Nonparametric locality reforming projection for linear discriminative dimensionality reduction

Discriminative dimensionality reduction (DDR) makes significant sense in high-dimensional data analysis. Over the decades, research has demonstrated that modeling the intrinsic local structure can well represent the data. Using pairwise neighboring data points to represent the between-class and within-class differences, local structure-based DDR methods are effective. However, how to set the parameters, e.g., the parameter of k-nearest neighbors, is still an open question, which makes the algorithms perform unstably. To address this issue, we propose a nonparametric local structure-based DDR method, named nonparametric locality reforming projection (NLRP). Also, we propose an effective analytical method for effectiveness analysis in both cases of sufficient and insufficient training samples for DDR methods. The experiment results on the AR, Carnegie Mellon University pose, illumination, and expression, and ORL databases are consistent with the theoretical analysis and verified the effectiveness of the proposed NLRP method. Especially, NLRP performs well in the case of very insufficient samples.