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A new data-driven bilateral generalized two-dimensional quaternion principalcomponent analysis (BiG2DQPCA) is presented to extract the features of matrixsamples from both row and column directions. This general framework directlyworks on the 2D color images without vectorizing and well preserves the spatialand color information, which makes it flexible to fit various real-worldapplications. A generalized ridge regression model of BiG2DQPCA is firstlyproposed with orthogonality constrains on aimed features. Applying thedeflation technique and the framework of minorization-maximization, a newquaternion optimization algorithm is proposed to compute the optimal featuresof BiG2DQPCA and a closed-form solution is obtained at each iteration. A newapproach based on BiG2DQPCA is presented for color face recognition and imagereconstruction with a new data-driven weighting technique. Sufficient numericalexperiments are implemented on practical color face databases and indicate thesuperiority of BiG2DQPCA over the state-of-the-art methods in terms ofrecognition accuracies and rates of image reconstruction.

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