Transfer Learning for Heterogeneous One-Class Collaborative - PowerPoint PPT Presentation

Transfer Learning for Heterogeneous One-Class Collaborative Filtering Weike Pan , Mengsi Liu and Zhong Ming ∗ panweike@szu.edu.cn, liumengsi@email.szu.edu.cn, mingz@szu.edu.cn College of Computer Science and Software Engineering Shenzhen University Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 1 / 27

Introduction Problem Definition For a user u ∈ U , we have a set of preferred items, i.e., P u , and a set of examined items, i.e., E u . Our goal is then to exploit such two types of one-class feedbacks and recommend a ranked list of items from I\P u for each user u . Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 2 / 27

Introduction Challenges Sparsity of positive feedbacks Uncertainty of implicit examinations Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 3 / 27

Introduction Overall of Our Solution Algorithm: Transfer via Joint Similarity Learning (TJSL) Learn a similarity between a candidate item and a preferred item Learn a similarity between a candidate item and an identified likely-to-prefer examined item Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 4 / 27

Introduction Advantage of Our Solution Joint similarity learning has the merit of being able to connect two seemingly not related items w.r.t. the sparse positive feedbacks only. Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 5 / 27

Introduction Notations user set, u ∈ U U item set, i , i ′ , j ∈ I I P positive feedbacks P u = { i | ( u , i ) ∈ P} preferred items by user u E implicit examinations E u = { i | ( u , i ) ∈ E} examined items by user u R = { ( u , i ) } all (user, item) pairs A ⊂ R\P sampled feedbacks P te test positive feedbacks d ∈ R latent feature number V i · , P i ′ · , E j · ∈ R 1 × d latent feature vectors b u ∈ R user bias b i ∈ R item bias r ui ∈ { 1 , 0 } preference of ( u , i ) r ui prediction of ( u , i ) ˆ T , L , L 0 iteration number ρ sampling parameter α v , α p , α e , β u , β v tradeoff parameters Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 6 / 27

Method Prediction Rule of FISM rmse for OCCF The predicted preference of user u on item i , r ui = b u + b i + s i ′ i , � ˆ (1) i ′ ∈P u \{ i } U − i u · V T i ′ ∈P u \{ i } s i ′ i = ¯ where � i · , and 1 U − i P i ′ · . ¯ � u · = |P u \{ i }| � i ′ ∈P u \{ i } U − i u · can be considered as a virtual user profile w.r.t. user u Note that ¯ and item i according to positive feedbacks. Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 7 / 27

Method Prediction Rule of TJSL(1,1) for HOCCF The predicted preference of user u on item i , r ui = b u + b i + s i ′ i + s ji , � � ˆ (2) i ′ ∈P u \{ i } j ∈E u U − i u · V T j ∈E u s ji = ˜ U u · V T i ′ ∈P u \{ i } s i ′ i = ¯ ¯ where � i · , � i · , and 1 U − i P i ′ · , ¯ � = u · |P u \{ i }| � i ′ ∈P u \{ i } 1 ˜ U u · E j · , ¯ � = � |E u | j ∈E u Note that ˜ U u · is a virtual user profile of user u according to implicit ¯ examinations. Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 8 / 27

Method Objective Function of TJSL(1,1) The objective function of TJSL(1,1), f ui , � min (3) Θ ( u , i ) ∈P∪A where Θ = { b u , b i , V i · , P i ′ · , E j · } , i , i ′ , j = 1 , . . . , m , u = 1 , . . . , n , and r ui ) 2 + α v f ui = 1 2 ( r ui − ˆ 2 || V i · || 2 F + α p i ′ ∈P u \{ i } || P i ′ · || 2 � F + 2 j ∈E u || E j · || 2 2 b 2 2 b 2 α e F + β u u + β v � i . 2 Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 9 / 27

Method Gradients of TJSL(1,1) For each ( u , i ) ∈ P ∪ A , we have the gradients, ∂ f ui ∇ b u = − e ui + β u b u = ∂ b u ∂ f ui ∇ b i = − e ui + β v b i = ∂ b i ∂ f ui U − i u · + ˜ ∇ V i · = − e ui (¯ U u · ) + α v V i · ¯ = ∂ V i · ∂ f ui 1 V i · + α p P i ′ · , i ′ ∈ P u \{ i } ∇ P i ′ · = − e ui = ∂ P i ′ · |P u \{ i }| � ∂ f ui 1 ∇ E j · = − e ui V i · + α e E j · , j ∈ E u = ∂ E j · � |E u | where e ui = r ui − ˆ r ui . Note that r ui = 1 if ( u , i ) ∈ P , and r ui = 0 if ( u , i ) ∈ A . Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 10 / 27

Method Update Rules of TJSL(1,1) For each ( u , i ) ∈ P ∪ A , we have the update rules, b u b u − γ ∇ b u = b i b i − γ ∇ b i = V i · V i · − γ ∇ V i · = P i ′ · − γ ∇ P i ′ · , i ′ ∈ P u \{ i } P i ′ · = E j · E j · − γ ∇ E j · , j ∈ E u = where e ui = r ui − ˆ r ui . Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 11 / 27

