1. Recommend User to Group in Flickr Zhe Zhao 4-29 2010

2. What I am going to present A problem seldom being studied in social media recommendation: – Recommend Flickr Group to User

3. What I am going to present A problem seldom being studied in social media recommendation: Why does this problem matters

4. What I am going to present A problem seldom being studied in social media recommendation: Why does this problem matters How to make use of meaningful information – A matrix factorization perspective to view the problem – A Topic Model Based Solution

5. What I am going to present A problem seldom being studied in social media recommendation: Why does this problem matters How to make use of meaningful information At last, Something about implementation

6. Recommend User to Group Background: – User Activity: Upload and favor photos, add contacts, and join groups, based on his/her interests and everyday life.

7. Recommend User to Group Our Problem: – Recommend Relevant Group to User user relevant to a group means that the topic and interests the group focused on is similar to the user’s interests, shown by the similarity of the content between the photos from the user and photos from the group pool.

8. Recommend User to Group Related Work – Problems: The first few works to recommend Flickr group to user, using content, social relations and collaborative information. – Approaches: Recommender systems. Expert Finding.

9. Our Proposed Solution Intuition: – Find User’s interests and Group’s topics/Interests, similar interests indicate user is relevant to Group. Solution: – Latent Interests Dimensions can be found by matrix factorization and graphical model. Considered Information(Interests are reflected in) – User Upload and Favor photos – Group collect photos in pool. – User join Group. – User add contacts.

10. Our Proposed Solution Modeling Interests via Matrix Factorization – Mining Latent Interests from origin feature space – Used Information: User Upload and Favor photos Group collect photos in pool. User join Group. User add contacts. A probabilistic solution on equivalent graphical model. Learning the model & Implementation

11. Modeling Interests via Matrix Factorization (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) Feature Space (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) ….. Photo1 Photo2 Photo3 Photot ….. Photo4 (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) User u

12. Modeling Interests via Matrix Factorization (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) Feature Space (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) ….. Photo1 Photo2 Photo3 Photot ….. Photo4 (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) =C u User u

13. Modeling Interests via Matrix Factorization (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) Feature Space (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) ….. Photo1 Photo2 Photo3 Photot ….. Photo4 (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) =C u User u C u ≈ F ×I u ’ = M C u Each row represent the latent interests of user in each photo

14. Modeling Interests via Matrix Factorization (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) Feature Space (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) ….. Photo1 Photo2 Photo3 Photot ….. Photo4 (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) =C u User u C 1 ≈ F ×I 1 ’ = M C 1 C 2 ≈ F ×I 2 ’ = M C 2 C n ≈ F ×I n ’ = M C n … For n Users

15. Modeling Interests via Matrix Factorization (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) Feature Space (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) ….. Photo1 Photo2 Photo3 Photot ….. Photo4 (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) =P g P g ≈ F ×T g ’ = M P g Each row represent the latent topics of group in each photo Group g

16. Modeling Interests via Matrix Factorization (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) Feature Space (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) ….. Photo1 Photo2 Photo3 Photot ….. Photo4 (f 1, f 2, f 3, f 4, f 5, f 6, f 7, …, f d ) =P g Group g P 1 ≈ F ×T 1 ’ = M P 1 P 2 ≈ F ×T 2 ’ = M P 2 P m ≈ F ×T m ’ = M P m … For m Groups

17. Modeling Interests via Matrix Factorization (v1, v2, v3, v4, v5, v6, v7, …, vn) Group1 Group2 Group3 Group4 Groupm ….. All Groups =R (v1, v2, v3, v4, v5, v6, v7, …, vn) User1User2User3User4Usern …… All Users R gu = |C u ∩ P g | / |C u |

18. Modeling Interests via Matrix Factorization (v1, v2, v3, v4, v5, v6, v7, …, vn) Group1 Group2 Group3 Group4 Groupm ….. All Groups =R (v1, v2, v3, v4, v5, v6, v7, …, vn) User1User2User3User4Usern …… All Users R ≈ f(LT ×LI’) = M TI Each row represent the latent topics of group Each row represent the latent interests of user ȣ LT ×LI’

19. Modeling Interests via Matrix Factorization Till now, our model can be written as: R ≈ f(LT ×LI’) = M TI C u ≈ F ×I u ’ = M C u P g ≈ F ×T g ’ = M P g ȣ LT ×LI’ n m

20. Modeling Interests via Matrix Factorization Till now, our model can be written as: – Constrains of User Contacts: Minimize the sum of Dis( I u1, I u2 ) = |I u1, I u2 | Euc where User u1 calls User u2 as contact. R ≈ f(LT ×LI’) = M TI C u ≈ F ×I u ’ = M C u P g ≈ F ×T g ’ = M P g ȣ LT ×LI’ n m

21. Modeling Interests via Matrix Factorization Used Information: – User Upload and Favor photos – Group collect photos in pool. – User join Group. – User add contacts.

