init.cfust: Initialization for Fitting Finite Mixtures of Canonical...

In EMMIXcskew: Fitting Mixtures of CFUST Distributions

Description

Computes different sets of initial values for finite mixtures of canonical fundamental skew t (FM-CFUST) model based on an initial clustering, transformation approiach, moment-based approach, or nested-model appraoch.

Usage

init.cfust(g, dat, q=p, initial=NULL, known=NULL, clust=NULL, nkmeans=20, 
    method=c("moments","transformation","EMMIXskew","EMMIXuskew"))
init.fmcfust(g, dat, q=p, initial=NULL, known=NULL, clust=NULL, nkmeans=20, 
    method=c("moments","transformation","EMMIXskew","EMMIXuskew"))

Arguments

g	a scalar specifying the number of components in the mixture model
dat	the data matrix giving the coordinates of the point(s) where the density is evaluated. This is either a vector of length p or a matrix with p columns.
q	a scalar specifying how many number of columns the skewness matrix delta has.
initial	(optional) a list containing the initial parameters of the mixture model. See the 'Details' section. The default is NULL.
known	(optional) a list containing parameters of the mixture model that are known and not required to be estimated. See the 'Details' section. The default is NULL.
clust	(optional) a numeric value of length nrow(dat) containing the initial labels for each data point in dat. The default is NULL, indicating no initial clustering is known.
nkmeans	(optional) a numeric value indicating how many k-means trials to be used when searching for initial values. The default is 20.
method	(optional) a string indicating which method to use to generate initial values. See Details.

Details

As the EM algorithm is sensitive to the starting value, it is highly recommended to apply a wide range different initializations. To obtain different sets of starting values using the strategy described in Section 5.1.3 of Lee and McLachlan (2014), init.cfust() can be used, which will return a list of objects with the same structure as initial. An example is given in the examples section below.

The argument known, if specified, is a list structure containing at least one of mu, sigma, delta, dof, pro (See dfmcfust for the structure of each of these elements). Note that although not all parameters need to be provided in known, the parameters that are provided must be fully specified. They cannot be partially specified, e.g. only some elements or some components are specified.

Value

a list object containing the following parameters:

mu	a list of g numeric matrices containing the location parameter for each component.
sigma	a list of g numeric matrices containing the scale parameter for each component.
delta	a list of g numeric matrices containing the skewness matrix for each component.
dof	a numeric vector of length g representing the degrees of freedom for each component.
pro	a vector of length of g specifying the mixing proportions for each component.
tau	an g by n matrix of initial probability of component membership.
clusters	a vector of length n of initial partition.
loglik	the initial log likelihood value.

References

Lee S.X. and McLachlan, G.J. (2016). Finite mixtures of canonical fundamental skew t-distributions: the unification of the restricted and unrestricted skew t-mixture models. Statistics and Computing 26, 573-589.

Lee S.X. and McLachlan, G.J. (2017). EMMIXcskew: An R Package for the Fitting of a Mixture of Canonical Fundamental Skew t-Distributions. Journal of Statistical Software 83(3), 1-32. URL 10.18637/jss.v083.i03.

See Also

rfmcfust, dfmcfust, fmcfust.contour.2d

Examples

	#a short demo using geyser data
	library(MASS)
	data(geyser)
	initial.transformation <- init.cfust(3, geyser, method="transformation") 
	initial.transformation$loglik

EMMIXcskew documentation built on May 2, 2019, 6:59 a.m.