A Promising Nonlinear Dimensionality Reduction Method: Kernel-Based Within Class Collaborative Preserving Discriminant Projection

Abstract

High-dimensional small sample size problems exist in the real world, which significantly increases the difficulty of data processing. In this paper, we propose a kernel-based within class collaborative preserving discriminant projection method to reduce data dimensionality. In order to deal with nonlinear problems and improve the discrimination of the projection subspace, the proposed method preserves the collaborative reconstruction relationship of the same class samples in the kernel space, and pursuits maximizing the between class scatter. A two-step eigenvalue decomposition method is used to stably obtain the optimal discriminant projection matrix. Moreover, simulation experiments show that, even in low dimensions and small sample size, the proposed method can achieve high recognition accuracy.