Table A3.

Parameterisation of the within-group covariance matrix for multidimensional data available in the mclust package and the corresponding geometric characteristics (Source: (Scrucca et al., 2016))

Model	${\mathbf{\Sigma }}_{\mathit{k}}$	Distribution	Volume	Shape	Orientation
EII	$\lambda \mathit{I}$	Spherical	Equal	Equal	–
VII	${\lambda }_k\mathit{I}$	Spherical	Variable	Equal	–
EEI	$\lambda \mathit{A}$	Diagonal	Equal	Equal	Coordinate axes
VEI	${\lambda }_k\mathit{A}$	Diagonal	Variable	Equal	Coordinate axes
EVI	$\lambda {\mathit{A}}_{\mathit{k}}$	Diagonal	Equal	Variable	Coordinate axes
VVI	${\lambda }_k{\mathit{A}}_{\mathit{k}}$	Diagonal	Variable	Variable	Coordinate axes
EEE	$\lambda \mathit{DA}{\mathit{D}}^{\text{T}}$	Ellipsoidal	Equal	Equal	Equal
EVE	$\lambda \mathit{D}{\mathit{A}}_{\mathit{k}}{\mathit{D}}^{\text{T}}$	Ellipsoidal	Equal	Variable	Equal
VEE	${\lambda }_k\mathit{DA}{\mathit{D}}^{\text{T}}$	Ellipsoidal	Variable	Equal	Equal
VVE	${\lambda }_k\mathit{D}{\mathit{A}}_{\mathit{k}}{\mathit{D}}^{\text{T}}$	Ellipsoidal	Variable	Variable	Equal
EEV	$\lambda {\mathit{D}}_{\mathit{k}}\mathit{A}{\mathit{D}}_{\mathit{k}}^{\text{T}}$	Ellipsoidal	Equal	Equal	Variable
VEV	${\lambda }_k{\mathit{D}}_{\mathit{k}}\mathit{A}{\mathit{D}}_{\mathit{k}}^{\text{T}}$	Ellipsoidal	Equal	Variable	Variable
EVV	$\lambda {\mathit{D}}_{\mathit{k}}{\mathit{A}}_{\mathit{k}}{\mathit{D}}_{\mathit{k}}^{\text{T}}$	Ellipsoidal	Variable	Equal	Variable
VVV	${\lambda }_k{\mathit{D}}_{\mathit{k}}{\mathit{A}}_{\mathit{k}}{\mathit{D}}_{\mathit{k}}^{\text{T}}$	Ellipsoidal	Variable	Variable	Variable