stpcm: Skew-t Parsimonious Clustering Models

In mixture: Mixture Models for Clustering and Classification

Skew-t Parsimonious Clustering Models

Description

Carries out model-based clustering or classification using some or all of the 14 parsimonious Skew-t clustering models (STPCM).

Usage

stpcm(data=NULL, G=1:3, mnames=NULL,
		start=2, label=NULL, 
		veo=FALSE, da=c(1.0),
		nmax=1000, atol=1e-8, mtol=1e-8, mmax=10, burn=5,
		pprogress=FALSE, pwarning=FALSE, 
		stochastic = FALSE, latent_method="standard") 

Arguments

data	A matrix or data frame such that rows correspond to observations and columns correspond to variables. Note that this function currently only works with multivariate data p > 1.
G	A sequence of integers giving the number of components to be used.
mnames	The models (i.e., covariance structures) to be used. If NULL then all 14 are fitted.
start	If 0 then the random soft function is used for initialization. If 1 then the random hard function is used for initialization. If 2 then the kmeans function is used for initialization. If >2 then multiple random soft starts are used for initialization. If is.matrix then matrix is used as an initialization matrix as along as it has non-negative elements. Note: only models with the same number of columns of this matrix will be fit.
label	If NULL then the data has no known groups. If is.integer then some of the observations have known groups. If label[i]=k then observation belongs to group k. If label[i]=0 then observation has no known group. See Examples.
veo	Stands for "Variables exceed observations". If TRUE then if the number variables in the model exceeds the number of observations the model is still fitted.
da	Stands for Determinstic Annealing. A vector of doubles.
nmax	The maximum number of iterations each EM algorithm is allowed to use.
atol	A number specifying the epsilon value for the convergence criteria used in the EM algorithms. For each algorithm, the criterion is based on the difference between the log-likelihood at an iteration and an asymptotic estimate of the log-likelihood at that iteration. This asymptotic estimate is based on the Aitken acceleration and details are given in the References.
mtol	A number specifying the epsilon value for the convergence criteria used in the M-step in the EM algorithms.
mmax	The maximum number of iterations each M-step is allowed in the GEM algorithms.
burn	The burn in period for imputing data. (Missing observations are removed and a model is estimated seperately before placing an imputation step within the EM.)
pprogress	If TRUE print the progress of the function.
pwarning	If TRUE print the warnings.
stochastic	If TRUE , it will run stochastic E step variant.
latent_method	If "standard", it will use the standard E step for latent variable of a Normal Variance Mean Mixture, if "random" it will run a random draw from a GIG distribution.

Details

The data x are either clustered or classified using Skew-t mixture models with some or all of the 14 parsimonious covariance structures described in Celeux & Govaert (1995). The algorithms given by Celeux & Govaert (1995) is used for 12 of the 14 models; the "EVE" and "VVE" models use the algorithms given in Browne & McNicholas (2014). Starting values are very important to the successful operation of these algorithms and so care must be taken in the interpretation of results.

Value

An object of class vgpcm is a list with components:

map	A vector of integers indicating the maximum a posteriori classifications for the best model.
model_objs	A list of all estimated models with parameters returned from the C++ call.
best_model	A class of vgpcm_best containing; the number of groups for the best model, the covariance structure, and Bayesian Information Criterion (BIC) value.
loglik	The log-likelihood values from fitting the best model.
z	A matrix giving the raw values upon which map is based.
BIC	A G by mnames by 3 dimensional array with values pertaining to BIC calculations. (legacy)
gpar	A list object for each cluster pertaining to parameters. (legacy)
startobject	The type of object inputted into start.
row_tags	If there were NAs in the original dataset, a vector of indices referencing the row of the imputed vectors is given.

Best Model

An object of class stpcm_best is a list with components:

model_type	A string containg summarized information about the type of model estimated (Covariance structure and number of groups).
model_obj	An internal list containing all parameters returned from the C++ call.
BIC	Bayesian Index Criterion (positive scale, bigger is better).
loglik	Log liklihood from the estimated model.
nparam	Number of a parameters in the mode.
startobject	The type of object inputted into start.
G	An integer representing the number of groups.
cov_type	A string representing the type of covariance matrix (see 14 models).
status	Convergence status of EM algorithm according to Aitken's Acceleration
map	A vector of integers indicating the maximum a posteriori classifications for the best model.
row_tags	If there were NAs in the original dataset, a vector of indices referencing the row of the imputed vectors is given.

Internal Objects

All classes contain an internal list called model_obj or model_objs with the following components:

zigs	a posteori matrix
G	An integer representing the number of groups.
sigs	A vector of covariance matrices for each group
mus	A vector of location vectors for each group
alphas	A vector containg skewness vectors for each group
gammas	A vector containing estimated gamma parameters for each group

Note

Dedicated print, plot and summary functions are available for objects of class vgpcm.

Author(s)

Nik Pocuca, Ryan P. Browne and Paul D. McNicholas.

Maintainer: Paul D. McNicholas <[e-mail]>

References

McNicholas, P.D. (2016), Mixture Model-Based Classification. Boca Raton: Chapman & Hall/CRC Press

Browne, R.P. and McNicholas, P.D. (2014). Estimating common principal components in high dimensions. Advances in Data Analysis and Classification 8(2), 217-226.

Wei, Y., Tang, Y. and McNicholas, P.D. (2019), 'Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data', Computational Statistics and Data Analysis 130, 18-41.

Celeux, G., Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern Recognition 28(5), 781-793.

Examples

data("sx3")

## Not run: 

### estimate "VVV" "EVE"
ax = stpcm(sx3, G=1:3, mnames=c("VVV","EVE"), start=0)
summary(ax)
ax


### estimate all 14 covariance structures 
ax = stpcm(sx3, G=1:3, mnames=NULL, start=0)
summary(ax)
ax

### model based classification
sx3.label = c(rep(1,1000),rep(2,1000))
plot(sx3, col=sx3.label)
axl = stpcm(sx3, G=2, mnames=c("VVV", "EVE"), label=sx3.label)
summary(axl)


## End(Not run)

mixture documentation built on Sept. 27, 2023, 1:06 a.m.