Generalized kernel function Fisher discriminant for pattern recognition

In this paper, according to the concept of generalized Fisher (1938) discriminant (GFD) presented by Foley and Sammon (1975) , the generalized kernel function Fisher discriminant (GKFD) is investigated and proved based on the linear Fisher discriminant (LFD) and kernel function Fisher discriminant (KFD). It generalizes the solution of two-class pattern recognition nonlinearly, and the decision function is obtained. In the process of decision, the competition principle is used, each test sample is determined as the class with the largest decision function value, and a valid approach is provided for multi-class pattern recognition. The GKFD has the characteristic of solid theory foundation and strong generalization capability, which embraces important meanings and application merits in multi-class pattern recognition.