F-2D-QPCA: A Quaternion Principal Component Analysis Method for Color Face Recognition

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.