Transfer to Rank for Heterogeneous One-Class Collaborative Filtering Weike Pan 1 , Qiang Yang 2 ∗ , Wanling Cai 1 , Yaofeng Chen 2 , Qing Zhang 1 , Xiaogang Peng 1 ∗ and Zhong Ming 1 ∗ panweike@szu.edu.cn, qyang@cse.ust.hk, wanling cai@qq.com, chenyaofeng@email.szu.edu.cn, qingzhang1992@qq.com, pengxg@szu.edu.cn, mingz@szu.edu.cn 1 College of Computer Science and Software Engineering and National Engineering Laboratory for Big Data System Computing Technology Shenzhen University, Shenzhen, China 2 Department of Computer Science and Engineering Hong Kong University of Science and Technology, Hong Kong, China Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 1 / 28
Introduction Problem Definition Heterogeneous One-Class Collaborative Filtering (HOCCF) Input: Browses B = { ( u , i ) } and Purchases P = { ( u , i ′ ) } Goal: Rank the not yet purchased items, i.e., I\P u , for each end user u ∈ U Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 2 / 28
Introduction Challenges Ambiguity of browses regarding the users’ preferences 1 Scarcity of purchases as compared with the browse data 2 Heterogeneity arising from different feedback 3 Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 3 / 28
Introduction Overall of Our Solution Role-based Transfer to Rank (RoToR) : In integrative RoToR: we leverage browses into the preference learning task of purchases, in which we take each user as a sophisticated customer (i.e., mixer ) that is able to take different types of feedback into consideration. In sequential RoToR, we aim to simplify the integrative one by decomposing it into two dependent phases according to a typical shopping process. Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 4 / 28
Introduction Advantages of Our Solution We design a novel transfer learning solution from the perspective 1 of users’ roles of mixer, browser and purchaser, which addresses the challenges of ambiguity, scarcity and heterogeneity well. Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 5 / 28
Introduction Notations (1/3) Table: Some notations and explanations (1/3). n = |U| user number m = |I| item number u ∈ U user ID i , i ′ ∈ I item ID R = { ( u , i ) } universe of all possible (user, item) pairs P = { ( u , i ) } (user, item) pairs denoting purchases P u set of items purchased by user u B = { ( u , i ′ ) } (user, item) pairs denoting browses B u set of items browsed by user u A sampled negative feedback from R\P r ui r ui = 1 if ( u , i ) ∈ P and r ui = − 1 if ( u , i ) ∈ A Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 6 / 28
Introduction Notations (2/3) Table: Some notations and explanations (2/3). d ∈ R number of latent dimensions b u ∈ R user bias b i ∈ R item bias U u · ∈ R 1 × d user-specific latent feature vector V i · ∈ R 1 × d item-specific latent feature vector W i ′ · ∈ R 1 × d item-specific latent feature vector Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 7 / 28
Introduction Notations (3/3) Table: Some notations and explanations (3/3). ˆ r ui predicted preference of user u to item i r ( F ) r uij , ˆ ˆ preference difference in pairwise preference learning uij , r ( F ) ˆ predicted preference of user u to item i in a factorization-based method ui r ( N ) ˆ predicted preference of user u to item i in a neighborhood-based method ui learned similarity between item i ′ and item i s ( ℓ ) i ′ i r ( N ′ ) ˆ predicted preference of user u to item i in item-oriented CF ui predefined similarity (Jaccard index) between item i ′ and item i s ( p ) i ′ i N i a nearest set of items of item i T iteration number in the algorithm Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 8 / 28
Method Integrative RoToR We follow the seminal work on integrating heterogeneous feedback of ratings and examinations [Koren, 2008], and have the estimated preference of user u to item i as follows, r ( F ) r ( N ) ˆ r ui = ˆ + ˆ (1) ui , ui r ( F ) = b u + b i + U u · V T where ˆ i · and ui r ( N ) i ′ ∈B u s ( ℓ ) 1 1 ˆ √ √ i ′ ∈B u W i ′ · V T = � i ′ i = � i · are the prediction rules ui |B u | |B u | of the classical factorization-based method and the neighborhood-based method, respectively. Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 9 / 28
