  Dimensionality reduction is a main step in the learning process which plays
an essential role in many applications. The most popular methods in this field
like SVD, PCA, and LDA, only can be applied to data with vector format. This
means that for higher order data like matrices or more generally tensors, data
should be fold to the vector format. So, in this approach, the spatial
relations of features are not considered and also the probability of
over-fitting is increased. Due to these issues, in recent years some methods
like Generalized low-rank approximation of matrices (GLRAM) and Multilinear PCA
(MPCA) are proposed which deal with the data in their own format. So, in these
methods, the spatial relationships of features are preserved and the
probability of overfitting could be fallen. Also, their time and space
complexities are less than vector-based ones. However, because of the fewer
parameters, the search space in a multilinear approach is much smaller than the
search space of the vector-based approach. To overcome this drawback of
multilinear methods like GLRAM, we proposed a new method which is a general
form of GLRAM and by preserving the merits of it have a larger search space.
Experimental results confirm the quality of the proposed method. Also, applying
this approach to the other multilinear dimensionality reduction methods like
MPCA and MLDA is straightforward.
