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