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.
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3-D array of matrix data indexed by the third dimension
a vector of prior probabilities of the same length as the number of classes
whether to use the normal distribution (
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
An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)
Returns a list of class
the following components:
the prior probabilities used.
the counts of group membership
the group means.
the scalar variance parameter
the between-row covariance matrix
the between-column covariance matrix
levels of the grouping factor
The number of observations used.
The method used.
The degrees of freedom parameter if the t distribution was used.
The (matched) function call.
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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, 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
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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)
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