MatManly.EM: EM algorithm for matrix clustering

In MatManlyMix: Matrix Clustering with Gaussian and Manly Mixture Models

Description

Runs the EM algorithm for matrix clustering

Usage

MatManly.EM(Y, X = NULL, initial = NULL, id = NULL, la = NULL, nu = NULL, tau = NULL, 
Mu = NULL, beta = NULL, Sigma = NULL, Psi = NULL, Mu.type = 0, Psi.type = 0, 
tol = 1e-05, max.iter = 1000, size.control = 0, silent = TRUE)

Arguments

Y	dataset of random matrices (p x T x n), n random matrices of dimensionality (p x T)
X	dataset of explanatory variables (T x q x n), q explanatory variables for modeling Y
initial	initialization parameters provided by function MatManly.init()
id	initial membership vector
la	initial transformation parameters (K x p)
nu	initial transformation parameters (K x T)
tau	initial mixing proportions (length K)
Mu	initial mean matrices (p x T x K)
beta	initial coefficient matrices (q x p x K)
Sigma	initial array of sigma (p x p x K)
Psi	initial array of psi (T x T x K)
Mu.type	mean structure: 0-unrestricted, 1-additive
Psi.type	covariance structure of the Psi matrix: 0-unrestricted, 1-AR1
tol	tolerance level
max.iter	maximum number of iterations
size.control	minimum size of clusters allowed for controlling spurious solutions
silent	whether to produce output of steps or not

Details

Runs the EM algorithm for modeling and clustering matrices for a provided dataset. Both matrix Gaussian mixture and matrix Manly mixture with given explanatory variables (data matrix X) or without explanatory variables (X is null) can be employed. A user has three options to initialize the EM algorithm. The user can use the MatManly.init() function to get initial parameters and input them as 'initial'. The second choice is to specify either initial id vector 'id' and transformation parameters 'la'. The third option is to input initial mode parameters 'la', 'tau', 'Mu', and 'Sigma' and 'Psi'. 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 mixture 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. A user also has three options to specify the covariance structure of the 'Psi' matrices, including unrestricted case, spherical matrices and autoregressive structured matrices. Notation: n - sample size, p x T - dimensionality of the random matrices, K - number of mixture components.

Value

la	matrix of the skewness parameters (K x p)
nu	matrix of the skewness parameters (K x T)
tau	vector of mixing proportions (length K)
Mu	matrix of the estimated mean matrices (p x T x K)
beta	matrix of the coefficient parameters (q x p x K)
Sigma	array of the estimated sigma (p x p x K)
Psi	array of the estimated psi (T x T x K)
Mu.type	mean structure: 0-unrestricted, 1-additive
Psi.type	covariance structure of the Psi matrix: 0-unrestricted, 1-AR1
gamma	matrix of the estimated 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)

Examples

set.seed(123)

data(crime)


Y <- crime$Y[c(2,7),,] / 1000

p <- dim(Y)[1]
T <- dim(Y)[2]
n <- dim(Y)[3]
K <-  2

#init <- MatManly.init(Y, K = K, la = matrix(0.1, K, p), nu = matrix(0.1, K, T))
#M1 <- MatManly.EM(Y, initial = init, max.iter = 1000)

MatManlyMix documentation built on May 2, 2019, 5:58 a.m.