Question: According to the new objective function, rewrite update functions analytically. (Context is shown in attached image).

Note the reconstructed ratings can be smaller than 1 and greater than 5. To confine ratings to between the allowed range, we can use the logistic function. Logistic function is defined as 1 h(x) = 1 tex It is straightforward to show the derivative is ex h (x) = (1 + ex) 2 = h(x)(1 - h(x)). Therefore, we can rescale the ratings from /mi E [1, 5] to /mi E [0, 1]. Then, we can find the best U and I to optimize the following: min || R - h(VUJ)Il} = >(mi - h(Umu]))2, U.V m,i where function h is applied elementwise. According to the new objective function, rewrite update functions analytically. [new = U + 2alm . Um Vnew = V + 2al'm . um