Abstract: In high-dimensional and small sample size case, how to extract the optimal Fisher discriminant features efficiently remains unsolved. In this paper, we take advantage of the idea of compressive mapping and isomorphic mapping, and gain a general algorithm for the computation of the optimal discriminant vectors in high-dimensional and singular case. Our algorithm runs in a low dimensional transformed space, and leads to significant computational reduction. Furthermore, a uniform algorithm framework for Fisher discriminant analysis in singular case is developed. Based on this framework, the generalized Foley-Sammon discriminant analysis (FSDA) and Jin-Yang uncorrelated discriminant analysis (JYDA) are presented firstly. Then, a combined Fisher diseriminant analysis (CFDA) is developed, which not only has the advantages of FSDA and JYDA but also overcomes their weakness. The CFDA is tested on the ORL face image database, the classification result is very robust, with a recognition accuracy of 97%. Experimental results demonstrate that CFDA is better than FSDA and JYDA and is superior to Eigenfaces and Fisherfaces as well.