  In practical applications, we often have to deal with high order data, such
as a grayscale image and a video sequence are intrinsically 2nd-order tensor
and 3rd-order tensor, respectively. For doing clustering or classification of
these high order data, it is a conventional way to vectorize these data before
hand, as PCA or FDA does, which often induce the curse of dimensionality
problem. For this reason, experts have developed many methods to deal with the
tensorial data, such as multilinear PCA, multilinear LDA, and so on. In this
paper, we still address the problem of high order data representation and
recognition, and propose to study the result of merging multilinear PCA and
multilinear LDA into one scenario, we name it \textbf{GDA} for the abbreviation
of Generalized Discriminant Analysis. To evaluate GDA, we perform a series of
experiments, and the experimental results demonstrate our GDA outperforms a
selection of competing methods such (2D)$^2$PCA, (2D)$^2$LDA, and MDA.