22. Our Proposed Solution Modeling Interests via Matrix Factorization: A probabilistic solution on equivalent graphical model. – Several Assumptions – Equivalent Graphical Model – Calculating the joint probability Learning the model & Implementation

23. A probabilistic solution on equivalent graphical model Several Assumptions Our Proposed Matrix-Factorization Model R ≈ f(LT ×LI’) = M TI C u ≈ F ×I u ’ = M C u P g ≈ F ×T g ’ = M P g ȣ LT ×LI’ n m

24. A probabilistic solution on equivalent graphical model Several Assumptions Rewrite the Model in row and entry form r gu ≈ f(lt g ×li u ’) c u i ≈ F ×i u i ’ p g j ≈ F ×t g j ’ ȣ lt g ×li u ’ Σ u |C u | Σ g |P g | m*n R ≈ f(LT ×LI’) = M TI C u ≈ F ×I u ’ = M C u P g ≈ F ×T g ’ = M P g ȣ LT ×LI’ n m

25. A probabilistic solution on equivalent graphical model Several Assumptions – i u i and t g j are hidden random variables. – lt g and li u are hidden random variables. Rewrite the Model in row and entry form R ≈ f(LT ×LI’) = M TI C u ≈ F ×I u ’ = M C u P g ≈ F ×T g ’ = M P g ȣ LT ×LI’ n m r gu ≈ f(lt g ×li u ’) c u i ≈ F ×i u i ’ p g j ≈ F ×t g j ’ ȣ lt g ×li u ’ Σ u |C u | Σ g |P g | m*n

26. A probabilistic solution on equivalent graphical model Several Assumptions – i u i and t g j are hidden random variables. – lt g and li u are hidden random variables. Add Gaussian noise to the right of the equations r gu = f(lt g ×li u ’) + ε c u i = F ×i u i ’ + ε c p g j = F ×t g j ’ + ε p ȣ lt g ×li u ’ Σ u |C u | Σ g |P g | m*n R ≈ f(LT ×LI’) = M TI C u ≈ F ×I u ’ = M C u P g ≈ F ×T g ’ = M P g ȣ LT ×LI’ n m

27. A probabilistic solution on equivalent graphical model Several Assumptions – i u i and t g j are hidden random variables. – lt g and li u are hidden random variables. – r gu are random varibles based on lt g and li u. – c u i and p g j are random variables based on i ui, F and t gj, F respectively – i u i and t g j are based on lt u and li g The revised model r gu = f(lt g ×li u ’) + ε c u i = F ×i u i ’ + ε c p g j = F ×t g j ’ + ε p ȣ lt g ×li u ’ Σ u |C u | Σ g |P g | m*n

28. A probabilistic solution on equivalent graphical model Several Assumptions – r gu |lt g,li u ~ N(f(lt g ×li u ’), δI) – c u i | i ui,F ~ N(F×i ui ’, δ c I) – c g j | t gj,F ~ N(F×t gj ’, δ p I) The revised model r gu = f(lt g ×li u ’) + ε c u i = F ×i u i ’ + ε c p g j = F ×t g j ’ + ε p ȣ lt g ×li u ’ Σ u |C u | Σ g |P g | m*n

29. A probabilistic solution on equivalent graphical model Several Assumptions – r gu |lt g,li u ~ N(f(lt g ×li u ’), δI) – c u i | i ui,F ~ N(F×i ui ’, δ c I) – c g j | t gj,F ~ N(F×t gj ’, δ p I) – i ui | li u ~ Bernoulli (Multinomial, Exponential) – t gj | lt g ~ Bernoulli (Multinomial, Exponential) The revised model r gu = f(lt g ×li u ’) + ε c u i = F ×i u i ’ + ε c p g j = F ×t g j ’ + ε p ȣ lt g ×li u ’ Σ u |C u | Σ g |P g | m*n

30. A probabilistic solution on equivalent graphical model Several Assumptions – r gu |lt g,li u ~ N(f(lt g ×li u ’), δI) – c u i | i ui,F ~ N(F×i ui ’, δ c I) – c g j | t gj,F ~ N(F×t gj ’, δ p I) – i ui | li u ~ Bernoulli (Multinomial, Exponential) – t gj | lt g ~ Bernoulli (Multinomial, Exponential) – i ui ~ Conjugate prior of i ui | li u – t gj ~ Conjugate prior of t gj | lt g The revised model r gu = f(lt g ×li u ’) + ε c u i = F ×i u i ’ + ε c p g j = F ×t g j ’ + ε p ȣ lt g ×li u ’ Σ u |C u | Σ g |P g | m*n

