EMMIXuskew (version 0.11-6)

fmmst.init: Initialization for Fitting Finite Mixtures of Unrestricted Multivariate Skew t Distributions

Description

Computes different sets of initial values for finite mixtures of unrestricted multivariate skew t (FM-uMST) model based on an initial clustering.

Usage

fmmst.init(g, dat, known=NULL, clust=NULL, nkmeans=20, tmethod=1)

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.

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.

tmethod

(optional) an integer indicating which method to use when computing t distribution function values. See pmt for details.

Value

a list of initializations for fmmst, each 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 parameter 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.

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), fmmst.init() 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 dfmmst 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.

References

Lee S, McLachlan G (2011). On the fitting of mixtures of multivariate skew t-distributions via the EM algorithm. arXiv:1109.4706 [stat.ME]

Lee, S. and McLachlan, G.J. (2014) Finite mixtures of multivariate skew t-distributions: some recent and new results. Statistics and Computing, 24, 181-202.

Lee, S. and McLachlan, G.J. (2013) EMMIXuskew: An R package for fitting mixtures of multivariate skew t-distributions via the EM algorithm. Journal of Statistical Software, 55(12), 1-22. URL http://www.jstatsoft.org/v55/i12/.

See Also

rfmmst, dfmmst, fmmst.contour.2d

Examples

#a short demo using AIS data
data(ais)
Fit.init <- fmmst.init(2, ais[,c(2,12)])  

#the number of available initializations
length(Fit.init)  

#getting the first set of available initialization
Fit.init[[1]]     
## Not run: 
# Fit1 <- fmmst(2, ais[,c(2,12)], initial=Fit.init[[1]])
# Fit2 <- fmmst(2, ais[,c(2,12)], initial=Fit.init[[2]])
# ## End(Not run)