mclustVariance {mclust} | R Documentation |
Template for variance specification for parameterized
Gaussian mixture models.
Description
Specification of variance parameters for the various types
of Gaussian mixture models.
Details
- The
variance
component in the {parameters} list from the
output to e.g. me
ormstep
or input to e.g.
estep
may contain one or more of the following
arguments, depending on the model:
- modelName
- A character string indicating the model.
- d
- The dimension of the data.
- G
- The number of components in the mixture model.
- sigmasq
- for the one-dimensional models ("E", "V") and spherical models
("EII", "VII"). This is either a vector whose kth
component is the variance for the kth component in the
mixture model ("V" and "VII"), or a scalar giving the common
variance for all components in the mixture model ("E" and
"EII").
- Sigma
- For the equal variance models "EII", "EEI", and "EEE".
A d by d matrix giving the common covariance for all
components of the mixture model.
- cholSigma
- For the equal variance model "EEE".
A d by d upper triangular matrix giving the
Cholesky factor of the common covariance for all
components of the mixture model.
- sigma
- For all multidimensional mixture models. A
d by d by G matrix array whose
[,,k]
th entry is the covariance matrix for
the kth component of the mixture model.
- cholsigma
- For the unconstrained covaraince mixture model "VVV".
A d by d by G matrix array whose
[,,k]
th entry is the upper triangular Cholesky factor
of the covariance matrix for the kth component of the
mixture model.
- scale
- For diagonal models "EEI", "EVI", "VEI", "VVI" and
constant-shape models "EEV" and "VEV".
Either a G-vector giving the scale of the covariance (the
dth root of its determinant) for each component in the
mixture model, or a single numeric value if the scale is the
same for each component.
- shape
- For diagonal models "EEI", "EVI", "VEI", "VVI" and
constant-shape models "EEV" and "VEV".
Either a G by d matrix in which the kth
column is the shape of the covariance matrix (normalized to have
determinant 1) for the kth component, or a
d-vector giving a common shape for all components.
- orientation
- For the constant-shape models "EEV" and "VEV".
Either a d by d by G array whose
[,,k]
th entry is the orthonomal matrix of eigenvectors of
the covariance matrix of the kth component, or a d
by d orthonormal matrix if the mixture components have a
common orientation. The orientation
component
is not needed in spherical and diagonal models, since
the principal components are parallel to the coordinate axes
so that the orientation matrix is the identity.
In all cases, the value
-1
is used as a placeholder for unknown nonzero entries.
References
C. Fraley and A. E. Raftery (2002).
Model-based clustering, discriminant analysis, and density estimation.
Journal of the American Statistical Association 97:611:631.
C. Fraley and A. E. Raftery (2006).
MCLUST Version 3 for R: Normal Mixture Modeling and Model-Based Clustering,
Technical Report no. 504, Department of Statistics,
University of Washington.
[Package
mclust version 3.1-10.3
Index]