Jointly Linear Embedding via L _2,1 -Norm for Dimensionality Reduction

In this study, we present a novel dimensionality reduction method called Jointly Linear Embedding (JLE). Unlike previous methods such as Neighborhood Preserving Embedding (NPE), in which local neighborhood information is preserved during the dimensionality reduction procedure, JLE aims to preserve the sparse reconstructive relationship of the original data by taking the merits of jointly sparse learning based on L _2,1 -norm. In the framework of JLE, the sparse weight matrix can reflect the intrinsic geometric structures of the original data and inherit the ability of discriminant analysis. By solving the L _2,1 -norm regularized objective function, the optimal projections, which are invariant to rotations and robust to outliers, can be obtained by JLE. Extensive experiments on visual recognition and fabric defect classification datasets demonstrate the superiority of the proposed L _2,1 -norm regularized learning method compared with the state-of-the-art methods.