emgm {xLLiM}

Perform EM algorithm for fitting a Gaussian mixture model (GMM)

Description

Perform EM algorithm for fitting a Gaussian mixture model (GMM). In the GLLiM context, this is done jointly on both responses and covariates

Usage

emgm(X, init, maxiter,verb)

Arguments

X

An (M x N) matrix with variables in rows and observations in columns. M is D+L in the proposed approach

init

This argument can be a number K of classes (integer), a matrix of posterior probabilities ((N x K) matrix) or a matrix of centers ((M x K) matrix)

maxiter

Maximum number of iterations for estimation of the GMM

verb

Print out the progression of the algorithm. If verb=0, there is no print, if verb=1, the progression is printed out. Default is 0.

Value

Returns a list with the following elements:

label

An N vector of class assignments provided by maximum a posteriori (MAP) on posterior probabilities to belong to each of the K components for each observation

model

A list with the estimated parameters of the GMM

model$mu

An (M x K) matrix of estimations of means in each cluster of the joint GMM

model$Sigma

An (M x M x K) array of estimations of covariance matrix in each cluster of the GMM

model$weight

An K vector of estimated prior probabilities of each cluster

llh

A vector of values of the log-likelihood for each iteration of the algorithm

R

An N x K matrix of estimations of posterior probabilities to belong to each of the K components for each observation

Author(s)

Emeline Perthame ([e-mail]), Florence Forbes ([e-mail]), Antoine Deleforge ([e-mail])

References

[1] A. Deleforge, F. Forbes, and R. Horaud. High-dimensional regression with Gaussian mixtures and partially-latent response variables. Statistics and Computing,25(5):893–911, 2015.

[2] E. Perthame, F. Forbes, and A. Deleforge. Inverse regression approach to robust nonlinear high-to-low dimensional mapping. Journal of Multivariate Analysis, 163(C):1–14, 2018. https://doi.org/10.1016/j.jmva.2017.09.009

[3] Y. Qiao and N. Minematsu. Mixture of probabilistic linear regressions: A unified view of GMM-based mapping techiques. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2009.

Converted to R from the Matlab code of the GLLiM toolbox available on: https://team.inria.fr/perception/gllim_toolbox/

See Also

xLLiM-package, gllim, sllim

Examples

# data(data.xllim)
# K=5
# r = emgm(data.xllim, init=K, verb=0);  
# r$R # estimation of posterior probabilities to belong to 
## each of the K components for each observation