Data-Driven Bilateral Generalized Two-Dimensional Quaternion Principal Component Analysis with Application to Color Face Recognition

A new data-driven bilateral generalized two-dimensional quaternion principal component analysis (BiG2DQPCA) is presented to extract the features of matrix samples from both row and column directions. This general framework directly works on the 2D color images without vectorizing and well preserves the spatial and color information, which makes it flexible to fit various real-world applications. A generalized ridge regression model of BiG2DQPCA is firstly proposed with orthogonality constrains on aimed features. Applying the deflation technique and the framework of minorization-maximization, a new quaternion optimization algorithm is proposed to compute the optimal features of BiG2DQPCA and a closed-form solution is obtained at each iteration. A new approach based on BiG2DQPCA is presented for color face recognition and image reconstruction with a new data-driven weighting technique. Sufficient numerical experiments are implemented on practical color face databases and indicate the superiority of BiG2DQPCA over the state-of-the-art methods in terms of recognition accuracies and rates of image reconstruction.