为了解决小样本情况下，类内散布矩阵不可逆时，Foley-Sammon最优鉴别矢量集的求解问题，给出了一种快速近似算法，首先从理论上说明了当类内散布矩阵不可逆时，将在原始特征空间内求解最佳鉴别矢量集的问题映射到等于或小于c-1（c为样本类别数）维的欧氏空间内进行是可行的，由于样本类别数远远小于原始特征空间的维数，故该算法不仅大大减少了特征抽取的时间，也提高了分类识别的速度，在ORL标准人脸库上的试验结果表明，该算法不仅在识别率和识别时间上优于传统的扰动法和补空间法，而且比经典的特征脸方法和Fisher脸方法更为有效。

It is well known that Foley Sammon transform is a very effective method for feature extraction and that face identification is a typical small sample size problem. In the problems, the dimension of original features is so high that the within class scatter matrix is always singular. In the singulas case, how to calculate Foley Sammon optimal discriminant vectors(FSDV) is a very difficult problem. This paper presents a fast algorithm for calculating FSDV for small sample size problems. The main idea of the proposed algorithm is to map the problem of calculating FSDV in the original feature space to another problem of calculating FSDV in a( c-1 ) dimensional (or less) Euclidean space(where c is the number of pattern classes). In the transformed space, the FSDV can be calculated directly. Generally speaking, the number of classes is much less than the dimension of original sample, so our approach needs less time for feature extraction. We do Experiments on Olivetti Research Laboratory(ORL) face database. The experimental results show that our approach is better than previous method such as Perturbation and Complementary Space in terms of discrimination power and computing time, and also superior to classical "Eigenfaces" and "Fisherfaces" method with respect to recognition rate.