统计不相关最佳鉴别矢量集的本质研究

对统计不相关最佳鉴别矢量集的本质进行研究，在基于总体散布矩阵特征分解的基础上，构造了一种白化变换，使得变换后的样本空间中的总体散布矩阵为单位矩阵，这样使得传统的最佳鉴别矢量集算法得到的均是具有统计不相关的最佳鉴别矢量集，从而揭示了统计不相关最佳鉴别变换的本质——白化变换加普通的线性鉴别变换。该方法的最大优点在于所获得的最优鉴别矢量同时具有正交性和统计不相关性。该方法对代数特征抽取具有普遍适用性。用ORL人脸数据库的数值实验，验证了该方法的有效性。

A Study on the Essence of Optimal Statistical Uncorrelated Discriminant Vectors

A study has been made on the essence of optimal set of uncorrelated discriminant vectors in this paper. A whitening transform has been constructed on the basis of the eigen decomposition of population scatter matrix, which makes the population scatter matrix an identity matrix in the transformed sample space. Thus, the optimal discriminant vectors solved by conventional LDA methods are statistical uncorrelated. The research indicates that the essence of the statistical uncorrelated discriminant transform is the whitening transform plus conventional linear discriminant transform. The distinguished characteristic of the proposed method is that the obtained optimal discriminant vectors are orthogonal and statistical uncorrelated. The proposed method suits for all the problems of algebraic feature extraction. The numerical experiments on facial database of ORL show the effectiveness of the proposed method.