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

A Report on Multilinear PCA Plus Multilinear LDA to Deal with Tensorial Data: Visual Classification as An Example