Optimal discriminant plane for a small number of samples and design method of classifier on the plane

摘要: Abstract In a previous work (Zi-Quan Hong and Jing-Yu Yang, Minimum distance classifier on the optimal discriminant plane), we suggested derived method for constructing plane using minimum criteria. this paper, problem of solving small number samples is discussed, which based above paper by same authors. case samples, generalized eigenequation AX = λBX established large usually has no solution because within-class scatter matrix singular. To obtain eigenequation, new suggested, in Singular Value Perturbation added to such that becomes nonsingular matrix. Therefore, can be solved existing algorithms. We proved eigenequations are stable respect eigenvalues eigenvectors indeed directions, if perturbation subject some certain conditions. The experimental results have shown our works well constructed with high performance even samples.