matrixqda {MixMatrix}

Quadratic Discriminant Analysis for Matrix Variate Observations

Description

See matrixlda: quadratic discriminant analysis for matrix variate observations.

Usage

matrixqda(
  x,
  grouping,
  prior,
  tol = 1e-04,
  method = "normal",
  nu = 10,
  ...,
  subset
)

Arguments

x

3-D array of matrix data indexed by the third dimension

grouping

vector

prior

a vector of prior probabilities of the same length as the number of classes

tol

by default, 1e-4. Tolerance parameter checks for 0 variance.

method

whether to use the normal distribution (normal) or the t distribution (t). By default, normal.

nu

If using the t-distribution, the degrees of freedom parameter. By default, 10.

...

Arguments passed to or from other methods, such as additional parameters to pass to MLmatrixnorm (e.g., row.mean)

subset

An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)

Details

This uses MLmatrixnorm or MLmatrixt to find the means and variances for the case when different groups have different variances.

Value

Returns a list of class matrixqda containing the following components:

prior

the prior probabilities used.

counts

the counts of group membership

means

the group means.

U

the between-row covariance matrices

V

the between-column covariance matrices

lev

levels of the grouping factor

N

The number of observations used.

method

The method used.

nu

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

call

The (matched) function call.

References

G Z Thompson, R Maitra, W Q Meeker, A Bastawros (2019),
"Classification with the matrix-variate-t distribution", arXiv
e-prints arXiv:1907.09565 <https://arxiv.org/abs/1907.09565>

Venables, W. N. & Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer, New York. ISBN 0-387-95457-0

Pierre Dutilleul.  The MLE algorithm for the matrix normal distribution.
Journal of Statistical Computation and Simulation, (64):105–123, 1999.

See Also

predict.matrixqda(), MASS::qda(), MLmatrixnorm(), MLmatrixt(), matrixlda(), and matrixmixture()

Examples

set.seed(20180221)
# construct two populations of 3x4 random matrices with different means
A <- rmatrixnorm(30, mean = matrix(0, nrow = 3, ncol = 4))
B <- rmatrixnorm(30, mean = matrix(1, nrow = 3, ncol = 4))
C <- array(c(A, B), dim = c(3, 4, 60)) # combine together
groups <- c(rep(1, 30), rep(2, 30)) # define groups
prior <- c(.5, .5) # set prior
D <- matrixqda(C, groups, prior)
logLik(D)
print(D)