matrixlda: LDA for matrix variate distributions

Description

Performs linear discriminant analysis on matrix variate data. This works slightly differently from the LDA function in MASS: it does not sphere the data or otherwise normalize it. It presumes equal variance matrices and probabilities are given as if the data are from a matrix variate normal distribution. The estimated variance matrices are weighted by the prior. However, if there are not enough members of a class to estimate a variance, this may be a problem. The function does not take the formula interface. If method = 't' is selected, this performs discrimination using the matrix variate t distribution, presuming equal covariances between classes.

Usage

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

Value

Returns a list of class matrixlda containing the following components:

prior: the prior probabilities used.
counts: the counts of group membership
means: the group means.
scaling: the scalar variance parameter
U: the between-row covariance matrix
V: the between-column covariance matrix
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.

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.)

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>
Ming Li, Baozong Yuan, "2D-LDA: A statistical linear discriminant
  analysis for image matrix", Pattern Recognition Letters, Volume 26,
  Issue 5, 2005, Pages 527-532, ISSN 0167-8655.

Aaron Molstad & Adam J. Rothman (2019), "A Penalized Likelihood Method for Classification With Matrix-Valued Predictors", Journal of Computational and Graphical Statistics, 28:1, 11-22, tools:::Rd_expr_doi("10.1080/10618600.2018.1476249") MatrixLDA

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

Examples

Run this code

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 <- matrixlda(C, groups, prior) # fit model
logLik(D)
print(D)