  Recently regression analysis becomes a popular tool for face recognition. The
existing regression methods all use the one-dimensional pixel-based error
model, which characterizes the representation error pixel by pixel individually
and thus neglects the whole structure of the error image. We observe that
occlusion and illumination changes generally lead to a low-rank error image. To
make use of this low-rank structural information, this paper presents a
two-dimensional image matrix based error model, i.e. matrix regression, for
face representation and classification. Our model uses the minimal nuclear norm
of representation error image as a criterion, and the alternating direction
method of multipliers method to calculate the regression coefficients. Compared
with the current regression methods, the proposed Nuclear Norm based Matrix
Regression (NMR) model is more robust for alleviating the effect of
illumination, and more intuitive and powerful for removing the structural noise
caused by occlusion. We experiment using four popular face image databases, the
Extended Yale B database, the AR database, the Multi-PIE and the FRGC database.
Experimental results demonstrate the performance advantage of NMR over the
state-of-the-art regression based face recognition methods.
