Semi-discrete Matrix Factorization

Abstract

Discrete matrix factorization (DMF) has been a promising solution to improve the inferring efficiency of matrix factorization (MF) against the rapidly growing numbers of users and items. However, DMF suffers from a serious encoding loss due to its oversimplified modeling on the original data geometry. In this article, we propose a semi-discrete matrix factorization (SDMF) model to combine the predicting efficacy of MF with the inferring efficiency of DMF. It first learns real-valued latent features by MF, and then, taking them as group-wise and point-wise smoothness, learns binary codes in the DMF framework, for preserving the geometrical structures collectively hidden in users and items, as well as aligning binary codes originated from Hamming space with their real-valued counterparts learned from vector space. Particularly, we devise a computationally efficient optimization algorithm to estimate model parameters. Extensive evaluations on three real-world datasets clearly demonstrate the superiority of our SDMF model over state-of-the-art hash-based recommendation methods.