Machine Learning Question

2 Feature transformations 10 points Consider the concept class C consisting of functions fr defined by a radius r as follows +1 17r1 16r Jr[21,12) 1 otherwise Note that the hypothesis class is not linearly separable in R2 Construct a function o( 2) that maps examples to a new space, such that the positive and negative examples are linearly separable in that space. The answer to this question should consist of two parts: I. A function that maps examples to a new space. 2. A proof that in the new space, the positive and negative points are linearly separated. You can show this by producing such a hyperplane in the new space (i.e. find a weight vector w and a bias b such that wo(1, r2)b if, and only if, fr(ri, 2)1 Hint: The feature transformation should not depend on r 2 Feature transformations 10 points Consider the concept class C consisting of functions fr defined by a radius r as follows +1 17r1 16r Jr[21,12) 1 otherwise Note that the hypothesis class is not linearly separable in R2 Construct a function o( 2) that maps examples to a new space, such that the positive and negative examples are linearly separable in that space. The answer to this question should consist of two parts: I. A function that maps examples to a new space. 2. A proof that in the new space, the positive and negative points are linearly separated. You can show this by producing such a hyperplane in the new space (i.e. find a weight vector w and a bias b such that wo(1, r2)b if, and only if, fr(ri, 2)1 Hint: The feature transformation should not depend on r