4. [30 points] Obtaining a distance from an inner product kernel: If we have two feature vectors x and y, the square of the Euclidean distance between the feature vectors is written as H): yll2 = 2:721 (132;; m.)2 where it should be understood that the feature vectors x and y live in a Ddimensional space. Now, if the feature vectors are projected into a [usually higher dimensional) Hilbert Space, the resulting new feature vectors can be written as @(x) and @(y) corresponding to x and y respectively with Cl)(-) denoting the mapping. a) [10 points] If the squared distance between x and y is dened as d(x,y) [if || U, derive a general formula for d(x,x + Ax) in terms of the partial derivatives of the kernel. This quantity is called the metric and plays an extremely important role in analysis