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Worksheet (non-assessed) Support vector machines a) What is the main idea behind linear Support Vector Machines (SVM)? Illustrate your explanation by drawing a figure. b) How can the linear SVM be made non-linear? c) The following kernels are examples of proper kernels: K1 ( x1 , x2 ) e || x1 x 2 || 2 30 K 2 ( x1 , x2 ) x1 x2 2 We know that: - given a proper kernel K, then aK, a > 0, is a proper kernel - given proper kernels K' and K'', then K' K'' is a proper kernel - if K is a proper kernel, for any real valued function f (x) over the input space, K ( x1, x2 ) f ( x1 ) f ( x2 ) is a proper kernel. Decide which of the following formulae define proper kernels and explain why. K 3 ( x1 , x2 ) 4 K 2 ( x1 , x2 ) K1 ( x1 , x2 ) K 4 ( x1 , x2 ) K1 ( x1 , x2 ) 2 K 2 ( x1 , x2 ) K 5 ( x1 , x2 ) 5 K1 ( x1 , x2 ) d) Consider the 2-dimensional inputs xi ( x1i , x2i ) 2 . Is the following a proper kernel? Explain why. K ( x1, x2 ) (( x11 )2 5x12 )(( x12 )2 5x22 )