Learning robust latent subspace for discriminative regression

In this paper, we present a generic effective formulation, dubbed discriminative latent linear regression (DLL-R), for multi-category classification. We formulate the DLLR optimization problem as a joint learning framework of discriminative latent feature selection and robust linear regression. Specifically, instead of directly projecting the original high-dimensional features onto a target space, DLLR learns discriminative latent representation by concurrently suppressing the redundant information from original features and constructing a robust latent subspace. To improve the effectiveness of the regression task, a capped l_p-norm regression model is formulated for robust linear regression. Furthermore, DLLR incorporates learning latent representation and building regressing prediction into one framework for reducing the classification error of the regression model. An efficient optimization algorithm is developed to solve the resulting optimization problem. Extensive experimental results conducted on diverse databases validate the effectiveness of the proposed DLLR method in comparison with state-of-the-art regression methods.