mixmodGaussianModel: Create an instance of the ['GaussianModel'] class In Rmixmod: Classification with Mixture Modelling

 mixmodGaussianModel R Documentation

Create an instance of the [GaussianModel] class

Description

Define a list of Gaussian model to test in MIXMOD.

Usage

mixmodGaussianModel(
family = "all",
listModels = NULL,
free.proportions = TRUE,
equal.proportions = TRUE
)


Arguments

 family character defining a family of models. "general" for the general family, "diagonal" for the diagonal family, "spherical" for the spherical family and "all" for all families. Default is "general". listModels a list of characters containing a list of models. It is optional. free.proportions logical to include models with free proportions. Default is TRUE. equal.proportions logical to include models with equal proportions. Default is TRUE.

Details

In the Gaussian mixture model, following Banfield and Raftery (1993) and Celeux and Govaert (1995), we consider a parameterization of the variance matrices of the mixture components consisting of expressing the variance matrix \Sigma_{k} in terms of its eigenvalue decomposition

 \Sigma_{k}= \lambda_{k} D_{k} A_{k}D'_{k}

where \lambda_{k}=|\Sigma_{k}|^{1/d}, D_{k} is the matrix of eigenvectors of \Sigma_{k} and A_{k} is a diagonal matrix, such that | A_{k} |=1, with the normalized eigenvalues of \Sigma_{k} on the diagonal in a decreasing order. The parameter \lambda_{k} determines the volume of the kth cluster, D_{k} its orientation and A_{k} its shape. By allowing some but not all of these quantities to vary between clusters, we obtain parsimonious and easily interpreted models which are appropriate to describe various clustering situations.

In general family, we can allow the volumes, the shapes and the orientations of clusters to vary or to be equal between clusters. Variations on assumptions on the parameters \lambda_{k}, D_{k} and A_{k} (1 \leq k \leq K) lead to 8 general models of interest. For instance, we can assume different volumes and keep the shapes and orientations equal by requiring that A_{k}=A (A unknown) and D_{k}=D (D unknown) for k=1,\ldots,K. We denote this model [\lambda_{k}DAD']. With this convention, writing [\lambda D_{k}AD'_{k}] means that we consider the mixture model with equal volumes, equal shapes and different orientations. In diagonal family, we assume that the variance matrices \Sigma_{k} are diagonal. In the parameterization, it means that the orientation matrices D_{k} are permutation matrices. We write \Sigma_{k}=\lambda_{k}B_{k} where B_{k} is a diagonal matrix with | B_{k}|=1. This particular parameterization gives rise to 4 models: [\lambda B], [\lambda_{k}B], [\lambda B_{k}] and [\lambda_{k}B_{k}].

In spherical family, we assume spherical shapes, namely A_{k}=I, I denoting the identity matrix. In such a case, two parsimonious models are in competition: [\lambda I] and [\lambda_{k}I].

Value

an object of [GaussianModel] which contains some of the 28 Gaussian Models:

 Model Family Prop. Volume Shape Orient. Gaussian_p_L_C General Equal Equal Equal Equal Gaussian_p_Lk_C Free Equal Equal Gaussian_p_L_D_Ak_D Equal Free Equal Gaussian_p_Lk_D_Ak_D Free Free Equal Gaussian_p_L_Dk_A_Dk Equal Equal Free Gaussian_p_Lk_Dk_A_Dk Free Equal Free Gaussian_p_L_Ck Equal Free Free Gaussian_p_Lk_Ck Free Free Free Gaussian_p_L_B Diagonal Equal Equal Equal Axes Gaussian_p_Lk_B Free Equal Axes Gaussian_p_L_Bk Equal Free Axes Gaussian_p_Lk_Bk Free Free Axes Gaussian_p_L_I Spherical Equal Equal Equal NA Gaussian_p_Lk_I Free Equal NA Gaussian_pk_L_C General Free Equal Equal Equal Gaussian_pk_Lk_C Free Equal Equal Gaussian_pk_L_D_Ak_D Equal Free Equal Gaussian_pk_Lk_D_Ak_D Free Free Equal Gaussian_pk_L_Dk_A_Dk Equal Equal Free Gaussian_pk_Lk_Dk_A_Dk Free Equal Free Gaussian_pk_L_Ck Equal Free Free Gaussian_pk_Lk_Ck Free Free Free Gaussian_pk_L_B Diagonal Free Equal Equal Axes Gaussian_pk_Lk_B Free Equal Axes Gaussian_pk_L_Bk Equal Free Axes Gaussian_pk_Lk_Bk Free Free Axes Gaussian_pk_L_I Spherical Free Equal Equal NA Gaussian_pk_Lk_I Free Equal NA

Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernacki and G. Celeux and G. Govaert contact@mixmod.org

References

C. Biernacki, G. Celeux, G. Govaert, F. Langrognet. "Model-Based Cluster and Discriminant Analysis with the MIXMOD Software". Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600. (2006)

Examples

mixmodGaussianModel()
# all Gaussian models with equal proportions
mixmodGaussianModel(family = "all", free.proportions = FALSE)
# Diagonal and Spherical Gaussian models
mixmodGaussianModel(family = c("diagonal", "spherical"))
# Gaussian models with a pre-defined list
mixmodGaussianModel(listModels = c("Gaussian_p_L_C", "Gaussian_p_L_Ck", "Gaussian_pk_L_I"))


Rmixmod documentation built on May 29, 2024, 7:32 a.m.