2Dtpca: A New Framework For Multilinear Principal Component Analysis

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 3$^\text{rd}$-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-1) 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, COIL-100, 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.