Discriminative Sparsity Preserving Projections for Semi-Supervised Dimensionality Reduction

In this letter, we propose a semi-supervised dimensionality reduction method named Discriminative Sparsity Preserving Projection (DSPP). In order to get the feature mapping f which projects the high-dimensional data into a low-dimensional intrinsic space, DSPP attempts to maintain the prior low-dimensional representation constructed by the data points and the known class labels and, meanwhile, considers the complexity of f in the ambient space and the smoothness of f in preserving the sparse representation of data. On one hand, the DSPP method obtains an explicit nonlinear feature mapping for the out-of-sample extrapolation. On the other hand, the DSPP method has a high discriminative ability which is inherited from the sparse representation of data. Experiment results show the effectiveness of the proposed method.