? 4 2 3. Collaborative Filtering for Recommendation Suppose that an online bookseller has collaborative filtering recommender system. The bookseller has collected ratings information from 20 past users (U1-U20) on a selection of recent books. The ratings range from 1 = worst to 5 = best. Two new users (NU1 and NU2) who have recently visited the site and rated some of the books as follows ("?" represents missing ratings): NU1 NU2 TRUE BELIEVER 4 THE DA VINCI CODE ? 5 THE WORLD IS FLAT 5 2 MY LIFE SO FAR 3 5 THE TAKING 2 THE KITE RUNNER 3 ? RUNNY BABBIT ? HARRY POTTER 4 ? Using the K-Nearest Neighbor algorithm predict the ratings of these new users for each of the books they have not yet rated. Use the Pearson correlation coefficient as the similarity measure. For your convenience, this data is given in the Excel spreadsheet "knn.xls". Note: In Microsoft Excel, you can use the CORREL function to compute correlation. a. First compute the correlations between the new users (NU1 and NU2) and all other users (you can show these as added columns in original spreadsheet). Then for each new user give the predicted rating for each of the unrated items using K=3 (i.e., 3 nearest neighbors). Use the weighted average function to compute the predictions based on ratings of the nearest neighbors. Be sure to show the intermediate steps in your work (or provide a short explanation of how you computed the predictions) b. Measure the Mean Absolute Error (MAE) on the predictions for NU1 and NU2. You can compute MAE by generating predictions for items already rated by the target user (e.g., for NU1 these are all items except "The DaVinci Code" and "Runny Babbit"). Then, for each of these items you can compute the absolute value of the difference between the predicted and the actual ratings. Finally, you can average these errors across all compared items to obtain the MAE. c. Consider the following simple "popularity-based" recommendation algorithm: Given a user U and an item I, compute the predicted rating of U on I as the mean rating for I among all users who have rated I. Using this algorithm instead of KNN re-compute the MAE on the predictions for NU1 and NU2 (as in part b). Which one of the algorithms (KNN or this algorithm) perform better? Briefly explain what you think are the pros and cons of each of these two recommendation approaches