  In this paper, we investigate the robust dictionary learning (DL) to discover
the hybrid salient low-rank and sparse representation in a factorized
compressed space. A Joint Robust Factorization and Projective Dictionary
Learning (J-RFDL) model is presented. The setting of J-RFDL aims at improving
the data representations by enhancing the robustness to outliers and noise in
data, encoding the reconstruction error more accurately and obtaining hybrid
salient coefficients with accurate reconstruction ability. Specifically, J-RFDL
performs the robust representation by DL in a factorized compressed space to
eliminate the negative effects of noise and outliers on the results, which can
also make the DL process efficient. To make the encoding process robust to
noise in data, J-RFDL clearly uses sparse L2, 1-norm that can potentially
minimize the factorization and reconstruction errors jointly by forcing rows of
the reconstruction errors to be zeros. To deliver salient coefficients with
good structures to reconstruct given data well, J-RFDL imposes the joint
low-rank and sparse constraints on the embedded coefficients with a synthesis
dictionary. Based on the hybrid salient coefficients, we also extend J-RFDL for
the joint classification and propose a discriminative J-RFDL model, which can
improve the discriminating abilities of learnt coeffi-cients by minimizing the
classification error jointly. Extensive experiments on public datasets
demonstrate that our formulations can deliver superior performance over other
state-of-the-art methods.