Method Integrative RoToR with Pointwise Preference Learning With the positive feedback in P and the sampled negative feedback in A , we have the objective function for pointwise preference learning [Johnson, 2014], � min f ui (2) Θ ( u , i ) ∈P∪A where Θ = { U u · , b u , u = 1 , 2 , . . . , n ; W i · , V i · , b i , i = 1 , 2 , . . . , m } are model parameters to be learned, and f ui = log ( 1 + exp ( − r ui ˆ r ui )) + α u F + α v F + α w F + β u u + β v 2 || U u · || 2 2 || V i · || 2 i ′ ∈B u || W i ′ · || 2 2 b 2 2 b 2 � i is the 2 tentative objective function for the ( u , i ) pair. Notice that the prediction rule is r ( F ) r ( N ) 1 ˆ r ui = ˆ + ˆ = b u + b i + U u · V T √ i ′ ∈B u W i ′ · V T i · + � i · , and r ui = 1 if ui ui |B u | ( u , i ) ∈ P and r ui = − 1 if ( u , i ) ∈ A , denoting a positive and negative preference, respectively. Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 10 / 28
Method Integrative RoToR with Pairwise Preference Learning We adopt the classical pairwise objective function for purchases for preference learning [Rendle et al., 2009], � � � min f uij , (3) ˜ Θ u ∈U i ∈P u j ∈I\P u where ˜ Θ = { U u · , u = 1 , 2 , . . . , n ; W i · , V i · , b i , i = 1 , 2 , . . . , m } denotes the set of parameters to be learned, and 2 � U u · � 2 + α v 2 � V i · � 2 + α v 2 � V j · � 2 + r uj ) + α u f uij = − ln σ (ˆ r ui − ˆ 2 � b i � 2 + β v 2 � b j � 2 is the tentative objective α w i ′ ∈B u � W i ′ · � 2 F + β v � 2 function for every two (user, item) pairs, i.e., ( u , i ) and ( u , j ) . Notice that the prediction rule is r ( F ) r ( N ) 1 ˆ r ui = ˆ + ˆ = b i + U u · V T √ i ′ ∈B u W i ′ · V T i · + � i · because the user ui ui |B u | bias b u will be of no use in preference difference ˆ r ui − ˆ r uj . Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 11 / 28
Method Sequential RoToR (1/2) We propose to decompose the integrative variant, i.e., RoToR(int.), and combine the two units in a sequential and coarse-to-fine manner, i.e., first neighborhood-based method and then factorization-based method. This mechanism is designed to make the preference learning task from less aggressive to more aggressive. Mathematically, we represent the decomposition from an integrative manner to a sequential manner as follows, r ( N ′ ) r ( N ) r ( F ) r ( F ) ˆ + ˆ ≈ ˆ → ˆ ui , (4) ui ui ui where “ ≈ ” and “ → ” are the decomposition (or approximation) procedure and the sequential relationship, respectively. Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 12 / 28
Method Sequential RoToR (2/2) In the first phase of RoToR(seq.), we obtain a candidate list of items via a neighborhood-based method, i.e., item-oriented collaborative filtering (ICF). Specifically, the prediction rule is as follows, r ( N ′ ) s ( p ) � ˆ = (5) i ′ i , ui i ′ ∈N i ∩ ( P u ∪B u ) where s ( p ) i ′ i is a predefined similarity (Jaccard index) between item i ′ and item i based on P ∪ B , and N i contains the most similar neighbors of item i . Notice that we treat purchases and browses the same and union two sets of user behaviors when calculating the predefined similarity with the goal of identifying some likely to be examined items in this phase. Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 13 / 28
Method Sequential RoToR with Pointwise Preference Learning For pointwise preference learning in the second phase of sequential RoToR, i.e., RoToR(poi.,seq.), we have a similar objective function to that of Eq.(2) in RoToR(poi.,int.) as follows, f ( F ) � min ui , (6) Φ ( u , i ) ∈P∪A where Φ = { U u · , b u , u = 1 , 2 , . . . , n ; V i · , b i , i = 1 , 2 , . . . , m } are the model parameters, and f ( F ) r ( F ) F + β u u + β v = log ( 1 + exp ( − r ui ˆ ui )) + α u 2 || U u · || 2 F + α v 2 || V i · || 2 2 b 2 2 b 2 i is ui the tentative prediction rule defined on the ( u , i ) pair. r ( F ) Notice that the prediction rule is ˆ = b u + b i + U u · V T i · . And r ui = 1 if ui ( u , i ) ∈ P and r ui = − 1 if ( u , i ) ∈ A denote the positive and negative preference orientation, respectively. Pan et al., (SZU & HKUST) HOCCF (RoToR) ACM TOIS 14 / 28
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