[Making data linearly separable by feature space mapping

3 [Making data linearly separable by feature space mapping] Consider the infinite dimen- sional feature space mapping Do : R - Ro (max ( 0, 1 - a-r QER (It may be helpful to sketch the function f(o) := max {0, 1 - a } for understanding the mapping and answering the questions below) (i) Show that for any n distinct points x1, . .., In, there exists a o > 0 such that the mapping Do can linearly separate any binary labeling of the n points. (ii) Show that one can efficiently compute the dot products in this feature space, by giving an analytical formula for . (x) . P. (x') for arbitrary points x and x