1. Page 1 A Random Walk Method for Alleviating the Sparsity Problem in Collaborative Filtering Hilmi Yıldırım and Mukkai S. Krishnamoorthy Rensselaer Polytechnic Institute Computer Science Department Troy, New York {yildih2,moorthy}@cs.rpi.edu 2011 Spring Seminar Presented by Sangkeun Lee

2. Page 2 Collaborative Filtering(CF) –Recommendation method rely on the past behavior (ratings, purchase history, time spent) of the users. –User-based CF (finding similar users) vs. Item-based CF (finding similar items)? Item-oriented collaborative filtering methods came into prominence –as they are more scalable compared to user- oriented methods (similarity between items is more stable than between users) –Prevents User Cold-Start problem(New User problem) In this paper, the authors propose a novel item-oriented algorithm –Based on finite numbers of Random Walk on item similarity graph –especially useful when training data is less than plentiful –enhance similarity matrices under sparse data I NTRODUCTION

3. Page 3 H ISTORICAL R EVIEW – U SER - BASED C F 5 4 77 8 Aggregation function: often weighted sum Weight depends on similarity Neighbours are people who have similar tastes as active user Reference Lecture Slide from ‘http://www.abdn.ac.uk/~csc263/teaching/AIS/AIS/lectures/abdn.only/CollaborativeFiltering.ppt’

4. Page 4 H ISTORICAL R EVIEW – I TEM - BASED C F Item 3 2 1 8 7 Aggregation function: often weighted sum Weight depends on similarity Item 5 Item 4 Item 2 Item 1 Item 2Item 3Item 4Item 5Item 6Item 7Item 8Item 9 User 113111 User 2532145 User 354515 User 412324 … User m53214?

5. Page 5 PageRank & A New Approach

6. Page 6 The Model

7. Page 7 ③ The Model ① ② ④ i 노드에서 j 노드로 넘어갈 확률값을 가지는 행렬 P 구성 K step 에 유저 u 가 아이템 j 에 있을 확 률 계산 종합하여 유저 u 가 아이템 j 에 있을 확 률 계산 최종 아이템의 랭 크는 단순 행렬 곱 으로 표현됨 Note that various similarity measures can be used Similar Item? Or uniform distribution? Scale Rank to Ratings

8. Page 8 More about the model Cosine Similarity Adjusted Cosine Similarity Computing Similarities Interpreting Rank Scores Basically the score is for top-K Recommendation But for Rating Prediction, authors linearly scaled up each row of values such that the maximum of each row corresponds to 5. I doubt it! Computational Cost computing similarity matrix is O(m^2n) vector-matrix multiplication which has complexity O (m^2) I doubt it! too 역행렬 계 산 cost 고려하지 않음

9. Page 9 Experiments MovieLens –This data set contains 1,000,209 ratings of 6040 anonymous MovieLens users on 3952 movies

10. Page 10 Discussion Summary –Presented and experimentally evaluated a model-based item-oriented collaborative filtering algorithm. –outperforms a slightly modified version of item based top-N algorithm in all test cases since top- N is a special case of Random Walk Recommender. –better than top-N algorithm especially when training data is sparse. –For extremely sparse data sets optimal α values approaches 1 whereas it approaches to 0 as data gets denser. –Random Walk Recommender captures some transitive associations between items. Questions? –Few doubts in Paper – Time Complexity, Linear scaling up? –Interesting application of random walk for recommendation –RWWR vs. finite steps of randomwalk