Elastic preserving projections based on L1-norm maximization

Elastic preserving projections (EPP) is a classical manifold learning technique for dimensionality reduction, which has demonstrated good performance in pattern recognition. However, EPP is sensitive to the outliers because it makes use of the L2-norm for optimization. In this paper, we propose an effective and robust EPP version based on L1-norm maxmization (EPP-L1), which can learn the optimal projection vectors by maximizing the ratio of the global dispersion to the local dispersion using the L1-norm rather than L2-norm. The proposed method is proved to be feasible and also robust to outliers while overcoming the singular problem of the local scatter matrix for EPP. Experiments on five popular face image databases demonstrate the effectiveness of the proposed method.