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.