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.

翻译：提出了一种新的数据驱动双边广义二维四元数主成分分析（BiG2DQPCA），用于从行和列两个方向提取矩阵样本的特征。该通用框架直接处理二维彩色图像，无需向量化，并能很好地保留空间和颜色信息，使其能够灵活适应各种实际应用。首先提出了一个带有目标特征正交约束的BiG2DQPCA广义岭回归模型。利用紧缩技术和最小化-最大化框架，提出了一种新的四元数优化算法来计算BiG2DQPCA的最优特征，并在每次迭代中获得闭式解。基于BiG2DQPCA，结合一种新的数据驱动加权技术，提出了一种用于彩色人脸识别和图像重建的新方法。在实际彩色人脸数据库上进行了充分的数值实验，结果表明BiG2DQPCA在识别准确率和图像重建率方面优于现有最先进方法。