  With the dramatic increase of dimensions in the data representation,
extracting latent low-dimensional features becomes of the utmost importance for
efficient classification. Aiming at the problems of unclear margin
representation and difficulty in revealing the data manifold structure in most
of the existing linear discriminant methods, we propose a new discriminant
feature extraction framework, namely Robust Locality-Aware Regression (RLAR).
In our model, we introduce a retargeted regression to perform the marginal
representation learning adaptively instead of using the general average
inter-class margin. Besides, we formulate a new strategy for enhancing the
local intra-class compactness of the data manifold, which can achieve the joint
learning of locality-aware graph structure and desirable projection matrix. To
alleviate the disturbance of outliers and prevent overfitting, we measure the
regression term and locality-aware term together with the regularization term
by the L2,1 norm. Further, forcing the row sparsity on the projection matrix
through the L2,1 norm achieves the cooperation of feature selection and feature
extraction. Then, we derive an effective iterative algorithm for solving the
proposed model. The experimental results over a range of UCI data sets and
other benchmark databases demonstrate that the proposed RLAR outperforms some
state-of-the-art approaches.
