Robust jointly sparse embedding for dimensionality reduction

As a famous linear manifold learning method, orthogonal neighborhood preserving projections (ONPP) is able to provide a set of orthogonal projections for dimensionality reduction. However, a problem of ONPP is that it takes the L2-norm as the basic measurement and therefore tends to be sensitive to the outliers or the variations of the data. Aiming at strengthening the robustness of the conventional method ONPP, in this paper, a robust and sparse dimensionality reduction method based on linear reconstruction, called Robust Jointly Sparse Embedding (RJSE), is proposed by introducing L2, 1-norm as the basic measurement and regularization term. We design a simple iterative algorithm to obtain the optimal solution of the proposed robust and sparse dimensionality reduction model. Experiments on four benchmark data sets demonstrate the competitive performance of the proposed method compared with the state-of-the-art methods.