Converts a set of covariance matrices from representation as a 3-D array to a parameterization by eigenvalue decomposition.

sigma2decomp(sigma, G = NULL, tol = sqrt(.Machine$double.eps), ...)

Arguments

sigma

Either a 3-D array whose [,,k]th component is the covariance matrix for the kth component in an MVN mixture model, or a single covariance matrix in the case that all components have the same covariance.

G

The number of components in the mixture. When sigma is a 3-D array, the number of components can be inferred from its dimensions.

tol

Tolerance for determining whether or not the covariances have equal volume, shape, and or orientation. The default is the square root of the relative machine precision, sqrt(.Machine$double.eps), which is about 1.e-8.

...

Catches unused arguments from an indirect or list call via do.call.

Value

The covariance matrices for the mixture components in decomposition form, including the following components:

modelName

A character string indicating the infered model. The help file for mclustModelNames describes the available models.

d

The dimension of the data.

G

The number of components in the mixture model.

scale

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

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

Either a d by d by G array whose [,,k]th entry is the orthonomal matrix whose columns are the 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 of decomp can be omitted in spherical and diagonal models, for which the principal components are parallel to the coordinate axes so that the orientation matrix is the identity.

See also

Examples

meEst <- meEEE(iris[,-5], unmap(iris[,5])) names(meEst$parameters$variance)
#> [1] "modelName" "d" "G" "sigma" "Sigma" "cholSigma"
meEst$parameters$variance$Sigma
#> Sepal.Length Sepal.Width Petal.Length Petal.Width #> Sepal.Length 0.26387916 0.08987702 0.16956251 0.03932391 #> Sepal.Width 0.08987702 0.11197340 0.05118186 0.03002534 #> Petal.Length 0.16956251 0.05118186 0.18637706 0.04196406 #> Petal.Width 0.03932391 0.03002534 0.04196406 0.03974960
sigma2decomp(meEst$parameters$variance$Sigma, G = length(unique(iris[,5])))
#> $sigma #> , , 1 #> #> [,1] [,2] [,3] [,4] #> [1,] 0.26387916 0.08987702 0.16956251 0.03932391 #> [2,] 0.08987702 0.11197340 0.05118186 0.03002534 #> [3,] 0.16956251 0.05118186 0.18637706 0.04196406 #> [4,] 0.03932391 0.03002534 0.04196406 0.03974960 #> #> , , 2 #> #> [,1] [,2] [,3] [,4] #> [1,] 0.26387916 0.08987702 0.16956251 0.03932391 #> [2,] 0.08987702 0.11197340 0.05118186 0.03002534 #> [3,] 0.16956251 0.05118186 0.18637706 0.04196406 #> [4,] 0.03932391 0.03002534 0.04196406 0.03974960 #> #> , , 3 #> #> [,1] [,2] [,3] [,4] #> [1,] 0.26387916 0.08987702 0.16956251 0.03932391 #> [2,] 0.08987702 0.11197340 0.05118186 0.03002534 #> [3,] 0.16956251 0.05118186 0.18637706 0.04196406 #> [4,] 0.03932391 0.03002534 0.04196406 0.03974960 #> #> #> $d #> [1] 4 #> #> $modelName #> [1] "EEE" #> #> $G #> [1] 3 #> #> $scale #> [1] 0.08114033 #> #> $shape #> [1] 5.4441760 1.0696919 0.6344826 0.2706384 #> #> $orientation #> [,1] [,2] [,3] [,4] #> [1,] -0.7401980 0.01338854 0.6352049 0.2200963 #> [2,] -0.3056652 -0.87119601 -0.2316293 -0.3064868 #> [3,] -0.5783262 0.47573614 -0.5625433 -0.3503698 #> [4,] -0.1556100 -0.12047151 -0.4758232 0.8572423 #>