A linear boundary might be too simple to capture the class structure.

One way of getting a nonlinear decision boundary in the input space is to find a linear decision boundary in an expanded space (e.g., for polynomial regression.)

Thus, \({{{\mathbf{x}}_i}}\) is replaced by \(\phi({{{\mathbf{x}}_i}})\), where \(\phi\) is called a

*feature mapping*