Q4. k-means Clustering In k-means clustering, , is the vector mean ofthe kth cluster. Assume the data vectors have 1 dimensions, so , is a (column) vector [ , ,1]. where the symbol T indicates vector transpose. a) Derive update rule for using the objective function N K where xn is the nth data vector, r, is 1 ifAn is in the k th class and 0 otherwise, and 1x12 =xTg = xixi = x, The update rule is derived by computing the gradient for each element of the kth mean and solving for the value where the gradient is zero. Express your answer first in scalar form for k'i and in vector form for A: (20P) b) Extra credit. Write a program that implements the k-means clustering algorithm on the iris data set. Plot the results of the learning process by showing the initial, intermediate, and converged cluster cen- ters for k-2 and k- 3. (+25 P. bonus) Q4. k-means Clustering In k-means clustering, , is the vector mean ofthe kth cluster. Assume the data vectors have 1 dimensions, so , is a (column) vector [ , ,1]. where the symbol T indicates vector transpose. a) Derive update rule for using the objective function N K where xn is the nth data vector, r, is 1 ifAn is in the k th class and 0 otherwise, and 1x12 =xTg = xixi = x, The update rule is derived by computing the gradient for each element of the kth mean and solving for the value where the gradient is zero. Express your answer first in scalar form for k'i and in vector form for A: (20P) b) Extra credit. Write a program that implements the k-means clustering algorithm on the iris data set. Plot the results of the learning process by showing the initial, intermediate, and converged cluster cen- ters for k-2 and k- 3. (+25 P. bonus)