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

TL;DR

This paper introduces GDA, a method combining multilinear PCA and LDA for high-order tensor data classification, demonstrating superior performance over existing tensor-based methods in visual recognition tasks.

Contribution

It proposes a novel approach called GDA that merges multilinear PCA and LDA for tensor data analysis, addressing high-dimensionality issues in visual classification.

Findings

GDA outperforms (2D)^2PCA, (2D)^2LDA, and MDA in experiments.

GDA effectively handles high-order tensor data without vectorization.

Experimental results validate the superiority of GDA in classification tasks.

Abstract

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.