  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.
