Low-Rank Linear Embedding for Image Recognition

Locality preserving projections (LPP) has been widely studied and extended in recent years, because of its promising performance in feature extraction. In this paper, we propose a modified version of the LPP by constructing a novel regression model. To improve the performance of the model, we impose a low-rank constraint on the regression matrix to discover the latent relations between different neighbors. By using the <inline-formula><tex-math notation="LaTeX"> $L_{2,1}$</tex-math></inline-formula>-norm as a metric for the loss function, we can further minimize the reconstruction error and derive a robust model. Furthermore, the <inline-formula><tex-math notation="LaTeX">$L_{2,1}$ </tex-math></inline-formula>-norm regularization term is added to obtain a jointly sparse regression matrix for feature selection. An iterative algorithm with guaranteed convergence is designed to solve the optimization problem. To validate the recognition efficiency, we apply the algorithm to a series of benchmark datasets containing face and character images for feature extraction. The experimental results show that the proposed method is better than some existing methods. The code of this paper can be downloaded from <uri>http://www.scholat.com/laizhihui</uri>.