Supervised Low-Rank Embedded Regression (SLRER) for Robust Subspace Learning

Locality-preserving projection (LPP) has been widely used in feature extraction. However, LPP does not use data category information and uses the ${L}_{2}$ -norm for distance measurement, which is highly sensitive to outliers. In this paper, we consider the LPP weight matrix from a supervised perspective and combine the low-rank regression method to propose a new model to discover and extract features. By using the ${L}_{2,1}$ -norm to constrain the loss function and the regression matrix, not only is the sensitivity to outliers reduced but the low-rank condition of the regression matrix is also restricted. Then, we propose a solution to the optimization problem. Finally, we apply the method to a series of face databases, handwriting digital datasets and palmprint datasets to test the performance, and the experimental results show that this method is effective compared with some existing methods.