PredictMN function

Classify matrix-valued data based on a matrix-normal linear discriminant; an object of class "MN".

A function for prediction based on an object of class "MN"; models fit by MatLDA or MN_MLE.

PredictMN(object, newdata, newclass = NULL)

Arguments

• object: An object of class "MN"; output from MatLDA or MN_MLE.
• newdata: New data to be classified; an $r \times c \times N_{\rm test}$ array.
• newclass: Class labels for new data; should be $in \left\{1, \dots, J\right\}$. Default is NULL.

Returns

• pred.class: An $N_{\rm test}$-vector of predicted class membership based on the inputed object.

• misclass: If newclass is non-NULL, returns the misclassification proportion on the test data set.

• prob.mat: A $N_{\rm test} \times J$ matrix with the value of discriminant evaluated at each test data point.

References

• Molstad, A. J., and Rothman, A. J. (2018). A penalized likelihood method for classification with matrix-valued predictors. Journal of Computational and Graphical Statistics.

Examples

## 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)
dat.array = array(0, dim=c(r,p,N.total))
class.total = numeric(length=N.total)
for(jj in 1:N.total){
        class.total[jj] = sample(1:C, 1, prob=pi.list)
        dat.array[,,jj] = tcrossprod(crossprod(Uinv.sqrt, matrix(rnorm(r*p), nrow=r)),
        Vinv.sqrt) + M.array[,,class.total[jj]]
}

## store generated data 
X = dat.array[,,1:N]
X.test = dat.array[,,(N+1):N.total]

class = class.total[1:N]
class.test = class.total[(N+1):N.total]

## fit matrix-normal model using maximum likelihood
out = MN_MLE(X = X, class = class)

## use output to classify test set
check = PredictMN(out, newdata = X.test, newclass = class.test)

## print misclassification proportion
check$misclass