31. A probabilistic solution on equivalent graphical model 0,1,0,0 Latent interests 1,0,1,0 1,1,0,1 Photo1 Photo2 Photo3 Photo4 1,1,1,0 User u Good color Cute animal Sony Camera Politics 0,1,0,0 1,0,1,0 0,1,0,0 Photo1 Photo2 Photo3 Photo4 0,1,1,0 Group g 0.4, 0.2, 0.1, 0.3 0.1, 0.2, 0.7, 0.0 li u lt g i u1 i u2 i u3 i u4 t g1 t g2 t g3 t g4 r gu ȣ 0.16

32. A probabilistic solution on equivalent graphical model Equivalent Graphical Model: Topic Model based Recommendation(TMR)

33. A probabilistic solution on equivalent graphical model Equivalent Graphical Model c u i = F ×i u i ’ + ε c Σ u |C u | p g j = F ×t g j ’ + ε p Σ g |P g | r gu = f(lt g ×li u ’) + ε ȣ lt g ×li u ’ m*n

34. Our Proposed Solution Modeling Interests via Matrix Factorization: A probabilistic solution on equivalent graphical model. Learning the model & Implementation – Gibbs Sampling based – User recommendation for group

35. Learning the model & Implementation Our task: – Predict r gu for user u and group g

36. Learning the model & Implementation Our task: – Predict r gu for user u and group g Our method: – Gibbs Sampling for the model Sample each iui and tgj in the model Chose the rgu based on pdf conditioned by iui and tgj

37. Learning the model & Implementation Gibbs sampling in our model – The joint probability of the model

38. Learning the model & Implementation Gibbs sampling in our model – The joint probability of the model

39. Learning the model & Implementation Gibbs sampling in our model – The joint probability of the model

40. Learning the model & Implementation Gibbs sampling in our model – The joint probability of the model – Sampling based on equations:

41. Learning the model & Implementation Implementation – Data structure and preprocessing Visual word extraction – Hierarchical clustering on 100k subset get 1019 centers Filter out high and low frequent tags – Tags appear in 90% photos or less than 2 times --- 48733 tags Build Hash table for User and Photo and Inverted Index for tags on a 30 group subset Use DBMS to store the 200 group dataset

42. Learning the model & Implementation Implementation – Sampling: 0. randomly select 20% of the rgu matrix as test set, user the rest as training set. 1. get a 5000 samples photos subset to perform svd to reduce dimensionality for tags (48733 -> 1000) 2. get a 5000 sampled photos subset after svd to perform svd to get the prior \miu in the model (2019->10, latent dimension set to be 10) 3. Init Iui for each photo of each user and init tgj for each photo of each group. 4. perform sampling in 1000 iterations (currently, 1 iteration cost 22 s) 5. select the sampling result having the max joint probability 6. predict rgu based on the result and relational function

43. Recent Works Problem in the Graphical Model – Photo feature is the sum of latent interest features Not a good/proper fitting for the feature

44. Recent Works Problem in the Graphical Model – Photo feature is the sum of latent interest features Not a good/proper fitting for the feature Note that, different from LDA: – LDA is document-word model – TMR is document-feature model – Different fitting schema – TMR is not linking of two LDA

45. Recent Works Problem in the Graphical Model Revised Model – Weighted TMR – Multiple(l)-interest TMR – Hierarchical LDA

46. Recent Works Problem in the Graphical Model Revised Model – Weighted TMR Weighting Parameters on User/Group Level

47. Recent Works Problem in the Graphical Model Revised Model – Multiple(l)-interest TMR Photo Interest formed by multiple basic interests

48. Recent Works Problem in the Graphical Model Revised Model – Hierarchical LDA Related Work: Blei NIPS04 hierarchical LDA

49. Recent Works Problem in the Graphical Model – Other problems: Multiple Sources of Feature – tags & visual Currently, not considering User Contact. – Solution: refer to Blei10 study on link prediction Implementation Problem: – Slow speed for sampling – Noise & data structure building

50. To sum up Recommend User to Group – First work in social media sharing websites, using content, social relations and collaborative information – Proposed Solution: Modeling the interests by matrix factorization A Probabilistic Approach on equivalent Graphical Model. Gibbs Sampling based Parameter Tuning – Future Work Efficient Implementation & Experiment Thank you!