一种求解Fisher最佳鉴别矢量的新算法及人脸识别

Ｆｉｓｈｅｒ最佳鉴别矢量是高维模式分析中的有效方法，当训练样本数相对于特征空间的维数较小时，就成了小样本问题。为了求解小样本问题，人们提出了一系列方法并取得了的效果。但在类内距离为零的情况下民的方法均得不到最佳解，该文从理论上说明了这一点，并给一种在任何情况下都能得到最佳解的新算法，试验结果这样的推断。

A Novel Algorithm Solving Fisher Optimal Discriminant Vector and Facial Recognition

Fisher optimal discriminant vectors method is an effective method in pattern analysis of high dimension. When the number of the training samples is small compared with the dimensionality of the feature space, the problem becomes the case of a small number of samples. People have proposed many methods for solving the problem of a small number of samples, and made great progress. However, none of the previous methods can obtain the optimal solution when within-class distance equals zero. This point is illustrated in terms of theory, and a new solving method that can obtain the optimal solution in any situations is presented in this paper. The experimental result confirms our inference.