Kernel neighborhood preserving embedding for classification

Abstract

The Neighborhood Preserving Embedding (NPE) algorithm is recently proposed as a new dimensionality reduction method. However, it is confined to linear transforms in the data space. For this, based on the NPE algorithm, a new nonlinear dimensionality reduction method is proposed, which can preserve the local structures of the data in the feature space. First, combined with the Mercer kernel, the solution to the weight matrix in the feature space is gotten and then the corresponding eigenvalue problem of the Kernel NPE (KNPE) method is deduced. Finally, the KNPE algorithm is resolved through a transformed optimization problem and QR decomposition. The experimental results on three real-world data sets show that the new method is better than NPE, Kernel PCA (KPCA) and Kernel LDA (KLDA) in performance.