nopenalty: Classical Model-based Clustering

In PARSE: Model-Based Clustering with Regularization Methods for High-Dimensional Data

Description

This function estimates the model-based clustering which is under the framework of finite mixture models.

Usage

nopenalty(K, y, N = 100, kms.iter = 100, kms.nstart = 100,
           eps.diff = 1e-5, eps.em = 1e-5,
           model.crit = 'gic', short.output = FALSE)

Arguments

K	A vector of the number of clusters
y	A p-dimensional data matrix. Each row is an observation
N	The maximum number of iterations in the EM algorithm. The default value is 100.
kms.iter	The maximum number of iterations in the K-means algorithm whose outputs are the starting values for the EM algorithm
kms.nstart	The number of starting values in K-means
eps.diff	The lower bound of pairwise difference of two mean values. Any value lower than it is treated as 0
eps.em	The lower bound for the stopping criterion.
model.crit	The criterion used to select the number of clusters K. It is either ‘bic’ for Bayesian Information Criterion or ‘gic’ for Generalized Information Criterion.
short.output	A short version of output is needed or not. A short version is used for computing the adaptive parameters in APFP or APL1 methods. The default value is FALSE.

Details

This function estimates parameters μ, Σ, π and the clustering assignments in the model-based clustering using the mixture model,

y \sim ∑_{k=1}^K π_k f(y|μ_k, Σ)

where f(y|μ_k, Σ_k) is the density function of Normal distribution with mean μ_k and variance Σ. Here we assume that each cluster has the same diagonal variance.

This function is also used to compute the adaptive parameters for functions apfp and apL1.

Value

This function returns the esimated parameters and some statistics of the optimal model within the given K and λ, which is selected by BIC when model.crit = 'bic' or GIC when model.crit = 'gic'.

mu.hat.best	The estimated cluster means.
sigma.hat.best	The estimated covariance.
p.hat.best	The estimated cluster proportions.
s.hat.best	The clustering assignments.
K.best	The value of K that provides the optimal model
llh.best	The log-likelihood of the optimal model
gic.best	The GIC of the optimal model
bic.best	The BIC of the optimal model
ct.mu.best	The degrees of freedom in the cluster means of the optimal model

References

Fraley, C., & Raftery, A. E. (2002) Model-based clustering, discriminant analysis, and density estimation. Journal of the American statistical Association 97(458), 611–631.

See Also

apfp apL1 parse

Examples

y <- rbind(matrix(rnorm(100,0,1),ncol=2), matrix(rnorm(100,4,1), ncol=2))
output <- nopenalty(K = c(1:2), y)
output$mu.hat.best

PARSE documentation built on May 2, 2019, 9:57 a.m.