emnmix_multivariate: Custom R implementation of the EM algorithm in the...

In bastienchassagnol/RGMMBench: A benchmark on Gaussian mixtures in R

Custom R implementation of the EM algorithm in the multivariate context

Description

Custom R implementation of the EM algorithm in the multivariate context

Usage

emnmix_multivariate(
  x,
  k,
  epsilon = 10^-4,
  itmax = 500,
  nstart = 10L,
  start = NULL,
  initialisation_algorithm = "kmeans",
  ...
)

em_Rmixmod_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  epsilon = 10^-4,
  itmax = 500,
  start = NULL,
  ...
)

em_EMCluster_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  epsilon = 10^-4,
  itmax = 500,
  start = NULL,
  ...
)

em_bgmm_multivariate(
  x = x,
  k = 2,
  epsilon = 10^-4,
  itmax = 500,
  initialisation_algorithm = "kmeans",
  start = NULL,
  ...
)

em_flexmix_multivariate(
  x = x,
  k = 2,
  epsilon = 10^-4,
  itmax = 500,
  minprior = 0.05,
  initialisation_algorithm = "kmeans",
  start = NULL,
  ...
)

em_mixtools_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  epsilon = 10^-4,
  itmax = 500,
  start = NULL,
  ...
)

em_mclust_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  start = NULL,
  epsilon = 10^-4,
  itmax = 500,
  ...
)

em_GMKMcharlie_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  embedNoise = 1e-06,
  epsilon = 10^-4,
  itmax = 500,
  start = NULL,
  parallel = FALSE,
  ...
)

em_clustvarsel_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  epsilon = 10^-4,
  itmax = 500,
  back_steps = 20,
  start = NULL,
  ...
)

em_HDclassif_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  epsilon = 10^-4,
  itmax = 500,
  start = NULL,
  kmeans.control = list(iter.max = 200L, nstart = 10L, algorithm = "Hartigan-Wong"),
  mc.cores = getOption("mc.cores", parallel::detectCores())
)

em_pgmm_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  epsilon = 10^-4,
  itmax = 500,
  aic_acc = 0.1,
  start = NULL,
  arguments_HDclassif = list(init = "kmeans", kmeans.control = list(iter.max = 200L,
    nstart = 10L, algorithm = "Hartigan-Wong"), mc.cores = getOption("mc.cores",
    parallel::detectCores()))
)

em_EMMIXmfa_multivariate(
  x = x,
  k = 2,
  initialisation_algorithm = "kmeans",
  conv_measure = "diff",
  epsilon = 10^-4,
  itmax = 500,
  start = NULL,
  nkmeans = 10L,
  arguments_HDclassif = list(init = "kmeans", kmeans.control = list(iter.max = 200L,
    nstart = 10L, algorithm = "Hartigan-Wong"), mc.cores = getOption("mc.cores",
    parallel::detectCores()))
)

Arguments

x	the vector of the observations
k	the number of components
epsilon	the criterion threshold considered as the tolerance between two consecutive log-likelihoods
itmax	the maximal number of iterations to reach the threshold
start	a list of initial estimates provided by the user, with 3 entries: The proportions p: p of each component (must be included between 0 and 1, and sum to one overall) The mean matrix mu: \mathrm{\mu}=(\mu_{i,j}) \in \mathbb{R}^{n \times k}, with each column giving the mean values of the variables within a given component The 3-dimensional covariance matrix array Sigma: \mathrm{\Sigma}=(\Sigma_{i,j,l}) \in \mathbb{R}^{n \times n \times k}, with each matrix \Sigma_{..l}, l \in \{ 1, \ldots, k\} storing the covariance matrix of a given component, whose diagonal terms correspond to the variance of each variable, and off-terms diagonal elements return the covariance matrix
initialisation_algorithm, nstart	hyper-parameters, when the user rather uses one of our implemented initialization algorithms
...	additional parameters for the reviewed packages
minprior	Minimum prior probability of clusters, components falling below this threshold are removed during the iteration.
embedNoise	A small constant added to the diagonal entries of all covariance matrices. This may prevent covariance matrices collapsing prematurely. A suggested value is 1e-6. Covariance degeneration is detected during Cholesky decomposition, and will lead the trainer to remove the corresponding mixture component. For high-dimensional problem, setting embedNoise to nonzero may pose the illusion of massive log-likelihood, all because one or more mixture components are so close to singular, which makes the densities around them extremely high.
parallel	only relevant for GMKMCharlie package which has a native parallel implementation (by default, takes half of the available clusters)

Value

a list of the estimated parameters, ordered by partial ordering on their respective mean components for identifiability issues

Author(s)

Bastien CHASSAGNOL

See Also

emnmix_univariate() for a bench of algorithms able to perform the Em estimation in the fully unconstrained case, in the univariate dimension

bastienchassagnol/RGMMBench documentation built on Oct. 26, 2023, 5:58 p.m.