smem: Select the number of mixture components and estimate the parameters of a Gaussian mixture model

Description

This function selects the number of mixture components and estimates the parameters of a Gaussian mixture model using a split-and-merge EM (SMEM) algorithm. At the first iteration, the classic EM algorithm is performed to update the parameters of the initial model. Then each following iteration consists in splitting a component into two or merging two components, before re-estimating the parameters with the EM algorithm. The selected split or merge operation is the one that maximizes a scoring function (after the re-estimation process). To avoid testing all possible operations, the split and merge candidates are initially ranked according to relevant criteria (Zhang et al., 2003). At first, the top-ranked split and top-ranked merge operations are tested. If neither of them increases the score, the second-ranked ones are considered, and so on. The SMEM algorithm stops if a given maximum rank is reached without improving the score.

Usage

smem(
  gmm,
  data,
  y = NULL,
  score = "bic",
  split = TRUE,
  merge = TRUE,
  min_comp = 1,
  max_comp = Inf,
  space = 0.5,
  max_rank = 1,
  max_iter_smem = 10,
  verbose = FALSE,
  ...
)

Value

A list with elements:

gmm: The final gmm object.
posterior: A numeric matrix containing the posterior probabilities for each observation.
seq_score: A numeric vector containing the sequence of scores measured initially and after each iteration.
seq_oper: A character vector containing the sequence of split and merge operations performed at each iteration.

Arguments

gmm: An initial object of class gmm.
data: A data frame or numeric matrix containing the data used in the SMEM algorithm. Its columns must explicitly be named after the variables of gmm and must not contain missing values.
y: A character vector containing the dependent variables if a conditional model is estimated (which involves maximizing a conditional score). If NULL (the default), the joint model is estimated.
score: A character string ("aic", "bic" or "loglik") corresponding to the scoring function.
split: A logical value indicating whether split operations are allowed (if FALSE, no mixture component can be split).
merge: A logical value indicating whether merge operations are allowed (if FALSE, no mixture component can be merged).
min_comp: A positive integer corresponding to the minimum number of mixture components.
max_comp: A positive integer corresponding to the maximum number of mixture components.
space: A numeric value in [0, 1[ corresponding to the space between two subcomponents resulting from a split.
max_rank: A positive integer corresponding to the maximum rank for testing the split and merge candidates.
max_iter_smem: A non-negative integer corresponding to the maximum number of iterations.
verbose: A logical value indicating whether iterations in progress are displayed.
...: Additional arguments passed to function em.

References

Zhang, Z., Chen, C., Sun, J. and Chan, K. L. (2003). EM algorithms for Gaussian mixtures with split-and-merge operation. Pattern Recognition, 36(9):1973--1983.

Examples

Run this code

data(data_body)
gmm_1 <- add_var(NULL, c("WAIST", "AGE", "FAT", "HEIGHT", "WEIGHT"))
res_smem <- smem(gmm_1, data_body, max_comp = 3, verbose = TRUE)