L1-norm based null space discriminant analysis

Null space based linear discriminant analysis (NSLDA) is a well-known feature extraction method, which can make use of the most discriminant information in the null space of within-class scatter matrix. However, the conventional formulation of NSLDA is based on L2-norm which makes NSLDA be sensitive to outlier. To address the problem of NSLDA, in this paper, we propose a simple and robust NSLDA based on L1-norm (L1-NSLDA). An iterative algorithm for solving L1-NSLDA is also proposed. Compared to NSLDA, L1-NSLDA is more robust than NSLDA since it is more robust to outliers and noise. Experiment results on some image databases confirm the effectiveness of the proposed L1-NSLDA.