Unsupervised feature extraction by low-rank and sparsity preserving embedding

Manifold based feature extraction has been proved to be an effective technique in dealing with the unsupervised classification tasks. However, most of the existing works cannot guarantee the global optimum of the learned projection, and they are sensitive to different noises. In addition, many methods cannot catch the discriminative information as much as possible since they only exploit the local structure of data while ignoring the global structure. To address the above problems, this paper proposes a novel graph based feature extraction method named low-rank and sparsity preserving embedding (LRSPE) for unsupervised learning. LRSPE attempts to simultaneously learn the graph and projection in a framework so that the global optimal projection can be obtained. Moreover, LRSPE exploits both global and local information of data for projection learning by imposing the low-rank and sparse constraints on the graph, which promotes the method to obtain a better performance. Importantly, LRSPE is more robust to noise by imposing the l2,1 sparsity norm on the reconstruction errors. Experimental results on both clean and noisy datasets prove that the proposed method can significantly improve classification accuracy and it is robust to different noises in comparison with the state-of-the-art methods.