R: Convert mixture component covariances to decomposition form.

sigma2decomp {mclust} | R Documentation

## Convert mixture component covariances to decomposition form.

### Description

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

### Usage

    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.

### 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, A. E. Raftery, T. B. Murphy and L. Scrucca (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington.

### See Also

`decomp2sigma`

### Examples

    meEst <- meEEE(iris[,-5], unmap(iris[,5]))
    names(meEst$parameters$variance)
    meEst$parameters$variance$Sigma

    sigma2decomp(meEst$parameters$variance$Sigma, G = length(unique(iris[,5])))

[Package mclust version 5.3 Index]