Basis Functions

Common Examples of Basis Functions:

• Polynomial: ${\varphi }_j(x)=x^j\to \varphi (x)=[1,x,x^2,x^3,\dots {]}^T$
• RBF (Gaussian): ${\varphi }_j(x)=\exp \left(-\frac{|x-{\mu }_j{|}^2}{2{\sigma }^2}\right)$
• Simple linear: ${\varphi }_j(x)=x_j$ (j-th component of input)