8. An alternative regularization for collaborative filtering is to minimize

????

⟨u, i, r⟩ ∈ D

((^r (u, i) − r)2 + λ(ib[i]2 + ub[u]2 +???? p (ip[i, p]2 + up[u, p]2)))

(a) How this differ from the regularization of Formula 15.1? [Hint: Compare the regularization for the items or users with few ratings with those with many ratings.]

(b) How does the code of Figure 15.5 need to be modified to implement this regularization?

(c) Which works better in on test data? [Hint: You will need to set λ to be different for each method; for each method, choose the value of λ by cross validation.]