The linear discriminant functions that we have discussed so far, have the advantage of being simple, easy to implement and computationally inexpensive. So, they are effective for linearly separable data. However, linear separability is not always expected for real data. In this and subsequent chapters, we will attempt to upgrade discriminant functions from linear to nonlinear in order to deal with data that are linearly nonseparable. The basic process is to transform patterns in a given feature space to another space by means of a nonlinear transformation. The classification process applied on the transformed space is nothing but the linear process introduced so far, while complex nonlinear processes can be realized on the original feature space.