Description Usage Arguments Value References Examples
A function for fitting the J-class matrix-normal model using maximum likelihood. Uses the so-called “flip-flop” algorithm after initializing at U = I_r.
1 |
X |
An r \times c \times N array of training set predictors. |
class |
N-vector of training set class labels; should be numeric from ≤ft\{1,...,J\right\}. |
max.iter |
Maximum number of iterations for “flip-flop” algorithm. |
tol |
Convergence tolerance for the “flip flop” algorithm; based on decrease in negative log-likelihood. |
quiet |
Logical. Should the objective function value be printed at each update? Default is |
Returns of list of class "MN", which contains the following elements:
Mean |
\bar{X}; An r \times c \times C array of sample class means. |
U |
\hat{U}^{\rm MLE}; the r \times r estimated precision matrix for the row variables. |
V |
\hat{V}^{\rm MLE}; the c \times c estimated precision matrix for the column variables. |
pi.list |
\hat{π}; J-vector with marginal class probabilities from training set. |
Molstad, A. J., and Rothman, A. J. (2018). A penalized likelihood method for classification with matrix-valued predictors. Journal of Computational and Graphical Statistics.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | ## Generate realizations of matrix-normal random variables
## set sample size, dimensionality, number of classes,
## and marginal class probabilities
N = 75
N.test = 150
N.total = N + N.test
r = 16
p = 16
C = 3
pi.list = rep(1/C, C)
## create class means
M.array = array(0, dim=c(r, p, C))
M.array[3:4, 3:4, 1] = 1
M.array[5:6, 5:6, 2] = .5
M.array[3:4, 3:4, 3] = -2
M.array[5:6, 5:6, 3] = -.5
## create covariance matrices U and V
Uinv = matrix(0, nrow=r, ncol=r)
for (i in 1:r) {
for (j in 1:r) {
Uinv[i,j] = .5^abs(i-j)
}
}
eoU = eigen(Uinv)
Uinv.sqrt = tcrossprod(tcrossprod(eoU$vec,
diag(eoU$val^(1/2))),eoU$vec)
Vinv = matrix(.5, nrow=p, ncol=p)
diag(Vinv) = 1
eoV = eigen(Vinv)
Vinv.sqrt = tcrossprod(tcrossprod(eoV$vec,
diag(eoV$val^(1/2))),eoV$vec)
## generate N.total realizations of matrix-variate normal data
set.seed(1)
X = array(0, dim=c(r,p,N.total))
class = numeric(length=N.total)
for(jj in 1:N.total){
class[jj] = sample(1:C, 1, prob=pi.list)
X[,,jj] = tcrossprod(crossprod(Uinv.sqrt,
matrix(rnorm(r*p), nrow=r)),
Vinv.sqrt) + M.array[,,class[jj]]
}
## fit matrix-normal model using maximum likelihood
out = MN_MLE(X = X, class = class)
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