2DTPCA: A New Framework for Multilinear Principal Component Analysis

Abstract

Two-directional two-dimensional principal component analysis ((2D$)^{2}$PCA) has shown promising results for it’s ability to both represent and recognize facial images. The current paper extends these results into a multilinear framework (referred to as two-directional Tensor PCA or 2DTPCA for short) using a recently defined tensor operator for 3rd-order tensors. The approach proceeds by first computing a low-dimensional projection tensor for the row-space of the image data (generally referred to as mode-l) and then subsequently computing a low-dimensional projection tensor for the column space of the image data (generally referred to as mode-3). Experimental results are presented on the ORL, extended Yale-B, COIL100, and MNIST data sets that show the proposed approach outperforms traditional “ tensor-based” PCA approaches with a much smaller subspace dimension in terms of recognition rates.