Adaptive Local Low-rank Matrix Approximation for Recommendation

Abstract

Low-rank matrix approximation (LRMA) has attracted more and more attention in the community of recommendation. Even though LRMA-based recommendation methods (including Global LRMA and Local LRMA) obtain promising results, they suffer from the complicated structure of the large-scale and sparse rating matrix, especially when the underlying system includes a large set of items with various types and a huge amount of users with diverse interests. Thus, they have to predefine the important parameters, such as the rank of the rating matrix and the number of submatrices. Moreover, most existing Local LRMA methods are usually designed in a two-phase separated framework and do not consider the missing mechanisms of rating matrix. In this article, a non-parametric unified Bayesian graphical model is proposed for A daptive Lo cal low-rank M atrix A pproximation ( ALoMA ). ALoMA has ability to simultaneously identify rating submatrices, determine the optimal rank for each submatrix, and learn the submatrix-specific user/item latent factors. Meanwhile, the missing mechanism is adopted to characterize the whole rating matrix. These four parts are seamlessly integrated and enhance each other in a unified framework. Specifically, the user-item rating matrix is adaptively divided into proper number of submatrices in ALoMA by exploiting the Chinese Restaurant Process. For each submatrix, by considering both global/local structure information and missing mechanisms, the latent user/item factors are identified in an optimal latent space by adopting automatic relevance determination technique. We theoretically analyze the model’s generalization error bounds and give an approximation guarantee. Furthermore, an efficient Gibbs sampling-based algorithm is designed to infer the proposed model. A series of experiments have been conducted on six real-world datasets ( Epinions , Douban , Dianping , Yelp , Movielens (10M), and Netflix ). The results demonstrate that ALoMA outperforms the state-of-the-art LRMA-based methods and can easily provide interpretable recommendation results.