Fits mixtures of multivariate modified t-factor analyzers via the alternating expectation-conditional maximization algorithm to the given data under a clustering (default) or classification paradigm (by giving either training index or percentage of data taken to be known) in serial or parallel.
mmtfa(x, Gs=1:4, Qs=1:2, clas=0, init="kmeans", scale=TRUE, models = "all",
dfstart=50, dfupdate="approx", gauss=FALSE, eps=0.05, known=NULL,
parallel.cores=FALSE)A numeric matrix or data frame.
An integer or integer vector indicating the number of groups to fit. Default is 1-4.
An integer or integer vector indicating the number of factors to fit. Default is 1-2.
Integer between 0--100 giving the percentage of data taken to be known. Simulates a classification scenario. Additional options to be provided in future updates...
A list of initializing classification of the form that init[[G]] contains the initializing vector for all G considered (see example below). Alternatively, the user can use a character string indicating initialization method. Currently the user can choose from "kmeans" (default), `hard" random - "hard", `soft" random - "soft", and "uniform" (classification only).
Logical indicating whether or not the function should scale the data. Default is TRUE and is the prescribed method --- tEIGEN models are not scale invariant.
A character string or character vector giving the models to fit. See details for instructions on choices.
The initialized value for the degrees of freedom. The default is 50.
Character string ("approx" uses a closed form aqpproximation, "numeric" uses the uniroot function) or logical FALSE to skip degrees of freedom updates.
A vector of known classifications that can be numeric or character - optional for clustering, necessary for classification. Must be the same length as the number of rows in the data set.
Logical indicating if the algorithm should use the gaussian distribution. Currently equivalent to setting dfstart=200 and dfupdate=FALSE. Will be improved in later updates...
Tolerance value for the convergence criterion for the AECM algorithm.
Logical or integer specifying number of computing cores to utilize for coarse-grain parallelization of the algorithm. If FALSE (default), then the algorithm is run in serial. If TRUE, then detectCores() from the parallel package will determine the number of cores and use all of them.
Data used for clustering/classification.
Vector of group classifications as determined by the BIC.
BIC of the best fitted model.
Name of the best model according to the BIC.
Matrix of BIC values according to model and G. A value of -Inf is returned when the model did not converge.
Character string giving best model (BIC) details.
Value corresponding to the number of components chosen by the BIC.
Classification table for BIC-selected model (only available when known is given). When classification is used the 'known' observations are left out of the table.
The fuzzy clustering matrix for the model selected by the BIC.
The log-likelihood corresponding to the model with the best BIC.
The number of iterations until convergence for the model selected by the BIC.
List containing the fitted parameters: mean - matrix of means where the rows correspond to the component and the columns are the variables; sigma - array of covariance matrices (multivariate). Upcoming updates will increase the number of saved parameters...
List containing all the previous outputs, except x and index, pertaining to the model chosen by the best ICL (all under the same name except allicl and icl are the equivalent of allbic and bic, respectively).
Model specification (via the models argument) follows nomenclature developed from the factor analyzer decomposition of the covariance matrix. The nomenclature refers to the decomposition and constraints on the covariance matrix: $$\Sigma_g = \Lambda_g \Lambda_g' + \omega_g \delta_g$$
The first letter can be a "C" (constrained across groups) or "U" (unconstrained) and that refers to setting \(\Lambda_g = \Lambda\) or not, respectively. The second letter has the same choices, resulting in \(\omega_g = \omega\) or not. The third letter is permitted as a "C", "U", or "I" (constrained to be the identity matrix), applying those constraints to \(\delta_g\). The fourth, and final, letter refers to the degrees of freedom, and again is permitted "C" or "U".
As many models as desired can be selected and ran via the vector supplied to models. The complete list of possible names is: "UUUU", "UUUC", "UCCU","UCCC", "UUIU", "UUIC", "UCIU", "UCIC", "CUUU", "CUUC", "CCCU", "CCCC", "CUIU", "CUIC", "CCIU", "CCIC", "CUCU", "CUCC", "UUCU", "UUCC", "UCUU", "UCUC", "CCUU", "CCUC".
More commonly, subsets can be called by the following character strings:
"all" runs all 24 MMtFA models (default),
"dfunconstrained" runs the 12 unconstrained degrees of freedom models,
"dfconstrained" runs the 12 constrained degrees of freedom models,
Also note that for G=1, several models are equivalent (for example, UUUU and CCCC). Thus, for G=1 only one model from each set of equivalent models will be run.
Andrews JL and McNicholas PD (2011a), 'Extending mixtures of multivariate t-factor analyzers'. Statistics and Computing 21(3), 361--373.
Andrews JL and McNicholas PD (2011b), 'Mixtures of modified t-factor analyzers for model-based clustering, classification, and discriminant analysis'. Journal of Statistical Planning and Inference 141(4), 1479--1486.
See package manual MMtFA
# NOT RUN {
###Note that only one model is run for each example
###in order to reduce computation time
#Clustering iris data with hard random start
tirisr <- mmtfa(iris[,-5], models="UUUU", Gs=1:3, Qs=1, init="hard")
#Clustering iris data with hierarchical starting values
initial_list <- list()
clustree <- hclust(dist(iris[,-5]))
for(i in 1:3){
initial_list[[i]] <- cutree(clustree,i)
}
tirish <- mmtfa(iris[,-5], models="CUCU", Gs=1:3, Qs=1, init=initial_list)
#Classification with the iris data set via percentage of data taken to have known membership
tirisc <- mmtfa(iris[,-5], Qs=1, models="CUIU", init="uniform",clas=50, known=iris[,5])
tirisc$tab
# }
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