Quadratic Discriminant Analysis for Matrix Variate Observations

See matrixlda: quadratic discriminant analysis for matrix variate observations.

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.)

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.

Details

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

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.

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)
#> 'log Lik.' -958.9359 (df=54)
print(D)
#> $prior
#>   1   2 
#> 0.5 0.5 
#> 
#> $counts
#>  1  2 
#> 30 30 
#> 
#> $means
#> , , 1
#> 
#>             [,1]        [,2]        [,3]        [,4]
#> [1,]  0.07351694 -0.08704738  0.13826608  0.06657800
#> [2,] -0.05562527 -0.08631880 -0.12719766 -0.07388404
#> [3,] -0.12802865 -0.33410177 -0.05220913 -0.03813562
#> 
#> , , 2
#> 
#>           [,1]     [,2]      [,3]     [,4]
#> [1,] 1.1213360 1.230815 0.9142843 1.082488
#> [2,] 1.3283770 1.244675 0.5694279 1.000457
#> [3,] 0.8961279 0.800175 1.1439663 1.048916
#> 
#> 
#> $U
#> , , 1
#> 
#>            [,1]       [,2]       [,3]
#> [1,] 1.00000000 0.14788530 0.02800227
#> [2,] 0.14788530 0.86714312 0.02258292
#> [3,] 0.02800227 0.02258292 0.98364372
#> 
#> , , 2
#> 
#>              [,1]       [,2]         [,3]
#> [1,]  1.000000000 -0.0173930 -0.004498732
#> [2,] -0.017392997  0.9987747 -0.100860770
#> [3,] -0.004498732 -0.1008608  0.977978559
#> 
#> 
#> $V
#> , , 1
#> 
#>             [,1]        [,2]        [,3]        [,4]
#> [1,]  0.81179597 -0.13499901  0.07550758 -0.15466849
#> [2,] -0.13499901  0.82945236 -0.04492883  0.06490810
#> [3,]  0.07550758 -0.04492883  1.03826075 -0.09438137
#> [4,] -0.15466849  0.06490810 -0.09438137  0.97282616
#> 
#> , , 2
#> 
#>             [,1]       [,2]       [,3]        [,4]
#> [1,]  0.76072995 0.01856625 0.03148175 -0.05903717
#> [2,]  0.01856625 0.67294239 0.05448755  0.10257451
#> [3,]  0.03148175 0.05448755 1.02451969  0.03848553
#> [4,] -0.05903717 0.10257451 0.03848553  1.03348309
#> 
#> 
#> $lev
#> [1] "1" "2"
#> 
#> $N
#> [1] 60
#> 
#> $method
#> [1] "normal"
#> 
#> $nu
#> NULL
#> 
#> $call
#> matrixqda(x = C, grouping = groups, prior = prior)
#> 
#> attr(,"class")
#> [1] "matrixqda"