Two-dimensional quaternion principal component analysis (2D-QPCA) is one of the successful dimensionality reduction methods for color face recognition. However, 2D-QPCA is sensitive to outliers. For solving this shortcoming, an efficient robust method(F-2D-QPCA) is presented by means of Frobenius norm(F-norm). The goal of F-2D-QPCA is to find the projection matrix such that the projected data has the maximum variance based on F-norm, and it is more robust to outliers and has higher recognition accuracy than other methods, such as 2D-QPCA,R 1-2-DPCA, F-norm 2DPCA and 2D-PCA, etc. Also, we study in detail a quaternion optimization problem, propose a nongreedy iterative algorithm and prove its convergence. Experiments on several color face databases illustrate the superiority of our proposed method.

Principal component analysis (PCA) is one of the successful dimensionality reduction approaches for color face recognition. For various PCA methods, the experiments show that the contribution of eigenvectors is different and different weights of eigenvectors can cause different effects. Based on this, a modified and simplified color two-dimensional quaternion principal component analysis (M2D-QPCA) method is proposed along the framework of the color two-dimensional quaternion principal component analysis (2D-QPCA) method and the improved two-dimensional quaternion principal component analysis (2D-GQPCA) method. The shortcomings of 2D-QPCA are corrected and the CPU time of 2D-GQPCA is reduced. The experiments on two real face data sets show that the accuracy of M2D-QPCA is better than that of 2D-QPCA and other PCA-like methods and the CPU time of M2D-QPCA is less than that of 2D-GQPCA.