Low-Rank Discriminative Adaptive Graph Preserving Subspace Learning

The global and local geometric structures of data play a key role in subspace learning. Although many manifold-based subspace learning methods have been proposed for preserving the local geometric structure of data, they usually use a predefined neighbor graph to characterize it. However, the predefined neighbor graph might be not optimal since it keeps fixed during the subsequent subspace learning process. Moreover, most manifold-based subspace learning methods ignore the global structure of data. To address these issues, we propose a low-rank discriminative adaptive graph preserving (LRDAGP) subspace learning method for image feature extraction and recognition by integrating the low-rank representation , adaptive manifold learning, and supervised regularizer into a unified framework. To capture the optimal local geometric structure of data for subspace learning, LRDAGP adopts an adaptive manifold learning strategy that the neighbor graph is adaptively updated during the subspace learning process. To capture the optimal global structure of data for subspace learning, LRDAGP also seeks the low-rank representations of data in a low-dimensional subspace during the subspace learning process. Moreover, for improving the discrimination ability of the learned subspace, a supervised regularizer is designed and incorporated into the LRDAGP model. Experimental results on several image datasets show that LRDAGP is effective for image feature extraction and recognition.