Cross-Selling with Collaborative Filtering Qiang Yang HKUST Thanks: Sonny chee
1 Cross-Selling with Collaborative Filtering Qiang Yang HKUST Thanks: Sonny Chee
Motivation Question: a user bought some products already what other products to recommend to a user Collaborative Filtering(CF Automates circle of advisors +
2 Motivation ◼ Question: ◼ A user bought some products already ◼ what other products to recommend to a user? ◼ Collaborative Filtering (CF) ◼ Automates “circle of advisors”. +
Collaborative Filtering people collaborate to help one another perform filtering by recording their reactions. ,(Tapestry) Finds users whose taste is similar to you and uses them to make recommendations Complimentary to IR/IF IR/IF finds similar documents-CF finds similar users
3 Collaborative Filtering “..people collaborate to help one another perform filtering by recording their reactions...” (Tapestry) ◼ Finds users whose taste is similar to you and uses them to make recommendations. ◼ Complimentary to IR/IF. ◼ IR/IF finds similar documents – CF finds similar users
Example Which movie would sammy watch next? Ratings 1--5 Titles Starship Sleepless Trooper in Seattle MI-2 Matrix Titanic (R (R) Sammy Beatrice Dylan g Mathew 44423 Gum-Fat A333445 333345 1344? 454? Basil If we just use the average of other users who voted on these movies then we get Matrix 3: Titanic 1474=3.5 Recommend titanic But is this reasonable?
4 Example ◼ Which movie would Sammy watch next? ◼ Ratings 1--5 • If we just use the average of other users who voted on these movies, then we get •Matrix= 3; Titanic= 14/4=3.5 •Recommend Titanic! •But, is this reasonable? Starship Trooper (A) Sleepless in Seattle (R) MI-2 (A) Matrix (A) Titanic (R) Sammy 3 4 3 ? ? Beatrice 3 4 3 1 1 Dylan 3 4 3 3 4 Mathew 4 2 3 4 5 Gum-Fat 4 3 4 4 4 Basil 5 1 5 ? ? Titles Users
Types of Collaborative Filtering Algorithms Collaborative filters Statistical collaborative filters Probabilistic Collaborative Filters [PHlooj Bayesian Filters [BP9 9][BHK98] Association Rules [agrawal, Han] Open problems Sparsity First Rater, scalability
5 Types of Collaborative Filtering Algorithms ◼ Collaborative Filters ◼ Statistical Collaborative Filters ◼ Probabilistic Collaborative Filters [PHL00] ◼ Bayesian Filters [BP99][BHK98] ◼ Association Rules [Agrawal, Han] ◼ Open Problems ◼ Sparsity, First Rater, Scalability
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
