L1-norm and maximum margin criterion based discriminant locality preserving projections via trace Lasso

• We propose a L1-norm and MMC based DLPP method via trace Lasso.
• Our proposed algorithm can simultaneously consider the sparsity and correlation.
• We also propose an efficient procedure for solving the proposed method.

Discriminant locality preserving projections based on maximum margin criterion (DLPP/MMC) is a useful feature extraction method since it has shown good performances in pattern recognition. The conventional DLPP/MMC, however, is not robust to noises and outliers since its objective function is based on L2-norm. In this paper, we propose a novel L1-norm and maximum margin criterion based discriminant locality preserving projections via trace Lasso (DLPP/MMC-L1TL). L1-norm rather than L2-norm is used in the formulation of DLPP/MMC-L1TL, which makes it be robust to noises and outliers. Besides, in order to improve the performance of DLPP/MMC-L1TL further, we use trace Lasso to regularize the basis vectors. Trace Lasso, which can balance L1-norm and L2-norm and consider sparsity and correlation of data simultaneously, is a recently proposed norm. An iterative procedure for solving DLPP/MMC-L1TL is also proposed in this paper. The experiment results on some data sets demonstrate the effectiveness of DLPP/MMC-L1TL.