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This paper first discusses some theoretical properties of 2D principal component analysis (2DPCA) and then presents a horizontal and vertical 2DPCA-based discriminant analysis (HVDA) method for face verification. The HVDA method, which applies 2DPCA horizontally and vertically on the image matrices (2D arrays), achieves lower computational complexity than the traditional PCA and Fisher linear discriminant analysis (LDA)-based methods that operate on high dimensional image vectors (1D arrays). The horizontal 2DPCA is invariant to vertical image translations and vertical mirror imaging, and the vertical 2DPCA is invariant to horizontal image translations and horizontal mirror imaging. The HVDA method is therefore less sensitive to imprecise eye detection and face cropping, and can improve upon the traditional discriminant analysis methods for face verification. Experiments using the face recognition grand challenge (FRGC) and the biometric experimentation environment system show the effectiveness of the proposed method. In particular, for the most challenging FRGC version 2 Experiment 4, which contains 12thinspace776 training images, 16 028 controlled target images, and 8014 uncontrolled query images, the HVDA method using a color configuration across two color spaces, namely, the YIQ and the YCbCr color spaces, achieves the face verification rate (ROC III) of 78.24% at the false accept rate of 0.1%.