Abstract: In order to construct the adaptive adjacency graph between data points, and also to overcome the disadvantage that the coefficients of sparse representation and collaborative representation were independent, the low-rank representation projections(LRRP)and discriminative low-rank representation projections(DLRRP)were proposed. In these two manifold learning methods, the weighted matrix was constructed by low-rank representation(LRR). The adjacencies defined by the coefficients were preserved in the feature space. By virtue of the clustering property of the coefficients, an within-class scatter minimum term was added in the optimization objective, which leaded to a discriminative projection. The experimental results showed that compared with other manifold learning algorithms, LRRP and DLRRP could obtain the better recognition accuracies. The proposed methods were effective feature extraction algorithms and enriched the manifold learning framework.

Key words: manifold learning, low-rank representation, face recognition, feature extraction, adjacency graph