3. An important task in machine learning is to group objects into clusters, according to some similarity criteria. For example, retailers group customers into clusters according to their shopping habits, and online streaming service companies group videos into clusters according to their contents and length. Each object essentially can be described by a feature vector. Then clustering tries to solve the following optimization problem: given m points u. Um E R", select p points out of the m points as the centers of p clusters such that the total distance among each point and its corresponding cluster center is minimized. In particular, we want to select p points vi, 2.... ,p among the m given points to minimize inla) i-1 rm minjel, plu; t, I in (1) gives the distance l etween a pint ", and its nearest cluster center. (a) Build a parametric model for this problem. Clearly define the sets, parameters, decision variables, constraints, and the objective. 3. An important task in machine learning is to group objects into clusters, according to some similarity criteria. For example, retailers group customers into clusters according to their shopping habits, and online streaming service companies group videos into clusters according to their contents and length. Each object essentially can be described by a feature vector. Then clustering tries to solve the following optimization problem: given m points u. Um E R", select p points out of the m points as the centers of p clusters such that the total distance among each point and its corresponding cluster center is minimized. In particular, we want to select p points vi, 2.... ,p among the m given points to minimize inla) i-1 rm minjel, plu; t, I in (1) gives the distance l etween a pint ", and its nearest cluster center. (a) Build a parametric model for this problem. Clearly define the sets, parameters, decision variables, constraints, and the objective