LFD Book Forum - View Single Post - Questions 1-4: Clarification

yaser · #2 05-18-2013, 01:42 PM

Quote:

Originally Posted by Kekeli

So the models k=3..7 correspond to

$\phi_3 = 1 + x_1 + x_2 + x_1^2$

$\phi_4 = 1 + x_1 + x_2 + x_1^2 + x_2^2$

etc.?

The transformed space in the case of

would be

${\bf z}=(\phi_0({\bf x}),\phi_1({\bf x}),\phi_2({\bf x}),\phi_3({\bf x}))=(1,x_1,x_2,x_1^2)$

The model (hypothesis set) would be a linear combination of these coordinates,

$h({\bf x})=\tilde{w}_0 \phi_0({\bf x})+\tilde{w}_1 \phi_1({\bf x})+\tilde{w}_2\phi_2({\bf x})+\tilde{w}_3\phi_3({\bf x})$