32_em.step: Single E- and M-step

In EMCluster: EM Algorithm for Model-Based Clustering of Finite Mixture Gaussian Distribution

Single E- and M-step

Description

These functions are single E- and M-step of EM algorithm for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion.

Usage

e.step(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL,
          norm = TRUE)
m.step(x, emobj = NULL, Gamma = NULL, assign.class = FALSE)

Arguments

x	the data matrix, dimension n\times p.
emobj	the desired model which is a list mainly contains pi, Mu, and LTSigma, usually a returned object from init.EM.
pi	the mixing proportion, length K.
Mu	the centers of clusters, dimension K\times p.
LTSigma	the lower triangular matrices of dispersion, K\times p(p+1)/2.
norm	if returning normalized Gamma.
Gamma	containing posterior probabilities if normalized, otherwise containing component densities weighted by mixing proportion, dimension n\times K.
assign.class	if assigning class id.

Details

These two functions are mainly used in debugging for development and post process after model fitting.

Value

The e.step returns a list contains Gamma, the posterior probabilities if norm=TRUE, otherwise it contains component densities. This is one E-step and Gamma is used to update emobj in the M-step next.

The m.step returns a new emobj according to the Gamma from the E-step above.

Author(s)

Wei-Chen Chen [e-mail] and Ranjan Maitra.

References

https://www.stat.iastate.edu/people/ranjan-maitra

See Also

init.EM.

Examples

library(EMCluster, quietly = TRUE)
x2 <- da2$da

emobj <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma)
eobj <- e.step(x2, emobj = emobj)
emobj <- m.step(x2, emobj = eobj)
emobj

EMCluster documentation built on April 3, 2025, 9:02 p.m.