Robust Discriminative Projective Dictionary Pair Learning by Adaptive Representations

Abstract

In this paper, we mainly propose a Robust Adaptive Projective Dictionary Pair Learning (RA-DPL) framework based on the adaptive discriminative representations. Our formulation can seamlessly integrate the robust projective dictionary pair learning and the adaptive sparse representation learning into a unified model. RA-DPL improves the existing DPL algorithm in threefold. First, RA-DPL aims at computing the robust projective dictionary pairs by employing the sparse and robust $l_{2,1}$ -norm to encode the reconstruction error. Second, RA-DPL regularizes the robust $l_{2,1}$ -norm on the analysis dictionary so that the analysis dictionary can extract sparse coefficients from the given samples explicitly. More importantly, the optimization of $l_{2,1}$ -norm is so efficient, that is, the sparse coding step will be time-saving. Third, RA-DPL can clearly preserve the local neighborhood relationship of the sparse coefficients within each class, which can make the learnt representations discriminating and can also improve the discriminating power of learnt dictionary. Extensive simulations on image databases demonstrate that our RA-DPL can obtain the superior performance over other state-of-the-arts.