Statistical Collaborative Filters Users annotate items with numeric ratings. Users who rate items "similarly" become mutual advisors Users U1 U2 Recommendation computed by taking a weighted aggregate of advisor ratings
6 Statistical Collaborative Filters ◼ Users annotate items with numeric ratings. ◼ Users who rate items “similarly” become mutual advisors. ◼ Recommendation computed by taking a weighted aggregate of advisor ratings. I1 I2 … Im U1 U2 . . Un U1 . . . . . . U1 . . . . . . U2 . . . . U2 . . . . . . . . … . . . . . . . . . . . . . . Un . . . . . . Un . . . . . . Items Users Users Users
Basic idea Nearest Neighbor Algorithm given a user a and item i First, find the the most similar users to a Let these be y Second, find how these users(y ranked i Then, calculate a predicted rating of a on i based on some average of all these users y How to calculate the similarity and average? 7
7 Basic Idea ◼ Nearest Neighbor Algorithm ◼ Given a user a and item i ◼ First, find the the most similar users to a, ◼ Let these be Y ◼ Second, find how these users (Y) ranked i, ◼ Then, calculate a predicted rating of a on i based on some average of all these users Y ◼ How to calculate the similarity and average?
Statistical Filters GroupLens [resnick et al 94, MiT Filters UseNet News postings Similarity: Pearson correlation Prediction: Weighted deviation from mean =ra+-∑(n1-rn) au
8 Statistical Filters ◼ GroupLens [Resnick et al 94, MIT] ◼ Filters UseNet News postings ◼ Similarity: Pearson correlation ◼ Prediction: Weighted deviation from mean = + − a u u u i a Pa,i r r , r w , ( ) 1
Pearson Correlation 76543210 Item 2 Item 3 Item 4 Item 5 Items User a - User B -UserC Pearson correlation User AbC B11-1
9 Pearson Correlation 0 1 2 3 4 5 6 7 Item 1 Item 2 Item 3 Item 4 Item 5 Items Rating User A User B User C Pearson Correlation A B C A 1 1 -1 B 1 1 -1 C -1 -1 1 User User
Pearson correlation a Weight between users a and u Compute similarity matrix between users Use Pearson Correlation(-1, 0, 1) Let items be all items that users rated Pearson correlation (ai-rari-ru) ser AbC items Items ∑ ru) B|11-1
10 Pearson Correlation ◼ Weight between users a and u ◼ Compute similarity matrix between users ◼ Use Pearson Correlation (-1, 0, 1) ◼ Let items be all items that users rated − − − − = items u u i items a a i items u u i a a i a u r r r r r r r r items w 2 , 2 , , , , ( ) ( ) ( )( ) | | 1 Pearson Correlation A B C A 1 1 -1 B 1 1 -1 C -1 -1 1 User User