  Low-rank learning has attracted much attention recently due to its efficacy
in a rich variety of real-world tasks, e.g., subspace segmentation and image
categorization. Most low-rank methods are incapable of capturing
low-dimensional subspace for supervised learning tasks, e.g., classification
and regression. This paper aims to learn both the discriminant low-rank
representation (LRR) and the robust projecting subspace in a supervised manner.
To achieve this goal, we cast the problem into a constrained rank minimization
framework by adopting the least squares regularization. Naturally, the data
label structure tends to resemble that of the corresponding low-dimensional
representation, which is derived from the robust subspace projection of clean
data by low-rank learning. Moreover, the low-dimensional representation of
original data can be paired with some informative structure by imposing an
appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a
novel constrained LRR method. The objective function is formulated as a
constrained nuclear norm minimization problem, which can be solved by the
inexact augmented Lagrange multiplier algorithm. Extensive experiments on image
classification, human pose estimation, and robust face recovery have confirmed
the superiority of our method.
