matrixmixture: Fit a matrix variate mixture model
In gzt/MixMatrix: Classification with Matrix Variate Normal and t Distributions

Description Usage Arguments Value References See Also Examples

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).

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
)

`x`	data, p q * n* array
`init`	a list containing an array of `K` of p q* means labeled `centers`, and optionally p p* and q 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.

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.

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}.

init_matrixmixture()

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