Non-negatve Matrix Factorization (NMF) is a typical linear system and a matrx factorization problem. Here we use least square technique to find solutions for NMF. A: the same time we use an Image data set as an example to show how NMF works and how to use some Ibrary routines to process Images. 1) In sclence and engineering felds, a data set can be represented by a matrix. For example, an mage which has 196 plxels can be represented by a 14 by 14 matrx or by any other two dimensional matrx. If we have a set of Images, we can use a 3 dimensional matrix to represent t. For example, there ls a set of 16 Images, each Image has 625 pkels. Then this set of Images can be represented by a 25 x 25 x 16 matrix. Given a data set, do the folowing operations. a) Check the dimensionalities of the glven data set using Ibrary routine slze b) Defne a two dimensional matrix to represent the glven data set. Represent each Image as a vector, a column of a matrix, all the Images together form a two dimensional matrix. (Hint: search library function reshape) c) Define a constant as 16. Thls constant is the second dimension of factor matr W, and the 1rst dimenslon of tactor matrix H. Then deine W, and H matrices. In Matiab, a two dimension matrix with all 0 values can be dened as A- zero8m,n), m, n are the dimenslonalties of A If defining a three dimension matrix wth all 1 values we can denne lt as A- ones(m,n,k), m, n, kare the dimensionalities of A, k is the third dimension. Here we should use rand) to generate W, H matrices with random values. d) Set up an Iteration criterion. One way Is simply to set up a big enough number as iteration cniterion, the other way is to compute the residual of V-WH, set an acceptable residual value as he teration criterion. e) Given the updating ruies of NMF, provide the corresponding Matab codes to Implement these updating rules. The updating rules should be repeatly run unti t meets the Iteration criterion. 2) Show some samples of ornginal Images in the image set. Show the factor matrix W, and H. For W, each column actualy represents an image. (Hint first convert column vectors In W to matrices, then display the matrices as Images.) a) How to show Images. Try lIbrary functions Imshow), (Imagesc), colormap0) Hint: when showing an Image, the Image should be In a matrx format but not vector format) b) How to draw a fngure. Use lIbrary function plot0, subplot)