In k-means clustering, is the vector mean of the kth cluster. Assume the data vectors have I dimensions, so is a (column) vector [,...,, where the symbol " indicates vector transpose. a) Derive update rule for p using the objective function NK D= [[Tnkxn-Pk || n=1k=1 T where xn is the nth data vector, nk is 1 if xn is in the kth class and 0 otherwise, and x2 = x x = Ei xixi = Ei 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 k.