Locality constrained dictionary learning for non‐linear dimensionality reduction and classification

In view of the incremental dimensionality reduction problem of existing non‐linear dimensionality reduction methods, a novel algorithm, based on locality constrained dictionary learning (LCDL), is proposed in this study. During the dictionary learning process, the neighbourhood size of some potential landmarks on a non‐linear manifold is constrained to maintain the intrinsic local geometric feature of the datasets. Meanwhile, to improve the dictionary's discrimination ability, a structured dictionary is learnt by LCDL, whose sub‐dictionaries are class‐specific. Then sparse coding and its reconstruction errors are used for classification. The experimental results of dimensionality reduction prove that, compared with the existing methods, the proposed method can solve the out of sample extension and large‐scale datasets problems efficiently. In addition, the experimental results of face, gender, and object category classification demonstrate that the authors’ algorithm outperforms some competing dictionary learning methods.