  A relaxed two dimensional principal component analysis (R2DPCA) approach is
proposed for face recognition. Different to the 2DPCA, 2DPCA-$L_1$ and G2DPCA,
the R2DPCA utilizes the label information (if known) of training samples to
calculate a relaxation vector and presents a weight to each subset of training
data. A new relaxed scatter matrix is defined and the computed projection axes
are able to increase the accuracy of face recognition. The optimal $L_p$-norms
are selected in a reasonable range. Numerical experiments on practical face
databased indicate that the R2DPCA has high generalization ability and can
achieve a higher recognition rate than state-of-the-art methods.
