Vladimir Mokeyev – Senior Researcher, Head of Department of Information Systems, Faculty of Economics and Entrepreneurship, South Ural State University.
Address: 76, Lenin prospekt, Chelyabinsk, 454080, Russian Federation.
E-mail:  mokeyev@mail.ru

Stanislav Tomilov – Post-Graduate Student, Department of Information Systems, Faculty of Economics and Entrepreneurship, South Ural State University.
Address: 76, Lenin prospekt, Chelyabinsk, 454080, Russian Federation.
E-mail:  tomilov_stas@mail.ru 

Due to large variety of application tasks which use either images itself or products of their processing the image processing is now in the center of research activity. The most relevant task in this sphere is facial recognition for identifying a person. One problem here is in the lack of photo images of a person to describe completely his individual variation.

Methods based on Linear Discriminant Analysis (LDA) are widely held in the sphere of facial recognition at the present day. LDA represents the projection of image space on feature space in such a way as to minimize intraclass space and to maximize interclass space in feature space. Though LDA is useful for pattern classification, LDA-based algorithms are prone to problems with small sample size. As a result, intraclass difference matrix  becomes singular. To solve this problem, different variants of LDA algorithms were developed.

The most successful practices to resolve this problem are approaches which combine LDA with principal component analysis (PCA). Though effectiveness of such approach is evident PCA does not ensure successful application of LDA. After transformation intraclass covariance matrix still can be singular. This article is concerned with algorithm of generalized LDA in which discriminant component calculation is carried out using generalized Jacobi method. Effectiveness of this approach is demonstrated by experiments on ORL database.