pcm: Parsimonious Clustering Models

In mixture: Mixture Models for Clustering and Classification

Parsimonious Clustering Models

Description

Carries out model-based clustering or classification using some or all of the 14 parsimonious settings with any one of the GPCM,STPCM,VGPCM, or GHPCM families.

Usage

pcm(data=NULL, G=1:3, pcmfamily=c(gpcm,vgpcm,tpcm),
		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) 

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.
pcmfamily	The family of models to be used. If NULL then all are fitted.
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.

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 pcm is a list with components:

gpcm	If applicable, the output of running the Gaussian Parsimonious Family.
vgpcm	If applicable, the output of running the Variance-Gamma Parsimonious Family.
stpcm	If applicable, the output of running the Skew-T Parsimonious Family.
ghpcm	If applicable, the output of running the Generalized Hyperbolic Parsimonious Family.
best_model	An object of corresponding to the output of the best performing family.

Note

Dedicated print, and summary functions are available for objects of class pcm, gpcm, ghpcm, stpcm, or 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.

Browne, R.P. and McNicholas, P.D. (2015), 'A mixture of generalized hyperbolic distributions', Canadian Journal of Statistics 43(2), 176-198.

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("x2")

## Not run: 

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

print(ax)


## End(Not run)

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