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 doe this differ from the regularization of formula (17.1) (page 738)?

[Hint: Compare the regularization for the items or users with few ratings with those with many ratings.]

(b) How does the code of Figure 17.2 (page 739) need to be modified to implement this regularization?

(c) Which works better 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.]