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Dimensionality reduction is a main step in the learning process which playsan essential role in many applications. The most popular methods in this fieldlike SVD, PCA, and LDA, only can be applied to data with vector format. Thismeans that for higher order data like matrices or more generally tensors, datashould be fold to the vector format. So, in this approach, the spatialrelations of features are not considered and also the probability ofover-fitting is increased. Due to these issues, in recent years some methodslike Generalized low-rank approximation of matrices (GLRAM) and Multilinear PCA(MPCA) are proposed which deal with the data in their own format. So, in thesemethods, the spatial relationships of features are preserved and theprobability of overfitting could be fallen. Also, their time and spacecomplexities are less than vector-based ones. However, because of the fewerparameters, the search space in a multilinear approach is much smaller than thesearch space of the vector-based approach. To overcome this drawback ofmultilinear methods like GLRAM, we proposed a new method which is a generalform of GLRAM and by preserving the merits of it have a larger search space.Experimental results confirm the quality of the proposed method. Also, applyingthis approach to the other multilinear dimensionality reduction methods likeMPCA and MLDA is straightforward.

A novel extension of Generalized Low-Rank Approximation of Matrices based on multiple-pairs of transformations