The theoretical analysis of GLRAM and its applications

Matrix-based methods such as two-dimensional principal component analysis (2DPCA) and generalized low rank approximations of matrices (GLRAM) have gained wide attention from researchers due to their computational efficiency. In this paper, we propose a non-iterative algorithm for GLRAM. Firstly, the optimal property of GLRAM is revealed, which is closely related to PCA. Moreover, it also shows that the reconstruction error of GLRAM is not smaller than that of PCA when considering the same dimensionality. Secondly, a non-iterative algorithm for GLRAM is derived. And the proposed method obtains smaller reconstruction error than 2DPCA or GLRAM. Finally, experimental results on face images and handwritten numeral characters show that the proposed method can achieve competitive results with some existing methods such as 2DPCA and PCA in terms of the classification performance or the reconstruction error.