Robust Projective Low-Rank and Sparse Representation by Robust Dictionary Learning

In this paper, we discuss the robust factorization based robust dictionary learning problem for data representation. A Robust Projective Low-Rank and Sparse Representation model (R-PLSR) is technically proposed. Our R-PLSR model integrates the L1-norm based robust factorization and robust low-rank & sparse representation by robust dictionary learning into a unified framework. Specifically, R-PLSR performs the joint low-rank and sparse representation over the informative low-dimensional representations by robust sparse factorization so that the results are more accurate. To make the factorization and representation procedures robust to noise and outliers, R-PLSR imposes the sparse L2, 1-norm jointly on the reconstruction errors based on the factorization and dictionary learning. Note that L2, 1-norm can also minimize the reconstruction error as much as possible, since the L2, 1-norm theoretically tends to force many rows of the reconstruction error matrix to be zeros. The Nuclear-norm and L1-norm are jointly used on the representation coefficients so that salient representations can be obtained. Extensive results on several image datasets show that our R-PLSR formulation can deliver superior performance over other state-of-the-arts.