Kernel Null Space Linear Discriminant Analysis and Its Applications in Face Recognition
Gan Jun · Chinese Journal of Computers · 2014
Null space linear discriminant analysis(NLDA)takes full advantage of the null space information of the total within-class scatter matrix of samples,in which the small sample size problem(S3problem)of LDA can be overcome.Through kernel method,the samples in the input space are transformed into a high-dimensional feature space by nonlinear mapping.Then,linear feature extraction algorithm is used in the high-dimensional feature space.Therefore,kernel method belongs to nonlinear feature extraction algorithm.In this paper,combined with the merits of LDA,NLDA and kernel method,kernel null space linear discriminant analysis(KNLDA)is investigated,in which kernel function is introduced and a low-dimensional matrix is obtained.The difficulty is avoided effectively that complex nonlinear mapping function is computed directly,and the problem is solved that there exists dimension disaster to high-dimensional within-class scatter matrix.In the meantime,KNLDA algorithm is applied in face recognition.Experimental results on ORL(Olivetti Research Laboratory)face database,ORL and Yale mixture face database show that KNLDA algorithm is valid in face recognition.