Kernel Neighborhood Preserving Embedding and its Essence Analysis

A new dimensionality reduction method, neighborhood preserving embedding (NPE) is recently proposed which offers a linear yet powerful method to preserve the local neighborhood structure on the data manifold. However, it is confined to linear transforms in the data space. For this, kernel NPE (KNPE) is presented, which preserves the local neighborhood structure in the higher-dimension feature space. To avoid computing the inverse matrix of the positive semi-definite kernel matrix, a transformed optimization problem and QR decomposition are used. Then the analysis on KNPE reveals that KNPE is equivalent to kernel principal component analysis (KPCA) plus NPE. The experimental results on the real-world data sets illustrate the effectiveness of the new algorithm.