基于核空间中最优变换和聚类中心的鉴别特征提取

Extraction of Discriminant Features Based on Optimal Transformation and Cluster Centers of Kernel Space

应用统计学习理论中的核化原理,可以将许多线性特征提取算法推广至非线性特征提取算法.提出了基于核化原理的最优变换与聚类中心算法,即通过非线性变换,将数据映射到高维核空间,应用最优变换算法,实现原空间数据的非线性特征提取,而求解过程却借助"核函数",回避了复杂非线性变换的具体表达形式.新算法可提取稳健的非线性鉴别特征,从而解决复杂分布数据的模式分类问题.大量数值实验表明新算法比传统的最优变换与聚类中心算法更有效,甚至优于经典的核Fisher判别分析.

As is known, kernel method is one of the most important research points in statistical learning theory, and the kernel-based learning methods are attracting extensive research interests. It has been proved that a lot of linear feature extraction methods can be generalized to the nonlinear learning methods by using kernel methods. In this paper, a new nonlinear learning method of optimal transformation and cluster centers （OT-CC） is presented by using kernel technique. Data are mapped into the high dimensional kernel space via nonlinear transformation from original space, and then the learning method of optimal transformation and cluster centers is applied for feature extraction. However, the kernel function is utilized in result resolving process so that the complex expression of nonlinear transformation is avoided. The novel method is named optimal transformation and cluster center algorithm of kernel space （KOT-CC）, which is a powerful technique for extracting nonlinear discriminant features and is very effective in solving pattern recognition problems where the overlap between patterns is serious. A large number of experiments demonstrate that the new algorithm outperforms OT-CC and kernel Fisher discriminant analysis （KFDA） in ability for extracting nonlinear diseriminant features and computation complexity. Furthermore, the problem of ＂course dimensionality＂ is avoided.