: Recently, a method called (PC)2 A was proposed to deal with face recognition with one training image per person. As an extension of the standard eigenface technique, (PC)2 A combines linearly each original face image with its corresponding first-order projection into a new face and then performs principal component analysis (PCA) on a set of the newly combined (training) images. It was reported that (PC)2 A could achieve higher accuracy than the eigenface technique through using 10%-15% fewer eigenfaces. In this paper, we generalize and further enhance (PC)2 A along two directions. In the first direction, we combine the original image with its second-order projections as well as its first-order projection in order to acquire more information from the original face, and then similarly apply PCA to such a set of the combined images. In the second direction, instead of combining them, we still regard the projections of each original image as single derived images to augment training ima...