We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green’s functions associated with closed ordinary differential operators on arbitrary intervals on the real line. Our approach determines the (2-modified) Fredholm determinants in terms of solutions of closely associate...

Generalized discriminant analysis (GDA) is an extension of the classical linear discriminant analysis (LDA) from linear domain to a nonlinear domain via the kernel trick. However, in the previous algorithm of GDA, the solutions may suffer from the degenerate eigenvalue problem (i.e., several eigenvectors with the same eigenvalue), which makes them not optimal in terms of the discriminant abilit...

In this paper, a framework of Discriminant Low-dimensional Subspace Analysis (DLSA) method is proposed to deal with the Small Sample Size (SSS) problem in face recognition area. Firstly, it is rigorously proven that the null space of the total covariance matrix, St , is useless for recognition. Therefore, a framework of Fisher discriminant analysis in a low-dimensional space is developed by pro...

In this paper, a framework of Discriminant Subspace Analysis (DSA) method is proposed to deal with the Small Sample Size (SSS) problem in face recognition area. Firstly, it is rigorously proven that the null space of the total covariance matrix, St, is useless for recognition. Therefore, a framework of Fisher discriminant analysis in a low-dimensional space is developed by projecting all the sa...