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(Solved): Exercise 1: Feature Map Let x,yinR^(2), i.e. x=(x_(1),x_(2)) and y=(y_(1),y_(2)). Define polynomial ...
Exercise 1: Feature Map Let
x,yinR^(2), i.e.
x=(x_(1),x_(2))and
y=(y_(1),y_(2)). Define polynomial kernel
K:R^(2)\times R^(2)->Rby
K(x,y)=(x^(TT)y)^(2). Find the feature map
\phi :R^(2)->R^(D). Please specify the dimension
D. Consider the same kernel function
K(x,y)=(x^(TT)y)^(2)which is defined on
R^(3)\times R^(3)in this part, i.e.
x,yinR^(3). What is the feature map
\phi :R^(3)->R^(D)? What is the dimension
D? In general, suppose that
x,yinR^(d)and polynomial kernel is defined as
K(x,y)=(x^(TT)y)^(2). Without writing the feature map
\phi :R^(d)->R^(D)explicitly, write down the dimension
Das a function of input dimension
d.
