Kernelization of Tensor Discriminant Analysis with Application to Image Recognition

Multilinear discriminant analysis (MLDA), a novel approach based upon recent developments in tensor-tensor decomposition, has been proposed recently and showed better performance than traditional matrix linear discriminant analysis (LDA). The current paper presents a nonlinear generalization of MLDA (referred to as KMLDA) by extending the well known "kernel trick" to multilinear data. The approach proceeds by defining a new dot product based on new tensor operators for third-order tensors. Experimental results on the ORL, extended Yale B, and COIL-100 data sets demonstrate that performing MLDA in feature space provides more class separability. It is also shown that the proposed KMLDA approach performs better than the Tucker-based discriminant analysis methods in terms of image classification.