A generalized Foley-Sammon transform based on generalized fisher discriminant criterion and its application to face recognition

As the generalization of Fisher discriminant criterion, in this paper, the conception of the generalized Fisher discriminant criterion is presented. On the basis of the generalized Fisher discriminant criterion, the generalized Foley-Sammon transform (GFST) is proposed. The main difference between the GFST and the Foley-Sammon transform (FST) is that the sample set has the minimum within-class scatter and the maximum between-class scatter in the subspace spanned by all discriminant vectors constituting GFST while the sample set has these properties only on the one-dimensional subspace spanned by each discriminant vector constituting FST, that is, the transformed sample set by GFST has the best discriminant ability in global sense while FST has this property only in part sense. To calculate the GFST, an iterative algorithm is proposed, which is proven to converge to the precise solution. The speed and errors of the iterative procedure are also analyzed in detail. Lastly, our method is applied to facial image recognition, and the experimental results show that present method is superior to the existing methods in terms of correct classification rate. (C) 2002 Elsevier Science B.V. All rights reserved.