  Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction
method specifically formulated to deal with tensor data. Precisely, the goal of
MDA is to find mode-specific projections that optimally separate tensor data
from different classes. However, to solve this task, standard MDA methods use
alternating optimization heuristics involving the computation of a succession
of tensor-matrix products. Such approaches are most of the time difficult to
solve and not natural, highligthing the difficulty to formulate this problem in
fully tensor form. In this paper, we propose to solve multilinear discriminant
analysis (MDA) by using the concept of transform domain (TD) recently proposed
in \cite{Kilmer2011}. We show here that moving MDA to this specific transform
domain make its resolution easier and more natural. More precisely, each
frontal face of the transformed tensor is processed independently to build a
separate optimization sub-problems easier to solve. Next, the obtained
solutions are converted into projective tensors by inverse transform. By
considering a large number of experiments, we show the effectiveness of our
approach with respect to existing MDA methods.
