Exercise 5. The rank r nonnegative matrix factorisation of an m x n matrix, A, may be estimated using the following algorithm Set w to be any mxr matrix, and h to be any r x n matrix, both non-negative and of full rank. Iteratively compute h = h - *(w? A). /(w? wh) w = w *((Aht). /(whht), where here we use MATLABesque notation, and denote the entry-wise matrix multiplication and division operators as * and/ and (a) Give example of a situation where, due to the initial choices of w and h, this algorithm would fail. (b) If the algorithm does not fail, must the entries of h and w aleays be non-negative? Explain your answer. (c) Use the algorithm to compute a nonnegative matrix factorisation of [34] A= 6 8 ] Exercise 5. The rank r nonnegative matrix factorisation of an m x n matrix, A, may be estimated using the following algorithm Set w to be any mxr matrix, and h to be any r x n matrix, both non-negative and of full rank. Iteratively compute h = h - *(w? A). /(w? wh) w = w *((Aht). /(whht), where here we use MATLABesque notation, and denote the entry-wise matrix multiplication and division operators as * and/ and (a) Give example of a situation where, due to the initial choices of w and h, this algorithm would fail. (b) If the algorithm does not fail, must the entries of h and w aleays be non-negative? Explain your answer. (c) Use the algorithm to compute a nonnegative matrix factorisation of [34] A= 6 8 ]