EM algorithm for Manly mixture model

Description

Runs the EM algorithm for a Manly mixture model with specified initial membership and transformation parameters.

Usage

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Manly.EM(X, id = NULL, la = NULL, tau = NULL, Mu = NULL, S = NULL, 
tol = 1e-5, max.iter = 1000)

Arguments

X

dataset matrix (n x p)

id

initial membership vector (length n)

la

initial transformation parameters (K x p)

tau

initial vector of mixing proportions (length K)

Mu

initial matrix of mean vectors (K x p)

S

initial array of covariance matrices (p x p x K)

tol

tolerance level

max.iter

maximum number of iterations

Details

Runs the EM algorithm for a Manly mixture model for a provided dataset. Manly mixture model assumes that a multivariate Manly transformation applied to each component allows to reach near-normality. A user has a choice to specify either initial id vector 'id' and transformation parameters 'la' or initial mode parameters 'la', 'tau', 'Mu', and 'S'. In the case when transformation parameters are not provided, the function runs the EM algorithm without any transformations, i.e., it is equivalent to the EM algorithm for a Gaussian mixtuire model. If some transformation parameters have to be excluded from the consideration, in the corresponding positions of matrix 'la', the user has to specify value 0. Notation: n - sample size, p - dimensionality of the dataset X, K - number of mixture components.

Value

la

matrix of the estimated transformation parameters (K x p)

tau

vector of mixing proportions (length K)

Mu

matrix of the estimated mean vectors (K x p)

S

array of the estimated covariance matrices (p x p x K)

gamma

matrix of posterior probabilities (n x K)

id

estimated membership vector (length n)

ll

log likelihood value

bic

Bayesian Information Criterion

iter

number of EM iterations run

flag

convergence flag (0 - success, 1 - failure)

See Also

Manly.select

Examples

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set.seed(123)

K <- 3; p <- 4
X <- as.matrix(iris[,-5])
id.true <- rep(1:K, each = 50)

# Obtain initial memberships based on the K-means algorithm
id.km <- kmeans(X, K)$cluster

# Run the EM algorithm for a Gaussian mixture model based on K-means solution
A <- Manly.EM(X, id.km)
id.Gauss <- A$id

table(id.true, id.Gauss)

# Run the EM algorithm for a Manly mixture model based on Gaussian mixture solution
la <- matrix(0.1, K, p)
B <- Manly.EM(X, id.Gauss, la)
id.Manly <- B$id

table(id.true, id.Manly)