Improvement and Kernelization of T-2DPCA with Application to Face Recognition

T-2DPCA, a novel approach considering the third-order tensors as linear operators on the space of oriented matrices, benefits from treating a 2D image as an inherently integrated object, has been proposed recently and showed better performance than traditional matrix PCA in image analysis and recognition. In T-2DPCA, a reconstructing tubal coefficient is obtained from the defined tensor product, called T-product, of a 2D image and a 2D basis element. In this study, by assuming that an eigenvector of the covariance tensor of the 2D training images is the tensor linear combination, called T-linear combination, of the training images, the T-2DPCA is improved to a new version with better performance. The improved method is further extended to a nonlinear version by using the general kernel trick in machine learning field, but with a new inner product called inside product defined with the T-product in the third-order tensor spaces, and simultaneously the general inner product defended in vector spaces. The effectiveness of the proposed algorithms is tested by face recognition experiment results.