Abstract Matrix Factorization (MF) is among the most widely used techniques for collaborative filtering based recommendation. Along this line, a critical demand is to incrementally refine the MF models when new ratings come in an online scenario. However, most of existing incremental MF algorithms are limited by specific MF models or strict use restrictions. In this paper, we propose a general incremental MF framework by designing a linear transformation of user and item latent vectors over time. This framework shows a relatively high accuracy with a computation and space efficient training process in an online scenario. Meanwhile, we explain 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 special cases. Finally, extensive experimental results on two real-world datasets clearly validate the effectiveness, efficiency and storage performance of the proposed framework.