For the following ratings given to items by the users, perform the tasks below: Item 1 Item 2 Item 3 Item 4 Item 5 User 1 ? 3 ? 3 4 User 2 4 ? ? 2 ? User 3 ? ? 3 ? ? User 4 3 ? 4 ? 3 User 5 4 3 2 4 4 a) Find nearest neighbors of user 1 for k=2. b) Apply user-based Collaborative Filtering to predict R(U1, 13) (read: rating for user 1 and item 3). c) Apply item-based Collaborative Filtering to predict R(U3, 12) and R(U4, 14). For all of these tasks, use Pearson Correlation Coefficient as similarity measure and mean-centered prediction function. d) Say we had an option of using mode-centered prediction function instead of using mean. What do you think would be the effect of using mode as a baseline instead of average? Can using mode ever improve the performance of recommender system?