Face Recognition based on Fuzzy Linear Discriminant Analysis

Abstract

Recently, linear discriminant analysis (LDA) was proposed to manifold learning and pattern classification. LDA, a supervised method, aims to find the optimal set of projection vectors that maximize the determinant of the between-class scatter matrix and at the same time minimise the determinant of the within-class scatter matrix. But, since the dimension of vectors is high and the number of observations is small,usually tens or hundreds of samples, an intrinsic limitation of traditional LDA is that it fails to work when the within-class scatter matrix becomes singular, which is known as the small sample size (SSS) problems. In the real-world applications, the performances of face recognition are always affected by variations in illumination conditions and different facial expressions. In this study, the fuzzy linear discriminant analysis (FLDA) algorithm is proposed, in which the fuzzy k-nearest neighbor (FKNN) is implemented to reduce these outer effects to obtain the correct local distribution information to persuit good performance. In the proposed method, a membership degree matrix is firstly calculated using FKNN, then the membership degree is incorporated into the definition of the Laplacian scatter matrix to obtain the fuzzy Laplacian scatter matrix. The optimal projections of FLDA can be obtained by solving a generalised eigenfunction. Experimental results on ORL face databases show the effectiveness of the proposed method.