, 2025, 5:43 a.m.