matrixlda {MixMatrix} | R Documentation |
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.
matrixlda(x, grouping, prior, tol = 1e-04, method = "normal", nu = 10, ..., subset)
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, |
method |
whether to use the normal distribution ( |
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 |
subset |
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 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.
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
predict.matrixlda
, lda
,
MLmatrixnorm
and MLmatrixt
matrixqda
, and matrixmixture
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)