Fisher极小准则不相关空间算法及其在人脸识别中的应用

不相关空间算法是一种基于广义Fisher准则求解不相关鉴别矢量集的快速算法，但该算法要求总体散度矩阵可逆。针对高维小样本的情况，文中提出求解不相关鉴别矢量集的改进方法。该方法的基本思路是在类间散度矩阵的值空间中运用广义Fisher极小准则求解鉴别矢量集，并讨论在该子空间中进行求解的合理性。针对高维情况下类间散度矩阵值空间的计算效率问题，提出首先利用PCA算法将数据降维，然后在低维空间中求解值空间的策略并讨论其合理性。在ORL人脸数据库上的实验验证该方法的有效性，其识别率高于传统的Fisher脸方法和不相关空间算法。

An Uncorrelated Space Algorithm Based on Fisher Minimum Criterion and Its Application to Face Recognition

Uncorrelated space algorithm is a fast method for extracting uncorrelated discriminant vectors based on the generalized fisher criterion,but it requires the total-scatter matrix to be reversible. To solve this problem,an improved uncorrelated features extraction method based on the generalized Fisher minimum criterion and uncorrelated space algorithm is proposed. The main idea of the proposed method is to solve the discriminant vectors of generalized fisher minimum criterion in the non-null subspace of the between-class scatter matrix. The rationality of the idea is discussed. A strategy including two steps is proposed to get the non-null subspace efficiently from high dimensional data. Firstly,the original data are mapped to a low dimensional subspace by PCA algorithm. Then,the non-null subspace of the between-class scatter matrix can be solved efficiently in the subspace,and the rationality of the process is discussed. The experimental results on standard face database show that the proposed method is efficient with higher accuracies compared with Fisherface algorithm and the uncorrelated space algorithm.