Efficient Collaborative Filtering via Data Augmentation and Step-size Optimization

Abstract

As a popular approach to collaborative filtering, matrix factorization (MF) models the underlying rating matrix as a product of two factor matrices, one for users and one for items. The MF model can be learned by Alternating Least Squares (ALS), which updates the two factor matrices alternately, keeping one fixed while updating the other. Although ALS improves the learning objective aggressively in each iteration, it suffers from high computational cost due to the necessity of inverting a separate matrix for every user and item. The softImpute-ALS reduces the per-iteration computation significantly using a strategy that requires only two matrix inversions; however, the computation saving leads to shrinkage of objective improvement. In this paper, we introduce a new algorithm, termed Data Augmentation with Optimal Step-size (DAOS), which alleviates the drawback of softImpute-ALS while still maintaining its low cost of computation per iteration. The DAOS is presented in the context that factor matrices may include fixed columns or rows, with this allowing bias terms and/or linear models to be incorporated into the ML model. Experimental results on synthetic and MovieLens 1M Dataset demonstrate the benefits of DAOS over ALS and softImpute-ALS in terms of generalization performance and computational time.