normalLocOrder: Estimate the Number of Components in a Multivariate Normal...

In tmanole/GroupSortFuse: Estimating the Number of Components in Finite Mixture Models

Description

Estimate the order of a finite mixture of multivariate normal densities with respect to the mean parameter, whose variance-covariance matrices are common but potentially unknown.

Usage

normalLocOrder(y, lambdas, K = NULL, sigma = NULL, arbSigma = TRUE,
  ...)

Arguments

y	n by D matrix consisting of the data, where n is the sample size and D is the dimension.
lambdas	Vector of tuning parameter values.
K	Upper bound on the true number of components. If K is NULL, at least one of theta and pii must be non-NULL, and K is inferred from their number of columns.
sigma	D by D matrix, which is the starting value for the common variance-covariance matrix. If NULL, arbSigma must be TRUE, and in this case the starting value is set to be the sample variance-covariance of the data.
arbSigma	Equals TRUE if the common variance-covariance matrix should be estimated, and FALSE if it should stay fixed, and equal to sigma.
...	Additional control parameters. See the Details section.

Details

The following is a list of additional control parameters.

mu

D by K matrix of starting values where each column is the mean vector for one component. If theta=NULL, the starting values are chosen using the procedure of Benaglia et al. (2009).

pii

Vector of size K whose elements must sum to 1, consisting of the starting values for the mixing proportions. If NULL, it will be set to a discrete uniform distribution with K support points.

penalty

Choice of penalty, which may be "SCAD", "MCP", "SCAD-LLA", "MCP-LLA" or "ADAPTIVE-LASSO". Default is "SCAD".

uBound

Upper bound on the tuning parameter of the proximal gradient descent algorithm.

C

Tuning parameter for penalizing the mixing proportions.

a

Tuning parameter for the SCAD or MCP penalty. Default is 3.7.

convMem

Convergence criterion for the modified EM algorithm.

convPgd

Convergence criterion for the proximal gradient descent algorithm.

maxMem

Maximum number of iterations of the modified EM algorithm.

maxPgd

Maximum number of iterations of the proximal gradient descent algorithm.

verbose

If TRUE, print updates while the function is running.

Value

An object with S3 classes gsf and normalLocGsf, consisting of a list with the estimates produced for every tuning parameter in lambdas.

References

Manole, T., Khalili, A. 2019. "Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedure".

Benaglia, T., Chauveau, D., Hunter, D., Young, D. 2009. "mixtools: An R package for analyzing finite mixture models". Journal of Statistical Software. 32(6): 1-29.

Examples

 # Example 1: Seeds Data.
   data(seeds) 
   y <- cbind(seeds[,2], seeds[,6])
   set.seed(1)
   out <- normalLocOrder(y, K=12, lambdas=seq(0.1, 1.7, 0.3), maxPgd=200, maxMem=500)
   tuning <- bicTuning(y, out)
   plot(out, gg=FALSE, eta=TRUE, vlines=TRUE, opt=tuning$result$lambda)
  
 # Example 2: Old Faithful Data.
   data(faithful)
   set.seed(1)
   out <- normalLocOrder(faithful, K=10, 
             lambdas=c(0.1, 0.25, 0.5, 0.75, 1.0, 2), penalty="MCP-LLA", a=2, maxPgd=200, maxMem=500)

   # Requires ggplot2.
   plot(out, gg=TRUE, eta=FALSE)

tmanole/GroupSortFuse documentation built on Jan. 12, 2022, 10:37 p.m.