8. Define the mean of the feature space a. Show that b. Show that = xi)....

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8. Define the mean of the feature space a. Show that b. Show that = xi). == n 11 .). i=1 j=1 IM |||(x)-||= (K) - ||Go where Tr(-) denotes the matrix trace, and K is the kernel Gram matrix [k(x1,xi) K = k(x1,xn) [k(xn, x1)k(x, xn) 9. The kernel SVM formulation in (4.27) is often called the I-SVM. In this problem, we are interested in obtaining the 2-SVM, which is defined by min f+Chinge (yi, f(x)), feH 2 i=1 (4.27) where linge is the square hinge loss: inge (y. )=(max{0, 1-y1). Write the primal and dual problems associated with the 2-SVM, and compare the result with the 1-SVM. 10. Consider the following kernel regression problem: min+clogit (yi. f(x;)), feHt i=1 where logit is the logistic regression loss: logit (y,y) = log(1+e). Write the dual problems and find the solution as simply as possible. 8. Define the mean of the feature space a. Show that b. Show that = xi). == n 11 .). i=1 j=1 IM |||(x)-||= (K) - ||Go where Tr(-) denotes the matrix trace, and K is the kernel Gram matrix [k(x1,xi) K = k(x1,xn) [k(xn, x1)k(x, xn) 9. The kernel SVM formulation in (4.27) is often called the I-SVM. In this problem, we are interested in obtaining the 2-SVM, which is defined by min f+Chinge (yi, f(x)), feH 2 i=1 (4.27) where linge is the square hinge loss: inge (y. )=(max{0, 1-y1). Write the primal and dual problems associated with the 2-SVM, and compare the result with the 1-SVM. 10. Consider the following kernel regression problem: min+clogit (yi. f(x;)), feHt i=1 where logit is the logistic regression loss: logit (y,y) = log(1+e). Write the dual problems and find the solution as simply as possible.