FEXIPRO: Fast and exact inner product retrieval in recommender systems

Recommender systems have many successful applications in e-commerce and social media, including Amazon, Netflix, and Yelp. Matrix Factorization (MF) is one of the most popular recommendation approaches; the original user-product rating matrix R with millions of rows and columns is decomposed into a user matrix Q and an item matrix P, such that the product QTP approximates R. Each column q (p) of Q (P) holds the latent factors of the corresponding user (item), and qTp is a prediction of the rating to item p by user q. Recommender systems based on MF suggest to a user in q the items with the top-k scores in qTP. For this problem, we propose a Fast and EXact Inner PROduct retrieval (FEXIPRO) framework, based on sequential scan, which includes three elements. First, FEXIPRO applies an SVD transformation to P, after which the first several dimensions capture a large percentage of the inner products. This enables us to prune item vectors by only computing their partial inner products with q. Second, we construct an integer approximation version of P, which can be used to compute fast upper bounds for the inner products that can prune item vectors. Finally, we apply a lossless transformation to P, such that the resulting matrix has only positive values, allowing for the inner products to be monotonically increasing with dimensionality. Experiments on real data demonstrate that our framework outperforms alternative approaches typically by an order of magnitude.