Method Algorithm of TJSL(1,1) 1: Input : Positive feedbacks P , implicit examinations E , itera- tion number T , and parameters ρ , α v , α p , α e , β u , β v . 2: Output : Learned model Θ 3: Initialize the model Θ 4: for t = 1 , . . . , T do 5: Randomly sample A ⊂ R\P with |A| = ρ |P| for t 2 = 1 , . . . , |P ∪ A| do 6: Randomly pick up ( u , i ) ∈ P ∪ A 7: U − i i ′ ∈P u \{ i } P i ′ · Calculate ¯ √ 1 8: u · = � |P u \{ i }| Calculate ˜ U u · = ¯ j ∈E u E j · √ 1 9: � |E u | U − i u · V T i · + ˜ U u · V T r ui = b u + b i + ¯ ¯ Calculate ˆ 10: i · Calculate e ui = r ui − ˆ r ui 11: Update b u , b i , V i · , P i ′ · , i ′ ∈ P u \{ i } and E j · , j ∈ E u 12: end for 13: 14: end for Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 12 / 27

Method Prediction Rule of TJSL The predicted preference of user u on item i , r ( ℓ ) ui = b u + b i s i ′ i + s ji , E ( ℓ ) � � ˆ ⊆ E u , (4) u i ′ ∈P u \{ i } j ∈E ( ℓ ) u where s i ′ i = |P u \{ i }| P i ′ · V T i · , and s ji = E j · V T √ 1 1 i · . � |E ( ℓ ) u | Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 13 / 27

Method Objective Function of TJSL The objective function of TJSL is as follows, f ( ℓ ) � min (5) ui Θ ( ℓ ) , E ( ℓ ) u ⊆E u ( u , i ) ∈P∪A where f ( ℓ ) 2 ( r ui − ˆ r ui ) 2 + α v 2 || V i · || 2 F + α p i ′ ∈P u \{ i } || P i ′ · || 2 = 1 � F + ui 2 u || E j · || 2 2 b 2 2 b 2 α e F + β u u + β v � i , and the model parameters are j ∈E ( ℓ ) 2 Θ ( ℓ ) = { b u , b i , V i · , P i ′ · , E j · | u ∈ U , i ∈ I , i ′ ∈ P u , j ∈ E ( ℓ ) u } . Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 14 / 27

Method Gradients of TJSL Given some selected examined items E ( ℓ ) u , we have the gradient of each corresponding θ ∈ Θ ( ℓ ) for ( u , i ) ∈ P ∪ A , ∇ θ = ∂ f ( ℓ ) ui ∂θ , (6) where ∇ θ can be ∇ b u = − e ui + β u b u , ∇ b i = − e ui + β v b i , ∇ V i · = − e ui ( i ′ ∈P u \{ i } P i ′ · + u E j · ) + α v V i · , 1 1 √ � � j ∈E ( ℓ ) |P u \{ i }| � |E ( ℓ ) u | ∇ P i ′ · = − e ui |P u \{ i }| V i · + α p P i ′ · , i ′ ∈ P u \{ i } , and √ 1 ∇ E j · = − e ui |E u | V i · + α e E j · , j ∈ E u . Note that e ui = r ui − ˆ r ui is the 1 √ difference between the true preference and the estimated preference. Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 15 / 27

Method Update Rule of TJSL Finally, we have the update rule for each corresponding θ ∈ Θ ( ℓ ) , θ ← θ − γ ∇ θ, (7) where γ ( γ > 0 ) is the learning rate. Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 16 / 27

Method Identification of Likely-to-Prefer Items Once we have learned the model parameters Θ ( ℓ ) , we can identify some likely-to-prefer items from E u via the prediction rule in Eq.(4). Specifically, for each examined item j ∈ E u by user u , we estimate r ( ℓ ) its preference score ˆ uj , and then take τ |E u | examined items with the highest scores. Note that τ (0 < τ ≤ 1) is a parameter for item selection, which is initialized as 1 in the beginning and is then gradually decreased via τ ← τ × 0 . 9 so as to ignore some unlikely-to-prefer items. Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 17 / 27

Method Algorithm of TJSL (part 1) Input: Positive feedbacks P , implicit examinations E , iteration numbers T , L , L 0 , and parameters ρ , α v , α p , α e , β u , β v . Output: Selected examinations E ( ℓ ) and learned models Θ ( ℓ ) , ℓ = L − L 0 + 1 , . . . , L . r ui = � L r ( ℓ ) ui / L 0 , where ˆ r ( ℓ ) The final prediction rule is ˆ ℓ = L − L 0 + 1 ˆ ui is the prediction using the ℓ th model parameters and data. Pan, Liu and Ming (CSSE, SZU) HOCCF (TJSL) IEEE Intelligent Systems 18 / 27