Potential Function Methods

In the previous chapter, we discussed nonlinear discriminant functions. The process introduced can be summarized as follows. (1) Map the learning patterns from the d-dimensional to the D-dimensional feature space by nonlinear transformation. (2) Set a linear discriminant function in the transformed D-dimensional space to obtain the decision boundary for class separation. (3) Transform the obtained decision boundary to the decision boundary in the original d-dimensional space. Although the above process ultimately sets up a nonlinear discriminant functionNonlinear discriminant function in the d-dimensional space, the main operation is to find a linear discriminant function in the D-dimensional space. In other words, it can be said that the nonlinear discriminant function is obtained indirectly through the D-dimensional space. Therefore, this chapter introduces the potential function method as a typical method for obtaining nonlinear discriminant functions directly in the original d-dimensional space.