Fast Foley-Sammon Transform and Face Identification
YANG Jian, TU Qing hua, YANG Jing yu (Department of Computer Science, Nanjing University of Science & Technology, Nanjing 210094)
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.