Research And Application Of Linear Feature Transformation In Incremental Matrix Factorization

Matrix Factorization(MF)is among the most widely used techniques for collab-orative filtering based recommendation because of its high accuracy,high efficiency,easy implementation and convenient expansion.And nowadays,most of MF models are batch-based which are usually required to have the clearly divided training phase and testing phase.Besides,the model will be rarely updated and modified after train-ing the training phase with big data.While in online scenarios of the real world,new data usually means the new change of the features.Therefore,a critical demand is to incrementally refine the MF models.Indeed,although many research efforts have been made to facilitate the performance of incremental MF,there are still some challenges to be addressed,such as efficiency,parameter reusability,model generality and error bound analysis.To that end,inspired by Vector AutoRegression(VAR)model,we propose a gen-eral framework for incremental MF,which can efficiently update user and item latent feature vectors when a bunch of new ratings come.The key idea of our proposed frame-work is that,instead of retraining all model parameters,we design a linear transforma-tion of user and item latent feature vectors over time.Furthermore,by leveraging the scale-invariant parameters in our framework,the cost of model parameter tuning can be largely alleviated with the increase of model size.In particular,through the for-mal definition,we demonstrate the generality of the proposed framework,which means most of the batch-based MF models with explicit objective function can be extended to incremental MF model by our framework.Meanwhile,we explain the rationality of the framework with a low-rank approximation perspective,and give an upper bound on the training error when this framework is used for incremental learning in some spe-cial cases.Finally,extensive experimental results on two real-world datasets clearly validate the framework's superiority in effectiveness,efficiency,storage overhead and sample usage rate.