Discriminant Locality Preserving Projections Based on L1-Norm Maximization

Conventional discriminant locality preserving projection (DLPP) is a dimensionality reduction technique based on manifold learning, which has demonstrated good performance in pattern recognition. However, because its objective function is based on the distance criterion using L2-norm, conventional DLPP is not robust to outliers which are present in many applications. This paper proposes an effective and robust DLPP version based on L1-norm maximization, which learns a set of local optimal projection vectors by maximizing the ratio of the L1-norm-based locality preserving between-class dispersion and the L1-norm-based locality preserving within-class dispersion. The proposed method is proven to be feasible and also robust to outliers while overcoming the small sample size problem. The experimental results on artificial datasets, Binary Alphadigits dataset, FERET face dataset and PolyU palmprint dataset have demonstrated the effectiveness of the proposed method.