Low-rank analysis–synthesis dictionary learning with adaptively ordinal locality

Analysis dictionary learning (ADL) has been successfully applied to a variety of learning systems. However, the ordinal locality of analysis dictionary has rarely been explored in constructing discriminative terms. In this paper, a discriminative low-rank analysis–synthesis dictionary learning (LR-ASDL) algorithm with the adaptively ordinal locality is proposed for object classification. Specifically, we first explicitly introduce the relations between the analysis atoms and profiles (i.e., row vectors of the coefficients matrix). That is, the similarity between two profiles depends on that between the corresponding analysis atoms. Moreover, an adaptively ordinal locality preserving(AOLP) term is constructed by simultaneously exploiting the profiles and analysis atoms, which can be learned in a supervised way. In this way, the neighborhood correlations between analysis atoms and the high-order ranking information of each analysis atom's neighbors can be simultaneously preserved in the learning process. Particularly, this helps to uncover the intrinsic underlying data factors and inherit the geometry structure information of training samples. Furthermore, the low-rank model is imposed on the synthesis atoms to further facilitate the learned dictionaries to be more discriminative. Extensive experimental results on eight databases demonstrate that the LR-ASDL algorithm clearly outperforms some analysis and synthesis dictionary learning algorithms using deep and hand-crafted features