Spare L1-norm-based maximum margin criterion

• We propose a new sparse L1-norm-based maximum margin criterion (SMMC-L1).
• L1-norm instead of L2-norm is used in the objective function of SMMC-L1.
• We also use the elastic net to regularize the basis vectors.
• L1-norm used in SMMC-L1 is used for both robust and sparse modelling simultaneously.

Maximum margin criterion (MMC) is a popular method for dimensionality reduction or feature extraction. MMC can alleviate the small size sample (SSS) problem encountered by linear discriminant analysis (LDA) and extract more discriminant vectors than LDA. However, the objective function of MMC is derived from L2-norm, which makes MMC be sensitive to noise and outliers. Besides, the basis vectors of MMC are dense, which makes it hard to explain the obtained features. To address the drawbacks of MMC, in this paper, we propose a novel sparse L1-norm-based maximum margin criterion (SMMC-L1). L1-norm rather than L2-norm is used in the objective function of SMMC-L1. Besides, L1-norm is also used as a lasso penalty to regularize the basis vectors. An iterative algorithm for solving SMMC-L1 is proposed. Experiment results on some databases show the effectiveness of the proposed SMMC-L1.