the starting point of any matrix factorization-based method is the utility matrixas shown in table - the utility matrix is matrix of user item dimension in which each row represents user and each column stands for an item table - example of utility matrix item user item item user user item item notice that we have lot of missing values in the matrixthese are the items that the user hasn' ratedeither because he hasn' watched it or because he doesn' want to watch it we can right away guesssay item is recommendation for user because user and user don' like item so it is likely they may end up liking the same itemsin this case item the process of matrix factorization means finding out low rank approximation of the utility matrix so we want to break down the utility matrix into two low rank matrices so that we can recreate the matrix by multiplying those two matrices mathematicallyr it and = * here is our original rating matrixu is our user matrixand is our item matrix assuming the process helps us identify latent featuresour aim is to find two matrices and such that their product (matrix multiplicationapproximates |ux matrix ( matrix with dimensions of num_users factorsy |px matrix ( matrix with dimensions of factors num_moviesfigure - matrix factorization