Nonnegative low-rank representation based manifold embedding for semi-supervised learning

The low-rank representation (LRR) can get essential row-representation of data and it is robust to illumination variation, occlusions and other types of noise. This paper presents a novel manifold embedding classification algorithm based on nonnegative low-rank representation for semi-supervised learning (MEC-NNLRR). In the proposed algorithm, label fitness, manifold smoothness and low-rank representation are integrated, and the label information from the labeled data and the manifold structure from all data are fully and effectively utilized. Based on LRR and manifold learning, the proposed MEC-NNLRR can capture the global and local structure information of the observed data. The obtained nonnegative low-rank representation coefficients can be used as a graph similarity matrix. Considering the physical interpretation of the graph matrix, we impose the non-negativity constraint on the coefficients. In addition, no matter whether the training samples or test samples are corrupted, the proposed MEC-NNLRR is little affected by noise. Extensive experiments on public image databases demonstrate that the proposed MEC-NNLRR is an excellent algorithm and achieves satisfactory results.