A New Framework For Multilinear Principal Component Analysis

Author: Cagri Ozdemir, Department of Computer Science and Engineering

Mentor: Dr. Randy Hoover, Department of Computer Science and Engineering

Principal component analysis (PCA) is a well-known dimension reduction technique widely used in the areas of image classification and pattern recognition. As traditional PCA requires “row-scanning”, it destroys the natural representation of the image and encounters small sample size problems. Two-directional two-dimensional principal component analysis ((2D)²PCA) has shown promising results for its 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-1) and then subsequently computing a low-dimensional projection tensor for the column space of the image data (generally referred to as mode-3). The proposed method obtains dimension reduction in both mode-1 and mode-3 directions. Experimental results are presented on the ORL, extended Yale-B, COIL100, and MNIST data sets that show the proposed approach outperforms other “tensor-based” PCA approaches with a much smaller subspace dimension in terms of recognition rates.