matrixmixture {MixMatrix}

Fit a matrix variate mixture model

Description

Clustering by fitting a mixture model using EM with K groups and unconstrained covariance matrices for a matrix variate normal or matrix variate t distribution (with specified degrees of freedom nu).

Usage

matrixmixture(
  x,
  init = NULL,
  prior = NULL,
  K = length(prior),
  iter = 1000,
  model = "normal",
  method = NULL,
  row.mean = FALSE,
  col.mean = FALSE,
  tolerance = 0.1,
  nu = NULL,
  ...,
  verbose = 0,
  miniter = 5,
  convergence = TRUE
)

Arguments

x

data, p \times q \times n array

init

a list containing an array of K of p \times q means labeled centers, and optionally p \times p and q \times q positive definite variance matrices labeled U and V. By default, those are presumed to be identity if not provided. If init is missing, it will be provided using the prior or K by init_matrixmix.

prior

prior for the K classes, a vector that adds to unity

K

number of classes - provide either this or the prior. If this is provided, the prior will be of uniform distribution among the classes.

iter

maximum number of iterations.

model

whether to use the normal or t distribution.

method

what method to use to fit the distribution. Currently no options.

row.mean

By default, FALSE. If TRUE, will fit a common mean within each row. If both this and col.mean are TRUE, there will be a common mean for the entire matrix.

col.mean

By default, FALSE. If TRUE, will fit a common mean within each row. If both this and row.mean are TRUE, there will be a common mean for the entire matrix.

tolerance

convergence criterion, using Aitken acceleration of the log-likelihood by default.

nu

degrees of freedom parameter. Can be a vector of length K.

...

pass additional arguments to MLmatrixnorm or MLmatrixt

verbose

whether to print diagnostic output, by default 0. Higher numbers output more results.

miniter

minimum number of iterations

convergence

By default, TRUE, using Aitken acceleration to determine convergence. If false, it instead checks if the change in log-likelihood is less than tolerance. Aitken acceleration may prematurely end in the first few steps, so you may wish to set miniter or select FALSE if this is an issue.

Value

A list of class MixMatrixModel containing the following components:

prior

the prior probabilities used.

init

the initialization used.

K

the number of groups

N

the number of observations

centers

the group means.

U

the between-row covariance matrices

V

the between-column covariance matrix

posterior

the posterior probabilities for each observation

pi

the final proportions

nu

The degrees of freedom parameter if the t distribution was used.

convergence

whether the model converged

logLik

a vector of the log-likelihoods of each iteration ending in the final log-likelihood of the model

model

the model used

method

the method used

call

The (matched) function call.

References

Andrews, Jeffrey L., Paul D. McNicholas, and Sanjeena Subedi. 2011.
  "Model-Based Classification via Mixtures of Multivariate
  T-Distributions." Computational Statistics & Data Analysis 55 (1):
  520–29. \doi{10.1016/j.csda.2010.05.019}.

Fraley, Chris, and Adrian E Raftery. 2002. "Model-Based Clustering,
   Discriminant Analysis, and Density Estimation." Journal of the
   American Statistical Association 97 (458). Taylor & Francis: 611–31.
   \doi{10.1198/016214502760047131}.

McLachlan, Geoffrey J, Sharon X Lee, and Suren I Rathnayake. 2019.
      "Finite Mixture Models." Annual Review of Statistics and Its
      Application 6. Annual Reviews: 355–78.
      \doi{10.1146/annurev-statistics-031017-100325}.

Viroli, Cinzia. 2011. "Finite Mixtures of Matrix Normal Distributions
      for Classifying Three-Way Data." Statistics and Computing 21 (4):
      511–22. \doi{10.1007/s11222-010-9188-x}.

See Also

init_matrixmixture()

Examples

set.seed(20180221)
A <- rmatrixt(20,mean=matrix(0,nrow=3,ncol=4), df = 5)
# 3x4 matrices with mean 0
B <- rmatrixt(20,mean=matrix(1,nrow=3,ncol=4), df = 5)
# 3x4 matrices with mean 1
C <- array(c(A,B), dim=c(3,4,40)) # combine into one array
prior <- c(.5,.5) # equal probability prior
# create an intialization object, starts at the true parameters
init = list(centers = array(c(rep(0,12),rep(1,12)), dim = c(3,4,2)),
              U = array(c(diag(3), diag(3)), dim = c(3,3,2))*20,
              V = array(c(diag(4), diag(4)), dim = c(4,4,2))
 )
# fit model
 res<-matrixmixture(C, init = init, prior = prior, nu = 5,
                    model = "t", tolerance = 1e-3, convergence = FALSE)
print(res$centers) # the final centers
print(res$pi) # the final mixing proportion
plot(res) # the log likelihood by iteration
logLik(res) # log likelihood of final result
BIC(res) # BIC of final result
predict(res, newdata = C[,,c(1,21)]) # predicted class membership