Matching Users and Items Across Domains to Improve the Recommendation Quality Created by: Chung-Yi Li, Shou-De Lin Presented by: I Gde Dharma Nugraha 1

Motivation  Lack of data is a serious concern in building a recommender system, in particular for newly established services.  Can we leverage the information from other domains to improve the quality of a recommender system? 2 2

Problem Definition Given: Two homogeneous rating matrices  They model the same type of preference.  Decent portion of overlap in users and in items. Target Rating Matrix ♫ ♫ ♫ Source Rating Matrix ♫ ♫ ♫ Challenge: The mapping of users is unknown, and so is the mapping of items. Goals: 1.Identify the user mapping and item mapping. 2.Use the identified mappings to boost the recommendation performance. 3 3

Why This Problem Is Challenging  When item correspondence is known, the problem is much easier  Define user similarity. If the similarity is large, they are likely to be the same users. [Narayanan 2008]  In our case, both sides are unknown  no clear solution yet ♫ ♫ ♫ 4 4

Basic Idea  low rank assumption and factorization models 5 R1R1 R2R2 n1n1 n2n2 n3n3 n4n4 m1m1 m2m2 m3m3 m4m4 m5m5 n4n4 n3n3 n2n2 n1n1 m5m5 m4m4 m3m3 m2m2 m1m1 = = n1n1 n2n2 n3n3 n4n4 m1m1 m2m2 m3m3 m4m4 m5m5 n4n4 n3n3 n2n2 n1n1 m5m5 m4m4 m3m3 m2m2 m1m1 ? ? 5

≈ M1×N1M1×N1 M2×N2M2×N2 M1×M2M1×M2 N2×N1N2×N1 A Two-Stage Model to Find the Matching ? O O ? ? O Rough Matching Result Final Matching Result 6 6

Stage 1: Latent Space Matching 1. Latent Space Matching 7 7

How can we perform SVD on a Partially Observed Matrix? 1. Latent Space Matching = = = 8 8

We want to solve G from Now we know how to get Thus Since SVD is unique, we can separate user and item sides: Matching in Latent Space Same subproblem S: sign matrix (K by K, diagonal, -1 or 1) 1. Latent Space Matching 9 9

Solving ≈ (M 1 × K) (M 1 × M 2 ) (M 2 × K) 1. Latent Space Matching

 More accurate but harder to solve.  Obtain good initialization and reduced search space from latent space matching.  Solve G user and G item alternatingly.  The objective value always decreases & converges. Rough Matching Result Final Matching Result 11

Goals 1.Identify the user mapping and item mapping 2.Then, use the identified mappings to boost recommendation performance Rough Matching Result Final Matching Result 12

 Matched latent factors are constrained to be similar Transferring Imperfect Matching to Predict Ratings 13

Experiment Setup Disjoint Split Overlap SplitContained Split Subset Split training set of R 1 training set of R 2 Partial Split users items Yahoo! Music Dataset 14

Accuracy and Mean Average Precision: The higher the better 15

Rating Prediction (Root Mean Square Error) RMSE: the lower the better 16

(root mean square error)

Conclusion  It is possible to identify user or item correspondence unsupervisedly based on homogeneous rating data  Even with imperfect matching, out model can still improve the recommendation accuracy.  Questions? 18 17