Non-Linear Regression

1. Consider the mapping of data instances to a new space using a set of basis functions. If x is the original data point, we will denote the transformed data instance as P(x). A kernel function computes the dot (or inner) product between a pair of data instances in the transformed space, i.e., k(1.2) = P(x)TY(z). Thus if the mapping was identity, i.e., (x) = 1, then the corresponding kemel function would be k(1,2)=x*z. However, some times the kernel function can be written as a direct function of original x and z, without the need to perform the mapping using 10. Which means that if, for a machine learning problem, every data instance always occurs as an dot product with another data instance, we can simply replace the dot product with k(x.z) and get a kernel (hopefully non-linear) version without doing the explicit mapping. In this problem, given a kemel function, k0, you will have to identify the correct mapping, 70, such that k(1,2) = (x)+7(2). We will assume that each data instance has two features, i.e., x = (x1,x2] and z = [21:22]. If k(1,2) = (x+2)2, what will be "(x)? a) [x12x22] Ob) (x2x22x1x2] c) [x x2,2x1x2] d) [x22x22,12x7x2]